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<title>idtxl.estimators_Rudelt — IDTxl 1.2.1 documentation</title>
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<h1>Source code for idtxl.estimators_Rudelt</h1><div class="highlight"><pre>
<span></span><span class="sd">"""Provide HDE estimators."""</span>
<span class="kn">import</span> <span class="nn">logging</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.optimize</span> <span class="kn">import</span> <span class="n">newton</span><span class="p">,</span> <span class="n">minimize</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="kn">from</span> <span class="nn">sys</span> <span class="kn">import</span> <span class="n">stderr</span>
<span class="kn">from</span> <span class="nn">idtxl.estimator</span> <span class="kn">import</span> <span class="n">Estimator</span>
<span class="kn">import</span> <span class="nn">idtxl.hde_utils</span> <span class="k">as</span> <span class="nn">utl</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">Counter</span>
<span class="kn">import</span> <span class="nn">mpmath</span> <span class="k">as</span> <span class="nn">mp</span>
<span class="n">FAST_EMBEDDING_AVAILABLE</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">try</span><span class="p">:</span>
<span class="kn">import</span> <span class="nn">idtxl.hde_fast_embedding</span> <span class="k">as</span> <span class="nn">fast_emb</span>
<span class="k">except</span><span class="p">:</span>
<span class="n">FAST_EMBEDDING_AVAILABLE</span> <span class="o">=</span> <span class="kc">False</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"""</span>
<span class="s2"> Error importing Cython fast embedding module. Continuing with slow Python implementation.</span><span class="se">\n</span><span class="s2"></span>
<span class="s2"> This may take a long time.</span><span class="se">\n</span><span class="s2"></span>
<span class="s2"> """</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="n">stderr</span><span class="p">,</span> <span class="n">flush</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">logger</span> <span class="o">=</span> <span class="n">logging</span><span class="o">.</span><span class="n">getLogger</span><span class="p">(</span><span class="vm">__name__</span><span class="p">)</span>
<div class="viewcode-block" id="RudeltAbstractEstimator"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator">[docs]</a><span class="k">class</span> <span class="nc">RudeltAbstractEstimator</span><span class="p">(</span><span class="n">Estimator</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Abstract class for implementation of nsb and plugin estimators from Rudelt.</span>
<span class="sd"> Abstract class for implementation of nsb and plugin estimators, child classes</span>
<span class="sd"> implement estimators for mutual information (MI) .</span>
<span class="sd"> References:</span>
<span class="sd"> [1]: L. Rudelt, D. G. Marx, M. Wibral, V. Priesemann: Embedding</span>
<span class="sd"> optimization reveals long-lasting history dependence in</span>
<span class="sd"> neural spiking activity, 2021, PLOS Computational Biology, 17(6)</span>
<span class="sd"> [2]: https://github.com/Priesemann-Group/hdestimator</span>
<span class="sd"> implemented in idtxl by Michael Lindner, Göttingen 2021</span>
<span class="sd"> Args:</span>
<span class="sd"> settings : dict</span>
<span class="sd"> - embedding_step_size : float [optional]</span>
<span class="sd"> Step size delta t (in seconds) with which the window is slid through the data</span>
<span class="sd"> (default = 0.005).</span>
<span class="sd"> - normalise : bool [optional]</span>
<span class="sd"> rebase spike times to zero</span>
<span class="sd"> (default=True)</span>
<span class="sd"> - return_averaged_R : bool [optional]</span>
<span class="sd"> If set to True, compute R̂tot as the average over R̂(T ) for T ∈ [T̂D, Tmax ] instead of</span>
<span class="sd"> R̂tot = R(T̂D ). If set to True, the setting for number_of_bootstraps_R_tot is ignored and</span>
<span class="sd"> set to 0</span>
<span class="sd"> (default=True)</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">settings</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="c1"># check settings</span>
<span class="n">settings</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_check_settings</span><span class="p">()</span>
<span class="c1"># import given settings</span>
<span class="bp">self</span><span class="o">.</span><span class="n">settings</span> <span class="o">=</span> <span class="n">settings</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="c1"># Get defaults for estimator settings</span>
<span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="s1">'normalize'</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="s1">'embedding_step_size'</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="s1">'return_averaged_R'</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
<span class="c1"># check settings</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_check_input_settings</span><span class="p">()</span>
<div class="viewcode-block" id="RudeltAbstractEstimator.is_parallel"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.is_parallel">[docs]</a> <span class="k">def</span> <span class="nf">is_parallel</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span></div>
<div class="viewcode-block" id="RudeltAbstractEstimator.is_analytic_null_estimator"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.is_analytic_null_estimator">[docs]</a> <span class="k">def</span> <span class="nf">is_analytic_null_estimator</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span></div>
<span class="k">def</span> <span class="nf">_check_settings</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">settings</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""Set default for settings dictionary.</span>
<span class="sd"> Check if settings dictionary is None. If None, initialise an empty</span>
<span class="sd"> dictionary. If not None check if type is dictionary. Function should be</span>
<span class="sd"> called before setting default values.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">settings</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="p">{}</span>
<span class="k">elif</span> <span class="nb">type</span><span class="p">(</span><span class="n">settings</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="nb">dict</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'settings should be a dictionary.'</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">settings</span>
<span class="k">def</span> <span class="nf">_check_input_settings</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="c1"># check that required settings are defined</span>
<span class="n">required_settings</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'normalize'</span><span class="p">,</span>
<span class="s1">'embedding_step_size'</span><span class="p">,</span>
<span class="s1">'return_averaged_R'</span><span class="p">]</span>
<span class="c1"># check if all settings are defined</span>
<span class="k">for</span> <span class="n">required_setting</span> <span class="ow">in</span> <span class="n">required_settings</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">required_setting</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">:</span>
<span class="n">sys</span><span class="o">.</span><span class="n">exit</span><span class="p">(</span><span class="s2">"Error in settings file: </span><span class="si">{}</span><span class="s2"> is not defined. Aborting."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">required_setting</span><span class="p">))</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'normalize'</span><span class="p">],</span> <span class="nb">bool</span><span class="p">)),</span> \
<span class="s2">"Error: setting 'normalize' needs to be boolean but is defined as </span><span class="si">{0}</span><span class="s2">. "</span> \
<span class="s2">"Aborting."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'normalize'</span><span class="p">]))</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'return_averaged_R'</span><span class="p">],</span> <span class="nb">bool</span><span class="p">)),</span>\
<span class="s2">"Error: setting 'return_averaged_R' needs to be boolean but is "</span> \
<span class="s2">"defined as </span><span class="si">{0}</span><span class="s2">. Aborting."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'normalize'</span><span class="p">]))</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'embedding_step_size'</span><span class="p">],</span> <span class="nb">float</span><span class="p">)),</span>\
<span class="s2">"Error: setting 'embedding_step_size' "</span> \
<span class="s2">"needs to be float but is defined "</span> \
<span class="s2">"as </span><span class="si">{0}</span><span class="s2">. Aborting."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'embedding_step_size'</span><span class="p">]))</span>
<span class="k">def</span> <span class="nf">_check_estimator_inputs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
<span class="n">symbol_array</span><span class="p">,</span>
<span class="n">past_symbol_array</span><span class="p">,</span>
<span class="n">current_symbol_array</span><span class="p">,</span>
<span class="n">bbc_tolerance</span><span class="p">):</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)),</span> \
<span class="s2">"Error: symbol_array needs to be a numpy array but is defines as </span><span class="si">{0}</span><span class="s2">."</span> \
<span class="s2">"Aborting."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">))</span>
<span class="k">if</span> <span class="n">past_symbol_array</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)),</span> \
<span class="s2">"Error: past_symbol_array needs to be a numpy array but is defines as </span><span class="si">{0}</span><span class="s2">."</span> \
<span class="s2">"Aborting."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">))</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">)),</span> \
<span class="s2">"Error: symbol_array and past_symbol_array need to have the same length but have:"</span> \
<span class="s2">"len(symbol_array): </span><span class="si">{0}</span><span class="s2"> len(past_symbol_array): </span><span class="si">{1}</span><span class="s2">. "</span> \
<span class="s2">"Aborting"</span><span class="o">.</span> <span class="nb">format</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">))</span>
<span class="k">if</span> <span class="n">current_symbol_array</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)),</span> \
<span class="s2">"Error: current_symbol_array needs to be a numpy array but is defines as </span><span class="si">{0}</span><span class="s2">."</span> \
<span class="s2">"Aborting."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">))</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">)),</span> \
<span class="s2">"Error: symbol_array and current_symbol_array need to have the same length but have:"</span> \
<span class="s2">"len(symbol_array): </span><span class="si">{0}</span><span class="s2"> len(current_symbol_array): </span><span class="si">{1}</span><span class="s2">. "</span> \
<span class="s2">"Aborting"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">))</span>
<span class="k">if</span> <span class="n">bbc_tolerance</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">assert</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">bbc_tolerance</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)),</span> \
<span class="s2">"Error: symbol array needs to be a numpy array but is defines as </span><span class="si">{0}</span><span class="s2">."</span> \
<span class="s2">"Aborting."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">_ensure_one_dim</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">var</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> check if array is 1D</span>
<span class="sd"> """</span>
<span class="n">var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="n">var</span><span class="p">)</span>
<span class="k">assert</span> <span class="p">(</span><span class="n">var</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">),</span> <span class="s2">"Input variable needs to be one dimensional. Aborting"</span>
<div class="viewcode-block" id="RudeltAbstractEstimator.get_past_range"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.get_past_range">[docs]</a> <span class="k">def</span> <span class="nf">get_past_range</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">,</span> <span class="n">first_bin_size</span><span class="p">,</span> <span class="n">scaling_k</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Get the past range T of the embedding, based on the parameters d, tau_1 and k.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">([</span><span class="n">first_bin_size</span> <span class="o">*</span> <span class="mi">10</span> <span class="o">**</span> <span class="p">((</span><span class="n">number_of_bins_d</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">*</span> <span class="n">scaling_k</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">number_of_bins_d</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)])</span></div>
<div class="viewcode-block" id="RudeltAbstractEstimator.get_window_delimiters"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.get_window_delimiters">[docs]</a> <span class="k">def</span> <span class="nf">get_window_delimiters</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">,</span> <span class="n">scaling_k</span><span class="p">,</span> <span class="n">first_bin_size</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Get delimiters of the window, used to describe the embedding. The</span>
<span class="sd"> window includes both the past embedding and the response.</span>
<span class="sd"> The delimiters are times, relative to the first bin, that separate</span>
<span class="sd"> two consequent bins.</span>
<span class="sd"> """</span>
<span class="n">bin_sizes</span> <span class="o">=</span> <span class="p">[</span><span class="n">first_bin_size</span> <span class="o">*</span> <span class="mi">10</span> <span class="o">**</span> <span class="p">((</span><span class="n">number_of_bins_d</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">*</span> <span class="n">scaling_k</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">number_of_bins_d</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
<span class="n">window_delimiters</span> <span class="o">=</span> <span class="p">[</span><span class="nb">sum</span><span class="p">([</span><span class="n">bin_sizes</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">)])</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">number_of_bins_d</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
<span class="n">window_delimiters</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">window_delimiters</span><span class="p">[</span><span class="n">number_of_bins_d</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'embedding_step_size'</span><span class="p">])</span>
<span class="k">return</span> <span class="n">window_delimiters</span></div>
<div class="viewcode-block" id="RudeltAbstractEstimator.get_median_number_of_spikes_per_bin"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.get_median_number_of_spikes_per_bin">[docs]</a> <span class="k">def</span> <span class="nf">get_median_number_of_spikes_per_bin</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">raw_symbols</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Given raw symbols (in which the number of spikes per bin are counted,</span>
<span class="sd"> ie not necessarily binary quantity), get the median number of spikes</span>
<span class="sd"> for each bin, among all symbols obtained by the embedding.</span>
<span class="sd"> """</span>
<span class="c1"># number_of_bins here is number_of_bins_d + 1,</span>
<span class="c1"># as it here includes not only the bins of the embedding but also the response</span>
<span class="n">number_of_bins</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">raw_symbols</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">spike_counts_per_bin</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">number_of_bins</span><span class="p">)]</span>
<span class="k">for</span> <span class="n">raw_symbol</span> <span class="ow">in</span> <span class="n">raw_symbols</span><span class="p">:</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">number_of_bins</span><span class="p">):</span>
<span class="n">spike_counts_per_bin</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="p">[</span><span class="n">raw_symbol</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
<span class="k">return</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">spike_counts_per_bin</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">number_of_bins</span><span class="p">)]</span></div>
<div class="viewcode-block" id="RudeltAbstractEstimator.symbol_binary_to_array"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.symbol_binary_to_array">[docs]</a> <span class="k">def</span> <span class="nf">symbol_binary_to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symbol_binary</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Given a binary representation of a symbol (cf symbol_array_to_binary),</span>
<span class="sd"> convert it back into its array-representation.</span>
<span class="sd"> """</span>
<span class="c1"># assert 2 ** number_of_bins_d > symbol_binary</span>
<span class="n">spikes_in_window</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">number_of_bins_d</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">):</span>
<span class="n">b</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">**</span> <span class="p">(</span><span class="n">number_of_bins_d</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span>
<span class="k">if</span> <span class="n">b</span> <span class="o"><=</span> <span class="n">symbol_binary</span><span class="p">:</span>
<span class="n">spikes_in_window</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">symbol_binary</span> <span class="o">-=</span> <span class="n">b</span>
<span class="k">return</span> <span class="n">spikes_in_window</span></div>
<div class="viewcode-block" id="RudeltAbstractEstimator.symbol_array_to_binary"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.symbol_array_to_binary">[docs]</a> <span class="k">def</span> <span class="nf">symbol_array_to_binary</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">spikes_in_window</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Given an array of 1s and 0s, representing spikes and the absence</span>
<span class="sd"> thereof, read the array as a binary number to obtain a</span>
<span class="sd"> (base 10) integer.</span>
<span class="sd"> """</span>
<span class="c1"># assert len(spikes_in_window) == number_of_bins_d</span>
<span class="c1"># TODO check if it makes sense to use len(spikes_in_window)</span>
<span class="c1"># directly, to avoid mismatch as well as confusion</span>
<span class="c1"># as number_of_bins_d here can also be number_of_bins</span>
<span class="c1"># as in get_median_number_of_spikes_per_bin, ie</span>
<span class="c1"># including the response</span>
<span class="k">return</span> <span class="nb">sum</span><span class="p">([</span><span class="mi">2</span> <span class="o">**</span> <span class="p">(</span><span class="n">number_of_bins_d</span> <span class="o">-</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">spikes_in_window</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">)])</span></div>
<div class="viewcode-block" id="RudeltAbstractEstimator.get_raw_symbols"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.get_raw_symbols">[docs]</a> <span class="k">def</span> <span class="nf">get_raw_symbols</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
<span class="n">spike_times</span><span class="p">,</span>
<span class="n">embedding</span><span class="p">,</span>
<span class="n">first_bin_size</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Get the raw symbols (in which the number of spikes per bin are counted,</span>
<span class="sd"> ie not necessarily binary quantity), as obtained by applying the</span>
<span class="sd"> embedding.</span>
<span class="sd"> """</span>
<span class="n">past_range_T</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">,</span> <span class="n">scaling_k</span> <span class="o">=</span> <span class="n">embedding</span>
<span class="c1"># the window is the embedding plus the response,</span>
<span class="c1"># ie the embedding and one additional bin of size embedding_step_size</span>
<span class="n">window_delimiters</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_window_delimiters</span><span class="p">(</span><span class="n">number_of_bins_d</span><span class="p">,</span>
<span class="n">scaling_k</span><span class="p">,</span>
<span class="n">first_bin_size</span><span class="p">)</span>
<span class="n">window_length</span> <span class="o">=</span> <span class="n">window_delimiters</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">num_spike_times</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">spike_times</span><span class="p">)</span>
<span class="n">last_spike_time</span> <span class="o">=</span> <span class="n">spike_times</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">num_symbols</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="n">last_spike_time</span> <span class="o">-</span> <span class="n">window_length</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'embedding_step_size'</span><span class="p">])</span>
<span class="n">raw_symbols</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">time</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">spike_index_lo</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">symbol_num</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_symbols</span><span class="p">):</span>
<span class="k">while</span> <span class="n">spike_index_lo</span> <span class="o"><</span> <span class="n">num_spike_times</span> <span class="ow">and</span> <span class="n">spike_times</span><span class="p">[</span><span class="n">spike_index_lo</span><span class="p">]</span> <span class="o"><</span> <span class="n">time</span><span class="p">:</span>
<span class="n">spike_index_lo</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">spike_index_hi</span> <span class="o">=</span> <span class="n">spike_index_lo</span>
<span class="k">while</span> <span class="p">(</span><span class="n">spike_index_hi</span> <span class="o"><</span> <span class="n">num_spike_times</span> <span class="ow">and</span>
<span class="n">spike_times</span><span class="p">[</span><span class="n">spike_index_hi</span><span class="p">]</span> <span class="o"><</span> <span class="n">time</span> <span class="o">+</span> <span class="n">window_length</span><span class="p">):</span>
<span class="n">spike_index_hi</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">spikes_in_window</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">number_of_bins_d</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">embedding_bin_index</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">spike_index</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">spike_index_lo</span><span class="p">,</span> <span class="n">spike_index_hi</span><span class="p">):</span>
<span class="k">while</span> <span class="p">(</span><span class="n">spike_times</span><span class="p">[</span><span class="n">spike_index</span><span class="p">]</span> <span class="o">></span> <span class="n">time</span> <span class="o">+</span> <span class="n">window_delimiters</span><span class="p">[</span><span class="n">embedding_bin_index</span><span class="p">]):</span>
<span class="n">embedding_bin_index</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">spikes_in_window</span><span class="p">[</span><span class="n">embedding_bin_index</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">raw_symbols</span> <span class="o">+=</span> <span class="p">[</span><span class="n">spikes_in_window</span><span class="p">]</span>
<span class="n">time</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s1">'embedding_step_size'</span><span class="p">]</span>
<span class="k">return</span> <span class="n">raw_symbols</span></div>
<div class="viewcode-block" id="RudeltAbstractEstimator.get_symbol_counts"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.get_symbol_counts">[docs]</a> <span class="k">def</span> <span class="nf">get_symbol_counts</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symbol_array</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Count how often symbols occur</span>
<span class="sd"> """</span>
<span class="n">symbol_counts</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">()</span>
<span class="k">for</span> <span class="n">symbol</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">):</span>
<span class="n">symbol_counts</span><span class="p">[</span><span class="n">symbol</span><span class="p">]</span> <span class="o">+=</span> <span class="nb">len</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">symbol_array</span> <span class="o">==</span> <span class="n">symbol</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span>
<span class="k">return</span> <span class="n">symbol_counts</span></div>
<div class="viewcode-block" id="RudeltAbstractEstimator.get_multiplicities"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractEstimator.get_multiplicities">[docs]</a> <span class="k">def</span> <span class="nf">get_multiplicities</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symbol_counts</span><span class="p">,</span> <span class="n">alphabet_size</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Get the multiplicities of some given symbol counts.</span>
<span class="sd"> To estimate the entropy of a system, it is only important how</span>
<span class="sd"> often a symbol/ event occurs (the probability that it occurs), not</span>
<span class="sd"> what it represents. Therefore, computations can be simplified by</span>
<span class="sd"> summarizing symbols by their frequency, as represented by the</span>
<span class="sd"> multiplicities.</span>
<span class="sd"> """</span>
<span class="n">mk</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(((</span><span class="n">value</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">symbol_counts</span><span class="o">.</span><span class="n">values</span><span class="p">()))</span>
<span class="n">number_of_observed_symbols</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">count_nonzero</span><span class="p">([</span><span class="n">value</span> <span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">symbol_counts</span><span class="o">.</span><span class="n">values</span><span class="p">()])</span>
<span class="k">for</span> <span class="n">symbol</span> <span class="ow">in</span> <span class="n">symbol_counts</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span>
<span class="n">mk</span><span class="p">[</span><span class="n">symbol_counts</span><span class="p">[</span><span class="n">symbol</span><span class="p">]]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="c1"># the number of symbols that have not been observed in the data</span>
<span class="n">mk</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">alphabet_size</span> <span class="o">-</span> <span class="n">number_of_observed_symbols</span>
<span class="k">return</span> <span class="n">mk</span></div></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator">[docs]</a><span class="k">class</span> <span class="nc">RudeltAbstractNSBEstimator</span><span class="p">(</span><span class="n">RudeltAbstractEstimator</span><span class="p">):</span>
<span class="sd">"""Abstract class for implementation of NSB estimators from Rudelt.</span>
<span class="sd"> Abstract class for implementation of Nemenman-Shafee-Bialek (NSB)</span>
<span class="sd"> estimators, child classes implement nsb estimators for mutual information</span>
<span class="sd"> (MI).</span>
<span class="sd"> implemented in idtxl by Michael Lindner, Göttingen 2021</span>
<span class="sd"> References:</span>
<span class="sd"> [1]: L. Rudelt, D. G. Marx, M. Wibral, V. Priesemann: Embedding</span>
<span class="sd"> optimization reveals long-lasting history dependence in</span>
<span class="sd"> neural spiking activity, 2021, PLOS Computational Biology, 17(6)</span>
<span class="sd"> [2]: I. Nemenman, F. Shafee, W. Bialek: Entropy and inference,</span>
<span class="sd"> revisited. In T.G. Dietterich, S. Becker, and Z. Ghahramani,</span>
<span class="sd"> editors, Advances in Neural Information Processing Systems 14,</span>
<span class="sd"> Cambridge, MA, 2002. MIT Press.</span>
<span class="sd"> Args:</span>
<span class="sd"> settings : dict</span>
<span class="sd"> - embedding_step_size : float [optional]</span>
<span class="sd"> Step size delta t (in seconds) with which the window is slid through the data</span>
<span class="sd"> (default = 0.005).</span>
<span class="sd"> - normalise : bool [optional]</span>
<span class="sd"> rebase spike times to zero</span>
<span class="sd"> (default=True)</span>
<span class="sd"> - return_averaged_R : bool [optional]</span>
<span class="sd"> If set to True, compute R̂tot as the average over R̂(T ) for T ∈ [T̂D, Tmax ] instead of</span>
<span class="sd"> R̂tot = R(T̂D ). If set to True, the setting for number_of_bootstraps_R_tot is ignored and</span>
<span class="sd"> set to 0</span>
<span class="sd"> (default=True)</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">settings</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="c1"># Set default estimator settings.</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">settings</span><span class="p">)</span>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.d_xi"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.d_xi">[docs]</a> <span class="k">def</span> <span class="nf">d_xi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> First derivative of xi(beta).</span>
<span class="sd"> xi(beta) is the entropy of the system when no data has been observed.</span>
<span class="sd"> d_xi is the prior for the nsb estimator</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">K</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">K</span> <span class="o">*</span> <span class="n">beta</span> <span class="o">+</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">-</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">beta</span> <span class="o">+</span> <span class="mf">1.</span><span class="p">)</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.d2_xi"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.d2_xi">[docs]</a> <span class="k">def</span> <span class="nf">d2_xi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Second derivative of xi(beta) (cf d_xi).</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">K</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">K</span> <span class="o">*</span> <span class="n">beta</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">beta</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.d3_xi"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.d3_xi">[docs]</a> <span class="k">def</span> <span class="nf">d3_xi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Third derivative of xi(beta) (cf d_xi).</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">K</span> <span class="o">**</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">K</span> <span class="o">*</span> <span class="n">beta</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">beta</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.rho"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.rho">[docs]</a> <span class="k">def</span> <span class="nf">rho</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> rho(beta, data) is the Dirichlet multinomial likelihood.</span>
<span class="sd"> rho(beta, data) together with the d_xi(beta) make up</span>
<span class="sd"> the posterior for the nsb estimator</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">([</span><span class="n">mp</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="n">mp</span><span class="o">.</span><span class="n">rf</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">(</span><span class="n">n</span><span class="p">)),</span> <span class="n">mk</span><span class="p">[</span><span class="n">n</span><span class="p">])</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">mk</span><span class="p">])</span> <span class="o">/</span> <span class="n">mp</span><span class="o">.</span><span class="n">rf</span><span class="p">(</span><span class="n">K</span> <span class="o">*</span> <span class="n">beta</span><span class="p">,</span>
<span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">(</span><span class="n">N</span><span class="p">))</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.unnormalized_posterior"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.unnormalized_posterior">[docs]</a> <span class="k">def</span> <span class="nf">unnormalized_posterior</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> The (unnormalized) posterior in the nsb estimator.</span>
<span class="sd"> Product of the likelihood rho and the prior d_xi;</span>
<span class="sd"> the normalizing factor is given by the marginal likelihood</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">)</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.d_log_rho"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.d_log_rho">[docs]</a> <span class="k">def</span> <span class="nf">d_log_rho</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> First derivate of the logarithm of the Dirichlet multinomial likelihood.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">K</span> <span class="o">*</span> <span class="p">(</span><span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">K</span> <span class="o">*</span> <span class="n">beta</span><span class="p">)</span> <span class="o">-</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">K</span> <span class="o">*</span> <span class="n">beta</span> <span class="o">+</span> <span class="n">N</span><span class="p">))</span> <span class="o">-</span> <span class="n">K</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span> \
<span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">mk</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="n">beta</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">mk</span><span class="p">))</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.d2_log_rho"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.d2_log_rho">[docs]</a> <span class="k">def</span> <span class="nf">d2_log_rho</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Second derivate of the logarithm of the Dirichlet multinomial likelihood.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">K</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">K</span> <span class="o">*</span> <span class="n">beta</span><span class="p">)</span> <span class="o">-</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">K</span> <span class="o">*</span> <span class="n">beta</span> <span class="o">+</span> <span class="n">N</span><span class="p">))</span> <span class="o">-</span> <span class="n">K</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span> \
<span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">mk</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="n">beta</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">mk</span><span class="p">))</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.d_log_rho_xi"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.d_log_rho_xi">[docs]</a> <span class="k">def</span> <span class="nf">d_log_rho_xi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> First derivative of the logarithm of the nsb (unnormalized) posterior.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_log_rho</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">d2_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">)</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.d2_log_rho_xi"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.d2_log_rho_xi">[docs]</a> <span class="k">def</span> <span class="nf">d2_log_rho_xi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Second derivative of the logarithm of the nsb (unnormalized) posterior.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">d2_log_rho</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> \
<span class="o">+</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">d3_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">d2_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">K</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.log_likelihood_DP_alpha"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.log_likelihood_DP_alpha">[docs]</a> <span class="k">def</span> <span class="nf">log_likelihood_DP_alpha</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">K1</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Alpha-dependent terms of the log-likelihood of a Dirichlet Process.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="p">(</span><span class="n">K1</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="o">-</span> <span class="n">mp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">mp</span><span class="o">.</span><span class="n">rf</span><span class="p">(</span><span class="n">a</span> <span class="o">+</span> <span class="mf">1.</span><span class="p">,</span> <span class="n">N</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">))</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.get_beta_MAP"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.get_beta_MAP">[docs]</a> <span class="k">def</span> <span class="nf">get_beta_MAP</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Get the maximum a posteriori (MAP) value for beta.</span>
<span class="sd"> Provides the location of the peak, around which we integrate.</span>
<span class="sd"> beta_MAP is the value for beta for which the posterior of the</span>
<span class="sd"> NSB estimator is maximised (or, equivalently, of the logarithm</span>
<span class="sd"> thereof, as computed here).</span>
<span class="sd"> """</span>
<span class="n">K1</span> <span class="o">=</span> <span class="n">K</span> <span class="o">-</span> <span class="n">mk</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_log_rho</span><span class="p">(</span><span class="mi">10</span> <span class="o">**</span> <span class="mi">1</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Warning: No ML parameter was found."</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="n">stderr</span><span class="p">,</span> <span class="n">flush</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">beta_MAP</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="s1">'nan'</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span>
<span class="c1"># first guess computed via posterior of Dirichlet process</span>
<span class="n">DP_est</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha_ML</span><span class="p">(</span><span class="n">mk</span><span class="p">,</span> <span class="n">K1</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">/</span> <span class="n">K</span>
<span class="n">beta_MAP</span> <span class="o">=</span> <span class="n">newton</span><span class="p">(</span><span class="k">lambda</span> <span class="n">beta</span><span class="p">:</span> <span class="nb">float</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">d_log_rho_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)),</span> <span class="n">DP_est</span><span class="p">,</span>
<span class="k">lambda</span> <span class="n">beta</span><span class="p">:</span> <span class="nb">float</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">d2_log_rho_xi</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)),</span>
<span class="n">tol</span><span class="o">=</span><span class="mf">5e-08</span><span class="p">,</span> <span class="n">maxiter</span><span class="o">=</span><span class="mi">500</span><span class="p">)</span>
<span class="k">except</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Warning: No ML parameter was found. (Exception caught.)"</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="n">stderr</span><span class="p">,</span> <span class="n">flush</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">beta_MAP</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="s1">'nan'</span><span class="p">)</span>
<span class="k">return</span> <span class="n">beta_MAP</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.alpha_ML"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.alpha_ML">[docs]</a> <span class="k">def</span> <span class="nf">alpha_ML</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K1</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compute first guess for the beta_MAP (cf get_beta_MAP) parameter</span>
<span class="sd"> via the posterior of a Dirichlet process.</span>
<span class="sd"> """</span>
<span class="n">mk</span> <span class="o">=</span> <span class="n">utl</span><span class="o">.</span><span class="n">remove_key</span><span class="p">(</span><span class="n">mk</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="c1"># rnsum = np.array([_logvarrhoi_DP(n, mk[n]) for n in mk]).sum()</span>
<span class="n">estlist</span> <span class="o">=</span> <span class="p">[</span><span class="n">N</span> <span class="o">*</span> <span class="p">(</span><span class="n">K1</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">/</span> <span class="n">r</span> <span class="o">/</span> <span class="p">(</span><span class="n">N</span> <span class="o">-</span> <span class="n">K1</span><span class="p">)</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">6.</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">)]</span>
<span class="n">varrholist</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">estlist</span><span class="p">:</span>
<span class="c1"># varrholist[_logvarrho_DP(a, rnsum, K1, N)] = a</span>
<span class="n">varrholist</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">log_likelihood_DP_alpha</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">K1</span><span class="p">,</span> <span class="n">N</span><span class="p">)]</span> <span class="o">=</span> <span class="n">a</span>
<span class="n">a_est</span> <span class="o">=</span> <span class="n">varrholist</span><span class="p">[</span><span class="nb">max</span><span class="p">(</span><span class="n">varrholist</span><span class="o">.</span><span class="n">keys</span><span class="p">())]</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">minimize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">a</span><span class="p">:</span> <span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">log_likelihood_DP_alpha</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">K1</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span>
<span class="n">a_est</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">'Nelder-Mead'</span><span class="p">)</span>
<span class="k">return</span> <span class="n">res</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.get_integration_bounds"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.get_integration_bounds">[docs]</a> <span class="k">def</span> <span class="nf">get_integration_bounds</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Find the integration bounds for the estimator.</span>
<span class="sd"> Typically it is a delta-like distribution so it is sufficient</span>
<span class="sd"> to integrate around this peak. (If not this function is not</span>
<span class="sd"> called.)</span>
<span class="sd"> """</span>
<span class="n">beta_MAP</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_beta_MAP</span><span class="p">(</span><span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">beta_MAP</span><span class="p">):</span>
<span class="n">intbounds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="s1">'nan'</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">std</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">d2_log_rho_xi</span><span class="p">(</span><span class="n">beta_MAP</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">**</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="n">intbounds</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">amax</span><span class="p">([</span><span class="mi">10</span> <span class="o">**</span> <span class="p">(</span><span class="o">-</span><span class="mi">50</span><span class="p">),</span> <span class="n">beta_MAP</span> <span class="o">-</span> <span class="mi">8</span> <span class="o">*</span> <span class="n">std</span><span class="p">])),</span>
<span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">beta_MAP</span> <span class="o">+</span> <span class="mi">8</span> <span class="o">*</span> <span class="n">std</span><span class="p">)]</span>
<span class="k">return</span> <span class="n">intbounds</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.H1"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.H1">[docs]</a> <span class="k">def</span> <span class="nf">H1</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compute the first moment (expectation value) of the entropy H.</span>
<span class="sd"> H is the entropy one obtains with a symmetric Dirichlet prior</span>
<span class="sd"> with concentration parameter beta and a multinomial likelihood.</span>
<span class="sd"> """</span>
<span class="n">norm</span> <span class="o">=</span> <span class="n">N</span> <span class="o">+</span> <span class="n">beta</span> <span class="o">*</span> <span class="n">K</span>
<span class="k">return</span> <span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">norm</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">mk</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="n">beta</span><span class="p">)</span> <span class="o">*</span>
<span class="n">mp</span><span class="o">.</span><span class="n">psi</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="n">beta</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">mk</span><span class="p">))</span> <span class="o">/</span> <span class="n">norm</span></div>
<div class="viewcode-block" id="RudeltAbstractNSBEstimator.nsb_entropy"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator.nsb_entropy">[docs]</a> <span class="k">def</span> <span class="nf">nsb_entropy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Estimate the entropy of a system using the NSB estimator.</span>
<span class="sd"> :param mk: multiplicities</span>
<span class="sd"> :param K: number of possible symbols/ state space of the system</span>
<span class="sd"> :param N: total number of observed symbols</span>
<span class="sd"> """</span>
<span class="n">mp</span><span class="o">.</span><span class="n">pretty</span> <span class="o">=</span> <span class="kc">True</span>
<span class="c1"># find the concentration parameter beta</span>
<span class="c1"># for which the posterior is maximised</span>
<span class="c1"># to integrate around this peak</span>
<span class="n">integration_bounds</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_integration_bounds</span><span class="p">(</span><span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">integration_bounds</span><span class="p">)):</span>
<span class="c1"># if no peak was found, integrate over the whole range</span>
<span class="c1"># by reformulating beta into w so that the range goes from 0 to 1</span>
<span class="c1"># instead of from 1 to infinity</span>
<span class="n">integration_bounds</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">unnormalized_posterior_w</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="n">sbeta</span> <span class="o">=</span> <span class="n">w</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">w</span><span class="p">)</span>
<span class="n">beta</span> <span class="o">=</span> <span class="n">sbeta</span> <span class="o">*</span> <span class="n">sbeta</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">unnormalized_posterior</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">sbeta</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">w</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">w</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">H1_w</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="n">sbeta</span> <span class="o">=</span> <span class="n">w</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">w</span><span class="p">)</span>
<span class="n">beta</span> <span class="o">=</span> <span class="n">sbeta</span> <span class="o">*</span> <span class="n">sbeta</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">H1</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">marginal_likelihood</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">quadgl</span><span class="p">(</span><span class="k">lambda</span> <span class="n">w</span><span class="p">:</span> <span class="n">unnormalized_posterior_w</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span>
<span class="n">integration_bounds</span><span class="p">)</span>
<span class="n">H_nsb</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">quadgl</span><span class="p">(</span><span class="k">lambda</span> <span class="n">w</span><span class="p">:</span> <span class="n">H1_w</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">*</span> <span class="n">unnormalized_posterior_w</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span>
<span class="n">integration_bounds</span><span class="p">)</span> <span class="o">/</span> <span class="n">marginal_likelihood</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># integrate over the possible entropies, weighted such that every entropy is equally likely</span>
<span class="c1"># and normalize with the marginal likelihood</span>
<span class="n">marginal_likelihood</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">quadgl</span><span class="p">(</span><span class="k">lambda</span> <span class="n">beta</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">unnormalized_posterior</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span>
<span class="n">integration_bounds</span><span class="p">)</span>
<span class="n">H_nsb</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">quadgl</span><span class="p">(</span><span class="k">lambda</span> <span class="n">beta</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">H1</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">unnormalized_posterior</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span>
<span class="n">integration_bounds</span><span class="p">)</span> <span class="o">/</span> <span class="n">marginal_likelihood</span>
<span class="k">return</span> <span class="n">H_nsb</span></div></div>
<div class="viewcode-block" id="RudeltNSBEstimatorSymbolsMI"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltNSBEstimatorSymbolsMI">[docs]</a><span class="k">class</span> <span class="nc">RudeltNSBEstimatorSymbolsMI</span><span class="p">(</span><span class="n">RudeltAbstractNSBEstimator</span><span class="p">):</span>
<span class="sd">"""History dependence NSB estimator</span>
<span class="sd"> Calculate the mutual information (MI) of one variable depending on its past</span>
<span class="sd"> using NSB estimator. See parent class for references.</span>
<span class="sd"> implemented in idtxl by Michael Lindner, Göttingen 2021</span>
<span class="sd"> Args:</span>
<span class="sd"> settings : dict</span>
<span class="sd"> - embedding_step_size : float [optional]</span>
<span class="sd"> Step size delta t (in seconds) with which the window is slid through the data</span>
<span class="sd"> (default = 0.005).</span>
<span class="sd"> - normalise : bool [optional]</span>
<span class="sd"> rebase spike times to zero</span>
<span class="sd"> (default=True)</span>
<span class="sd"> - return_averaged_R : bool [optional]</span>
<span class="sd"> If set to True, compute R̂tot as the average over R̂(T ) for T ∈ [T̂D, Tmax ] instead of</span>
<span class="sd"> R̂tot = R(T̂D ). If set to True, the setting for number_of_bootstraps_R_tot is ignored and</span>
<span class="sd"> set to 0</span>
<span class="sd"> (default=True)</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">settings</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="c1"># Set default estimator settings.</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">settings</span><span class="p">)</span>
<div class="viewcode-block" id="RudeltNSBEstimatorSymbolsMI.nsb_estimator"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltNSBEstimatorSymbolsMI.nsb_estimator">[docs]</a> <span class="k">def</span> <span class="nf">nsb_estimator</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
<span class="n">symbol_counts</span><span class="p">,</span>
<span class="n">past_symbol_counts</span><span class="p">,</span>
<span class="n">alphabet_size</span><span class="p">,</span>
<span class="n">alphabet_size_past</span><span class="p">,</span>
<span class="n">H_uncond</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Estimate the entropy of a system using the NSB estimator.</span>
<span class="sd"> """</span>
<span class="n">mk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_multiplicities</span><span class="p">(</span><span class="n">symbol_counts</span><span class="p">,</span> <span class="n">alphabet_size</span><span class="p">)</span>
<span class="n">mk_past</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_multiplicities</span><span class="p">(</span><span class="n">past_symbol_counts</span><span class="p">,</span> <span class="n">alphabet_size_past</span><span class="p">)</span>
<span class="n">N</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">((</span><span class="n">mk</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">mk</span><span class="o">.</span><span class="n">keys</span><span class="p">()))</span>
<span class="n">H_nsb_joint</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">nsb_entropy</span><span class="p">(</span><span class="n">mk</span><span class="p">,</span> <span class="n">alphabet_size</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">H_nsb_past</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">nsb_entropy</span><span class="p">(</span><span class="n">mk_past</span><span class="p">,</span> <span class="n">alphabet_size_past</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">H_nsb_cond</span> <span class="o">=</span> <span class="n">H_nsb_joint</span> <span class="o">-</span> <span class="n">H_nsb_past</span>
<span class="n">I_nsb</span> <span class="o">=</span> <span class="n">H_uncond</span> <span class="o">-</span> <span class="n">H_nsb_cond</span>
<span class="n">R_nsb</span> <span class="o">=</span> <span class="n">I_nsb</span> <span class="o">/</span> <span class="n">H_uncond</span>
<span class="k">return</span> <span class="n">I_nsb</span><span class="p">,</span> <span class="n">R_nsb</span></div>
<div class="viewcode-block" id="RudeltNSBEstimatorSymbolsMI.estimate"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltNSBEstimatorSymbolsMI.estimate">[docs]</a> <span class="k">def</span> <span class="nf">estimate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symbol_array</span><span class="p">,</span> <span class="n">past_symbol_array</span><span class="p">,</span> <span class="n">current_symbol_array</span><span class="p">):</span>
<span class="sd">"""Estimate mutual information using NSB estimator.</span>
<span class="sd"> Args:</span>
<span class="sd"> symbol_array : 1D numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> past_symbol_array : numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> current_symbol_array : numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> Returns:</span>
<span class="sd"> I (float)</span>
<span class="sd"> MI (AIS)</span>
<span class="sd"> R (float)</span>
<span class="sd"> MI / H_uncond (History dependence)</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_check_estimator_inputs</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">,</span>
<span class="n">past_symbol_array</span><span class="p">,</span>
<span class="n">current_symbol_array</span><span class="p">,</span>
<span class="kc">None</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">)</span>
<span class="n">symbol_counts</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_symbol_counts</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">)</span>
<span class="n">current_symbol_counts</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_symbol_counts</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">)</span>
<span class="n">H_uncond</span> <span class="o">=</span> <span class="n">utl</span><span class="o">.</span><span class="n">get_H_spiking</span><span class="p">(</span><span class="n">symbol_counts</span><span class="p">)</span>
<span class="n">past_symbol_counts</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_symbol_counts</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">)</span>
<span class="n">number_of_bins_d_join</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">binary_repr</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">))))</span>
<span class="n">alphabet_size_past</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">**</span> <span class="nb">int</span><span class="p">(</span><span class="n">number_of_bins_d_join</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="c1"># K for past activity</span>
<span class="n">alphabet_size</span> <span class="o">=</span> <span class="n">alphabet_size_past</span> <span class="o">*</span> <span class="mi">2</span> <span class="c1"># K</span>
<span class="n">I</span><span class="p">,</span> <span class="n">R</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">nsb_estimator</span><span class="p">(</span><span class="n">symbol_counts</span><span class="p">,</span>
<span class="n">past_symbol_counts</span><span class="p">,</span>
<span class="n">alphabet_size</span><span class="p">,</span>
<span class="n">alphabet_size_past</span><span class="p">,</span>
<span class="n">H_uncond</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">I</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">R</span><span class="p">)</span></div></div>
<div class="viewcode-block" id="RudeltPluginEstimatorSymbolsMI"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltPluginEstimatorSymbolsMI">[docs]</a><span class="k">class</span> <span class="nc">RudeltPluginEstimatorSymbolsMI</span><span class="p">(</span><span class="n">RudeltAbstractEstimator</span><span class="p">):</span>
<span class="sd">"""Plugin History dependence estimator</span>
<span class="sd"> Calculate the mutual information (MI) of one variable depending on its past</span>
<span class="sd"> using plugin estimator. See parent class for references.</span>
<span class="sd"> implemented in idtxl by Michael Lindner, Göttingen 2021</span>
<span class="sd"> Args:</span>
<span class="sd"> settings : dict</span>
<span class="sd"> - embedding_step_size : float [optional] - Step size delta t (in seconds) with which the window is slid</span>
<span class="sd"> through the data (default = 0.005).</span>
<span class="sd"> - normalise : bool [optional] - rebase spike times to zero (default=True)</span>
<span class="sd"> - return_averaged_R : bool [optional] - rebase spike times to zero (default=True)</span>
<span class="sd"> """</span>
<div class="viewcode-block" id="RudeltPluginEstimatorSymbolsMI.plugin_entropy"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltPluginEstimatorSymbolsMI.plugin_entropy">[docs]</a> <span class="k">def</span> <span class="nf">plugin_entropy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mk</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Estimate the entropy of a system using the Plugin estimator.</span>
<span class="sd"> (In principle this is the same function as utl.get_shannon_entropy,</span>
<span class="sd"> only here it is a function of the multiplicities, not the probabilities.)</span>
<span class="sd"> :param mk: multiplicities</span>
<span class="sd"> :param N: total number of observed symbols</span>
<span class="sd"> """</span>
<span class="n">mk</span> <span class="o">=</span> <span class="n">utl</span><span class="o">.</span><span class="n">remove_key</span><span class="p">(</span><span class="n">mk</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="k">return</span> <span class="o">-</span> <span class="nb">sum</span><span class="p">((</span><span class="n">mk</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="n">N</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="n">N</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">mk</span><span class="p">))</span></div>
<div class="viewcode-block" id="RudeltPluginEstimatorSymbolsMI.plugin_estimator"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltPluginEstimatorSymbolsMI.plugin_estimator">[docs]</a> <span class="k">def</span> <span class="nf">plugin_estimator</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
<span class="n">symbol_counts</span><span class="p">,</span>
<span class="n">past_symbol_counts</span><span class="p">,</span>
<span class="n">alphabet_size</span><span class="p">,</span>
<span class="n">alphabet_size_past</span><span class="p">,</span>
<span class="n">H_uncond</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Estimate the entropy of a system using the BBC estimator.</span>
<span class="sd"> """</span>
<span class="n">mk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_multiplicities</span><span class="p">(</span><span class="n">symbol_counts</span><span class="p">,</span> <span class="n">alphabet_size</span><span class="p">)</span>
<span class="n">mk_past</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_multiplicities</span><span class="p">(</span><span class="n">past_symbol_counts</span><span class="p">,</span> <span class="n">alphabet_size_past</span><span class="p">)</span>
<span class="n">N</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">((</span><span class="n">mk</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">mk</span><span class="o">.</span><span class="n">keys</span><span class="p">()))</span>
<span class="n">H_plugin_joint</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">plugin_entropy</span><span class="p">(</span><span class="n">mk</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">H_plugin_past</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">plugin_entropy</span><span class="p">(</span><span class="n">mk_past</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">H_plugin_cond</span> <span class="o">=</span> <span class="n">H_plugin_joint</span> <span class="o">-</span> <span class="n">H_plugin_past</span>
<span class="n">I_plugin</span> <span class="o">=</span> <span class="n">H_uncond</span> <span class="o">-</span> <span class="n">H_plugin_cond</span>
<span class="n">R_plugin</span> <span class="o">=</span> <span class="n">I_plugin</span> <span class="o">/</span> <span class="n">H_uncond</span>
<span class="k">return</span> <span class="n">I_plugin</span><span class="p">,</span> <span class="n">R_plugin</span></div>
<div class="viewcode-block" id="RudeltPluginEstimatorSymbolsMI.estimate"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltPluginEstimatorSymbolsMI.estimate">[docs]</a> <span class="k">def</span> <span class="nf">estimate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symbol_array</span><span class="p">,</span> <span class="n">past_symbol_array</span><span class="p">,</span> <span class="n">current_symbol_array</span><span class="p">):</span>
<span class="sd">"""Estimate mutual information using plugin estimator.</span>
<span class="sd"> Args:</span>
<span class="sd"> symbol_array : 1D numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> past_symbol_array : numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> current_symbol_array : numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> Returns:</span>
<span class="sd"> I (float)</span>
<span class="sd"> MI (AIS)</span>
<span class="sd"> R (float)</span>
<span class="sd"> MI / H_uncond (History dependence)</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_check_estimator_inputs</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">,</span>
<span class="n">past_symbol_array</span><span class="p">,</span>
<span class="n">current_symbol_array</span><span class="p">,</span>
<span class="kc">None</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">)</span>
<span class="n">symbol_counts</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_symbol_counts</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">)</span>
<span class="n">current_symbol_counts</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_symbol_counts</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">)</span>
<span class="c1"># H_uncond_orig = utl.get_H_spiking(symbol_counts)</span>
<span class="n">H_uncond</span> <span class="o">=</span> <span class="n">utl</span><span class="o">.</span><span class="n">get_H_spiking</span><span class="p">(</span><span class="n">symbol_counts</span><span class="p">)</span>
<span class="c1"># past_symbol_counts = utl.get_past_symbol_counts(symbol_counts)</span>
<span class="n">past_symbol_counts</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_symbol_counts</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">)</span>
<span class="c1"># number_of_bins_d_join = np.array(list(np.binary_repr(np.max(past_symbol_array)))).astype(np.int8)</span>
<span class="n">number_of_bins_d_join</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">binary_repr</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">))))</span>
<span class="n">alphabet_size_past</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">**</span> <span class="nb">int</span><span class="p">(</span><span class="n">number_of_bins_d_join</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="c1"># K for past activity</span>
<span class="n">alphabet_size</span> <span class="o">=</span> <span class="n">alphabet_size_past</span> <span class="o">*</span> <span class="mi">2</span> <span class="c1"># K</span>
<span class="n">I</span><span class="p">,</span> <span class="n">R</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">plugin_estimator</span><span class="p">(</span><span class="n">symbol_counts</span><span class="p">,</span>
<span class="n">past_symbol_counts</span><span class="p">,</span>
<span class="n">alphabet_size</span><span class="p">,</span>
<span class="n">alphabet_size_past</span><span class="p">,</span>
<span class="n">H_uncond</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">I</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">R</span><span class="p">)</span></div></div>
<div class="viewcode-block" id="RudeltBBCEstimator"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltBBCEstimator">[docs]</a><span class="k">class</span> <span class="nc">RudeltBBCEstimator</span><span class="p">(</span><span class="n">RudeltAbstractEstimator</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Bayesian bias criterion (BBC) Estimator using NSB and Plugin estimator</span>
<span class="sd"> Calculate the mutual information (MI) of one variable depending on its past</span>
<span class="sd"> using nsb and plugin estimator and check if bias criterion is passed.</span>
<span class="sd"> See parent class for references.</span>
<span class="sd"> implemented in idtxl by Michael Lindner, Göttingen 2021</span>
<span class="sd"> Args:</span>
<span class="sd"> settings : dict</span>
<span class="sd"> - embedding_step_size : float [optional]</span>
<span class="sd"> Step size delta t (in seconds) with which the window is slid through the data</span>
<span class="sd"> (default = 0.005).</span>
<span class="sd"> - normalise : bool [optional]</span>
<span class="sd"> rebase spike times to zero</span>
<span class="sd"> (default=True)</span>
<span class="sd"> - return_averaged_R : bool [optional]</span>
<span class="sd"> If set to True, compute R̂tot as the average over R̂(T ) for T ∈ [T̂D, Tmax ] instead of</span>
<span class="sd"> R̂tot = R(T̂D ). If set to True, the setting for number_of_bootstraps_R_tot is ignored and</span>
<span class="sd"> set to 0</span>
<span class="sd"> (default=True)</span>
<span class="sd"> """</span>
<div class="viewcode-block" id="RudeltBBCEstimator.bayesian_bias_criterion"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltBBCEstimator.bayesian_bias_criterion">[docs]</a> <span class="k">def</span> <span class="nf">bayesian_bias_criterion</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">R_nsb</span><span class="p">,</span> <span class="n">R_plugin</span><span class="p">,</span> <span class="n">bbc_tolerance</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Get whether the Bayesian bias criterion (bbc) is passed.</span>
<span class="sd"> :param R_nsb: history dependence computed with NSB estimator</span>
<span class="sd"> :param R_plugin: history dependence computed with plugin estimator</span>
<span class="sd"> :param bbc_tolerance: tolerance for the Bayesian bias criterion</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_bbc_term</span><span class="p">(</span><span class="n">R_nsb</span><span class="p">,</span> <span class="n">R_plugin</span><span class="p">)</span> <span class="o"><</span> <span class="n">bbc_tolerance</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">0</span></div>
<div class="viewcode-block" id="RudeltBBCEstimator.get_bbc_term"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltBBCEstimator.get_bbc_term">[docs]</a> <span class="k">def</span> <span class="nf">get_bbc_term</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">R_nsb</span><span class="p">,</span> <span class="n">R_plugin</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Get the bbc tolerance-independent term of the Bayesian bias</span>
<span class="sd"> criterion (bbc).</span>
<span class="sd"> :param R_nsb: history dependence computed with NSB estimator</span>
<span class="sd"> :param R_plugin: history dependence computed with plugin estimator</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">R_nsb</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">R_nsb</span> <span class="o">-</span> <span class="n">R_plugin</span><span class="p">)</span> <span class="o">/</span> <span class="n">R_nsb</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span></div>
<div class="viewcode-block" id="RudeltBBCEstimator.estimate"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltBBCEstimator.estimate">[docs]</a> <span class="k">def</span> <span class="nf">estimate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symbol_array</span><span class="p">,</span> <span class="n">past_symbol_array</span><span class="p">,</span> <span class="n">current_symbol_array</span><span class="p">,</span> <span class="n">bbc_tolerance</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Calculate the mutual information (MI) of one variable depending on its past</span>
<span class="sd"> using nsb and plugin estimator and check if bias criterion is passed/</span>
<span class="sd"> Args:</span>
<span class="sd"> symbol_array : 1D numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> past_symbol_array : numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> current_symbol_array : numpy array</span>
<span class="sd"> realisations of symbols based on current and past states.</span>
<span class="sd"> (first output of get_realisations_symbol from data_spiketimes object)</span>
<span class="sd"> Returns:</span>
<span class="sd"> I (float)</span>
<span class="sd"> MI (AIS)</span>
<span class="sd"> R (float)</span>
<span class="sd"> MI / H_uncond (History dependence)</span>
<span class="sd"> bbc_term (float)</span>
<span class="sd"> bbc tolerance-independent term of the Bayesian bias</span>
<span class="sd"> criterion (bbc)</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_check_estimator_inputs</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">,</span>
<span class="n">past_symbol_array</span><span class="p">,</span>
<span class="n">current_symbol_array</span><span class="p">,</span>
<span class="n">bbc_tolerance</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">past_symbol_array</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_ensure_one_dim</span><span class="p">(</span><span class="n">current_symbol_array</span><span class="p">)</span>
<span class="n">estnsb</span> <span class="o">=</span> <span class="n">RudeltNSBEstimatorSymbolsMI</span><span class="p">()</span>
<span class="n">I_nsb</span><span class="p">,</span> <span class="n">R_nsb</span> <span class="o">=</span> <span class="n">estnsb</span><span class="o">.</span><span class="n">estimate</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">,</span> <span class="n">past_symbol_array</span><span class="p">,</span> <span class="n">current_symbol_array</span><span class="p">)</span>
<span class="n">estplugin</span> <span class="o">=</span> <span class="n">RudeltPluginEstimatorSymbolsMI</span><span class="p">()</span>
<span class="n">I_plugin</span><span class="p">,</span> <span class="n">R_plugin</span> <span class="o">=</span> <span class="n">estplugin</span><span class="o">.</span><span class="n">estimate</span><span class="p">(</span><span class="n">symbol_array</span><span class="p">,</span> <span class="n">past_symbol_array</span><span class="p">,</span> <span class="n">current_symbol_array</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">bbc_tolerance</span> <span class="o">==</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">bayesian_bias_criterion</span><span class="p">(</span><span class="n">R_nsb</span><span class="p">,</span> <span class="n">R_plugin</span><span class="p">,</span> <span class="n">bbc_tolerance</span><span class="p">):</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">I_nsb</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">R_nsb</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">None</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">I_nsb</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">R_nsb</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">get_bbc_term</span><span class="p">(</span><span class="n">R_nsb</span><span class="p">,</span>
<span class="n">R_plugin</span><span class="p">))</span></div></div>
<div class="viewcode-block" id="RudeltShufflingEstimator"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltShufflingEstimator">[docs]</a><span class="k">class</span> <span class="nc">RudeltShufflingEstimator</span><span class="p">(</span><span class="n">RudeltAbstractEstimator</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Estimate the history dependence in a spike train using the shuffling estimator.</span>
<span class="sd"> See parent class for references.</span>
<span class="sd"> implemented in idtxl by Michael Lindner, Göttingen 2021</span>
<span class="sd"> """</span>
<div class="viewcode-block" id="RudeltShufflingEstimator.get_P_X_uncond"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltShufflingEstimator.get_P_X_uncond">[docs]</a> <span class="k">def</span> <span class="nf">get_P_X_uncond</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">number_of_symbols</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compute P(X), the probability of the current activity using</span>
<span class="sd"> the plug-in estimator.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="p">[</span><span class="n">number_of_symbols</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">number_of_symbols</span><span class="p">),</span>
<span class="n">number_of_symbols</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">number_of_symbols</span><span class="p">)]</span></div>
<div class="viewcode-block" id="RudeltShufflingEstimator.get_P_X_past_uncond"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltShufflingEstimator.get_P_X_past_uncond">[docs]</a> <span class="k">def</span> <span class="nf">get_P_X_past_uncond</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">past_symbol_counts</span><span class="p">,</span> <span class="n">number_of_symbols</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compute P(X_past), the probability of the past activity using</span>
<span class="sd"> the plug-in estimator.</span>
<span class="sd"> """</span>
<span class="n">P_X_past_uncond</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">response</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]:</span>
<span class="k">for</span> <span class="n">symbol</span> <span class="ow">in</span> <span class="n">past_symbol_counts</span><span class="p">[</span><span class="n">response</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">symbol</span> <span class="ow">in</span> <span class="n">P_X_past_uncond</span><span class="p">:</span>
<span class="n">P_X_past_uncond</span><span class="p">[</span><span class="n">symbol</span><span class="p">]</span> <span class="o">+=</span> <span class="n">past_symbol_counts</span><span class="p">[</span><span class="n">response</span><span class="p">][</span><span class="n">symbol</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">P_X_past_uncond</span><span class="p">[</span><span class="n">symbol</span><span class="p">]</span> <span class="o">=</span> <span class="n">past_symbol_counts</span><span class="p">[</span><span class="n">response</span><span class="p">][</span><span class="n">symbol</span><span class="p">]</span>
<span class="n">number_of_symbols_uncond</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">number_of_symbols</span><span class="p">)</span>
<span class="k">for</span> <span class="n">symbol</span> <span class="ow">in</span> <span class="n">P_X_past_uncond</span><span class="p">:</span>
<span class="n">P_X_past_uncond</span><span class="p">[</span><span class="n">symbol</span><span class="p">]</span> <span class="o">/=</span> <span class="n">number_of_symbols_uncond</span>
<span class="k">return</span> <span class="n">P_X_past_uncond</span></div>
<div class="viewcode-block" id="RudeltShufflingEstimator.get_P_X_past_cond_X"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltShufflingEstimator.get_P_X_past_cond_X">[docs]</a> <span class="k">def</span> <span class="nf">get_P_X_past_cond_X</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">past_symbol_counts</span><span class="p">,</span> <span class="n">number_of_symbols</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compute P(X_past | X), the probability of the past activity conditioned</span>
<span class="sd"> on the response X using the plug-in estimator.</span>
<span class="sd"> """</span>
<span class="n">P_X_past_cond_X</span> <span class="o">=</span> <span class="p">[{},</span> <span class="p">{}]</span>
<span class="k">for</span> <span class="n">response</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]:</span>
<span class="k">for</span> <span class="n">symbol</span> <span class="ow">in</span> <span class="n">past_symbol_counts</span><span class="p">[</span><span class="n">response</span><span class="p">]:</span>
<span class="n">P_X_past_cond_X</span><span class="p">[</span><span class="n">response</span><span class="p">][</span><span class="n">symbol</span><span class="p">]</span> \
<span class="o">=</span> <span class="n">past_symbol_counts</span><span class="p">[</span><span class="n">response</span><span class="p">][</span><span class="n">symbol</span><span class="p">]</span> <span class="o">/</span> <span class="n">number_of_symbols</span><span class="p">[</span><span class="n">response</span><span class="p">]</span>
<span class="k">return</span> <span class="n">P_X_past_cond_X</span></div>
<div class="viewcode-block" id="RudeltShufflingEstimator.get_H0_X_past_cond_X_eq_x"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltShufflingEstimator.get_H0_X_past_cond_X_eq_x">[docs]</a> <span class="k">def</span> <span class="nf">get_H0_X_past_cond_X_eq_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">marginal_probabilities</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compute H_0(X_past | X = x), cf get_H0_X_past_cond_X.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">utl</span><span class="o">.</span><span class="n">get_shannon_entropy</span><span class="p">(</span><span class="n">marginal_probabilities</span><span class="p">)</span> \
<span class="o">+</span> <span class="n">utl</span><span class="o">.</span><span class="n">get_shannon_entropy</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">marginal_probabilities</span><span class="p">)</span></div>
<div class="viewcode-block" id="RudeltShufflingEstimator.get_H0_X_past_cond_X"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltShufflingEstimator.get_H0_X_past_cond_X">[docs]</a> <span class="k">def</span> <span class="nf">get_H0_X_past_cond_X</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">marginal_probabilities</span><span class="p">,</span> <span class="n">number_of_bins_d</span><span class="p">,</span> <span class="n">P_X_uncond</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compute H_0(X_past | X), the estimate of the entropy for the past</span>
<span class="sd"> symbols given a response, under the assumption that activity in</span>
<span class="sd"> the past contributes independently towards the response.</span>
<span class="sd"> """</span>
<span class="n">H0_X_past_cond_X_eq_x</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="k">for</span> <span class="n">response</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]:</span>
<span class="n">H0_X_past_cond_X_eq_x</span><span class="p">[</span><span class="n">response</span><span class="p">]</span> \
<span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_H0_X_past_cond_X_eq_x</span><span class="p">(</span><span class="n">marginal_probabilities</span><span class="p">[</span><span class="n">response</span><span class="p">],</span>
<span class="n">number_of_bins_d</span><span class="p">)</span>
<span class="k">return</span> <span class="nb">sum</span><span class="p">([</span><span class="n">P_X_uncond</span><span class="p">[</span><span class="n">response</span><span class="p">]</span> <span class="o">*</span> <span class="n">H0_X_past_cond_X_eq_x</span><span class="p">[</span><span class="n">response</span><span class="p">]</span> <span class="k">for</span> <span class="n">response</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span></div>
<div class="viewcode-block" id="RudeltShufflingEstimator.get_H_X_past_uncond"><a class="viewcode-back" href="../../idtxl_process_analysis.html#idtxl.estimators_Rudelt.RudeltShufflingEstimator.get_H_X_past_uncond">[docs]</a> <span class="k">def</span> <span class="nf">get_H_X_past_uncond</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P_X_past_uncond</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compute H(X_past), the plug-in estimate of the entropy for the past symbols, given</span>
<span class="sd"> their probabilities.</span>
<span class="sd"> """</span>