notebook/NeuroBoostedTrees.ipynb

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    "# NeuroBoostedTrees\n",
    "\n",
    "This notebook illustrates the analyses presented in the following paper:\n",
    "\"[Brain-state invariant thalamo-cortical coordination revealed by non-linear encoders, Viejo et al., PLoS Comp Biol, 2018][2]\"\n",
    "\n",
    "We made an extensive use of [XGBoost][3] for analysing thalamo-cortical neuronal interactions in the head-direction circuit.\n",
    "\n",
    "The dataset for this tutorial can be found [here.][1]\n",
    "\n",
    "Related work: \"[Modern machine learning far outperforms GLMs at predicting spikes;Benjamin et al. 2017][2]\".\n",
    "\n",
    "We present two of our analyses: prediction scoring of spiking activity in relation to behaviour and dissectiong of the gradient boosted tree branching after learning (i.e. the splitting positions and gains). All the Python code used for the manuscript can be found [here][4] (or you can send us a message). Sorry, still a bit messy, but we're working on it! \n",
    "\n",
    " \n",
    "## Table of content\n",
    "\n",
    "I. Predicting firing rate as a function of head-direction\n",
    "    1. Loading data\n",
    "    2. Integrating data into Panda framework\n",
    "    3. Prediction score functions and cross validations\n",
    "    4. Definitions of the learners\n",
    "    5. Supervised learning\n",
    "    \n",
    "II. Analysing the tree structure\n",
    "    1. Extracting tree threshold from XGB\n",
    "    2. Learning XGB examples\n",
    "    3. Tuning curves\n",
    "    4. Extracting tree structure\n",
    "    5. Correlation with Fisher Information\n",
    "    \n",
    "III. Miscellaneous\n",
    "    1. Computing the gain    \n",
    "    \n",
    "## Dependencies\n",
    "\n",
    "Basics\n",
    " - matplotlib\n",
    " - numpy\n",
    " - pandas\n",
    " - scipy\n",
    " - warnings\n",
    " - itertools\n",
    " \n",
    "Methods\n",
    " - xgboost\n",
    " \n",
    "\n",
    "[1]:www.peyrachelab.com/data/data_test_boosted_tree_20ms.mat\n",
    "[2]:http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1006041\n",
    "[3]:http://xgboost.readthedocs.io/en/latest/\n",
    "[4]:https://github.com/gviejo/Prediction_xgb_head_direction\n",
    "[5]:http://biorxiv.org/content/early/2017/06/13/148643"
   ]
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   "source": [
    "import warnings\n",
    "import pandas as pd\n",
    "import scipy.io\n",
    "import numpy as np\n",
    "import sys, os\n",
    "import itertools\n"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "\n",
    "## I. Predicting firing rate as a function of head-direction\n",
    "\n",
    "### 1. Loading data\n",
    "\n",
    "First, a dictionnary of array is loaded.\n",
    "Keys are :\n",
    "    - 'Ang'   : head-direction (an angular value)\n",
    "    - 'X'     : x position \n",
    "    - 'Y'     : y position\n",
    "    - 'ADn'   : Antero-dorsal nucleus spiking activity (17 neurons)\n",
    "    - 'Pos'   : Post-subiculum spiking activity (15 neurons)\n",
    "    - 'speed' : animal speed"
   ]
  },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Ang', 'Pos', '__header__', '__globals__', 'ADn', 'Y', 'X', '__version__', 'speed']\n"
     ]
    }
   ],
   "source": [
    "#head direction data\n",
    "hd_data = scipy.io.loadmat('../python/data_test_boosted_tree_20ms.mat') # 20 ms is the size of the time bin\n",
    "print(hd_data.keys())\n"
   ]
  },
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   "source": [
    "### 2. Integrating data into Panda framework\n",
    "\n",
    "Pandas makes life much easier when dealing with different subgroups of features. It allows to retrieve quickly time series.\n",
    "Neurons are ordered based on their tuning curves (from 0 to 2pi). In Pandas, their name reflects their order ['ADn.0', 'ADn.1', 'ADn.2', ...].\n"
   ]
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index([u'time', u'ang', u'x', u'y', u'vel', u'Pos.0', u'Pos.1', u'Pos.2',\n",
      "       u'Pos.3', u'Pos.4', u'Pos.5', u'Pos.6', u'Pos.7', u'Pos.8', u'Pos.9',\n",
      "       u'Pos.10', u'Pos.11', u'Pos.12', u'Pos.13', u'Pos.14', u'ADn.0',\n",
      "       u'ADn.1', u'ADn.2', u'ADn.3', u'ADn.4', u'ADn.5', u'ADn.6', u'ADn.7',\n",
      "       u'ADn.8', u'ADn.9', u'ADn.10', u'ADn.11', u'ADn.12', u'ADn.13',\n",
      "       u'ADn.14', u'ADn.15', u'ADn.16'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "data            =   pd.DataFrame()\n",
    "data['time']    =   np.arange(len(hd_data['Ang']))     \n",
    "data['ang']     =   hd_data['Ang'].flatten()            \n",
    "data['x']       =   hd_data['X'].flatten()              \n",
    "data['y']       =   hd_data['Y'].flatten()              \n",
    "data['vel']     =   hd_data['speed'].flatten()\n",
    "# neurons activity \n",
    "for i in xrange(hd_data['Pos'].shape[1]): data['Pos'+'.'+str(i)] = hd_data['Pos'][:,i]\n",
    "for i in xrange(hd_data['ADn'].shape[1]): data['ADn'+'.'+str(i)] = hd_data['ADn'][:,i]\n",
    "\n",
    "print data.keys()"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 3. Prediction score functions and cross validations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This section requires Scikit-learn.\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "from sklearn.model_selection import KFold\n",
    "\n",
    "def poisson_pseudoR2(y, yhat, ynull):\n",
    "    \"\"\" Compute the pseudo R2 score\n",
    "        y : real firing rate\n",
    "        yhat : predicted firing rate\n",
    "        ynull : mean of the real firing rate\n",
    "    \"\"\"    \n",
    "    yhat = yhat.reshape(y.shape)\n",
    "    eps = np.spacing(1)\n",
    "    L1 = np.sum(y*np.log(eps+yhat) - yhat)\n",
    "    L1_v = y*np.log(eps+yhat) - yhat\n",
    "    L0 = np.sum(y*np.log(eps+ynull) - ynull)\n",
    "    LS = np.sum(y*np.log(eps+y) - y)\n",
    "    R2 = 1-(LS-L1)/(LS-L0)\n",
    "    return R2\n",
    "\n",
    "def fit_cv(X, Y, algorithm, n_cv=10):\n",
    "    \"\"\"Performs cross-validated fitting. Returns (Y_hat, pR2_cv); a vector of predictions Y_hat with the\n",
    "    same dimensions as Y, and a list of pR2 scores on each fold pR2_cv.\n",
    "    X  = input data\n",
    "    Y = spiking data\n",
    "    algorithm = a function of (Xr, Yr, Xt) {training data Xr and response Yr and testing features Xt}\n",
    "                and returns the predicted response Yt\n",
    "    n_cv = number of cross-validations folds\n",
    "    \"\"\"\n",
    "    if np.ndim(X)==1:\n",
    "        X = np.transpose(np.atleast_2d(X))\n",
    "    cv_kf = KFold(n_splits=n_cv, shuffle=True, random_state=42)\n",
    "    skf  = cv_kf.split(X)\n",
    "    Y_hat=np.zeros(len(Y))\n",
    "    pR2_cv = list()\n",
    "    for idx_r, idx_t in skf:\n",
    "        Xr = X[idx_r, :]\n",
    "        Yr = Y[idx_r]\n",
    "        Xt = X[idx_t, :]\n",
    "        Yt = Y[idx_t]           \n",
    "        Yt_hat = eval(algorithm)(Xr, Yr, Xt)        \n",
    "        Y_hat[idx_t] = Yt_hat\n",
    "        pR2 = poisson_pseudoR2(Yt, Yt_hat, np.mean(Yr))\n",
    "        pR2_cv.append(pR2)\n",
    "\n",
    "    return Y_hat, pR2_cv\n"
   ]
  },
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   "source": [
    "### 4. Definitions of learners\n",
    "\n",
    "As in the paper, we define :\n",
    "    - xgb_run  : XGBoost \n",
    "    - mb       : the model-based tuning curves of the neuron\n",
    "    - lin_comb : a simple linear regression\n",
    "    - kernel   : the kernel model that transforms the angular feature into a combination of cosinus and sinus (and their harmonics)"
   ]
  },
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   "source": [
    "import xgboost as xgb\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "def xgb_run(Xr, Yr, Xt):\n",
    "    \"\"\" XGBoost model\n",
    "        Return the predicted firing rate\n",
    "    \"\"\"\n",
    "    params = {'objective': \"count:poisson\", #for poisson output\n",
    "    'eval_metric': \"poisson-nloglik\", #loglikelihood loss\n",
    "    'seed': 2925,\n",
    "    'silent': 1,\n",
    "    'learning_rate': 0.1,\n",
    "    'min_child_weight': 2, \n",
    "    # 'subsample': 0.6, \n",
    "    'max_depth': 5, \n",
    "    'gamma': 0.5\n",
    "    }    \n",
    "    dtrain = xgb.DMatrix(Xr, label=Yr)\n",
    "    dtest = xgb.DMatrix(Xt)\n",
    "    num_round = 100\n",
    "    bst = xgb.train(params, dtrain, num_round)\n",
    "    Yt = bst.predict(dtest)\n",
    "    return Yt\n",
    "\n",
    "def mb(Xr, Yr, Xt):\n",
    "    \"\"\" Compute the model-based tuning curve of the hd cells\n",
    "        And return the predicted firing rate        \n",
    "    \"\"\"\n",
    "    nb_bins = 60\n",
    "    bins = np.linspace(np.vstack((Xr, Xt)).min(), np.vstack((Xr, Xt)).max()+1e-8, nb_bins+1)\n",
    "    index = np.digitize(Xr, bins).flatten()    \n",
    "    tcurve = np.array([np.sum(Yr[index == i]) for i in xrange(1, nb_bins+1)])\n",
    "    occupancy = np.array([np.sum(index == i) for i in xrange(1, nb_bins+1)])\n",
    "    tcurve = (tcurve/occupancy)*40.0  \n",
    "    new_index = np.digitize(Xt, bins).flatten()    \n",
    "    return tcurve[new_index-1]/40.0 \n",
    "\n",
    "def lin_comb(Xr, Yr, Xt):\n",
    "    \"\"\" Linear model\n",
    "        Return the predicted firing rate\n",
    "    \"\"\"\n",
    "    lr = LinearRegression()\n",
    "    lr.fit(Xr, Yr)\n",
    "    Yt = lr.predict(Xt)    \n",
    "    #rectify outputs\n",
    "    Yt = np.maximum(Yt,np.zeros(Yt.shape))\n",
    "    return Yt \n",
    "\n",
    "def kernel(Xr, Yr, Xt):\n",
    "    \"\"\" Kernel model, cos and sin of the angle to the linear model\n",
    "        Return the predicted firing rate\n",
    "    \"\"\"\n",
    "    newX = np.zeros((Xr.shape[0], 12)) # up to six order    \n",
    "    newXt = np.zeros((Xt.shape[0], 12))\n",
    "    for i, j in zip(xrange(1,7), xrange(0, 12, 2)):\n",
    "        newX[:,j] = np.cos(i*Xr).flatten()\n",
    "        newX[:,j+1] = np.sin(i*Xr).flatten()\n",
    "        newXt[:,j] = np.cos(i*Xt).flatten()\n",
    "        newXt[:,j+1] = np.sin(i*Xt).flatten()\n",
    "    Yt = lin_comb(newX, Yr, newXt)    \n",
    "    return Yt"
   ]
  },
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    "editable": true
   },
   "source": [
    "### 5 Supervised learning\n",
    "\n",
    "The function test_features takes as argument a list of features and targets and runs the supervised learning procedure using cross-validation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "source": [
    "def test_features(features, targets, learners):\n",
    "    '''\n",
    "    features : a list of features, for example ['ang', 'x', 'y']\n",
    "    targets :  the list of neurons to predict ['ADn.0', 'ADn.1']\n",
    "    learners : the list of model to use, for example ['xgb']        \n",
    "    Return : dictionnary with for each models the score PR2 and Yt_hat (the prediction of the firing rate)\n",
    "    '''\n",
    "    X = data[features].values\n",
    "    Y = data[targets].values    \n",
    "    output = {method:{'PR2':[],'Yt_hat':[]} for method in learners}\n",
    "    learners_ = list(learners)\n",
    "    for i in xrange(Y.shape[1]):\n",
    "        y = Y[:,i]        \n",
    "        for method in learners_:        \n",
    "            print('Running '+method+' to predict '+targets[i])                              \n",
    "            Yt_hat, PR2 = fit_cv(X, y, algorithm = method, n_cv=8)       \n",
    "            output[method]['Yt_hat'].append(Yt_hat)\n",
    "            output[method]['PR2'].append(PR2)           \n",
    "    for m in output.iterkeys():\n",
    "        output[m]['Yt_hat'] = np.array(output[m]['Yt_hat'])\n",
    "        output[m]['PR2'] = np.array(output[m]['PR2'])        \n",
    "    return output\n",
    "    "
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
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    "editable": true
   },
   "source": [
    " The combinations to be learned are defined here in a dictionnary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'features': ['ang'], 'targets': ['ADn.0', 'ADn.1', 'ADn.2', 'ADn.3', 'ADn.4', 'ADn.5', 'ADn.6', 'ADn.7', 'ADn.8', 'ADn.9', 'ADn.10', 'ADn.11', 'ADn.12', 'ADn.13', 'ADn.14', 'ADn.15', 'ADn.16']}\n",
      "{'features': ['ang'], 'targets': ['Pos.0', 'Pos.1', 'Pos.2', 'Pos.3', 'Pos.4', 'Pos.5', 'Pos.6', 'Pos.7', 'Pos.8', 'Pos.9', 'Pos.10', 'Pos.11', 'Pos.12', 'Pos.13', 'Pos.14']}\n"
     ]
    }
   ],
   "source": [
    "combination = {\n",
    "    'Pos':  {\n",
    "            'features'  :   ['ang'],\n",
    "            'targets'   :   [i for i in list(data) if i.split(\".\")[0] == 'Pos'], \n",
    "            },          \n",
    "    'ADn':  {\n",
    "            'features'  :   ['ang'],\n",
    "            'targets'   :   [i for i in list(data) if i.split(\".\")[0] == 'ADn'],\n",
    "            }\n",
    "}\n",
    "print(combination['ADn'])\n",
    "print(combination['Pos'])\n"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "- The main loop"
   ]
  },
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   "cell_type": "code",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running mb to predict ADn.0\n",
      "Running xgb_run to predict ADn.0\n",
      "Running lin_comb to predict ADn.0\n",
      "Running kernel to predict ADn.0\n",
      "Running mb to predict ADn.1\n",
      "Running xgb_run to predict ADn.1\n",
      "Running lin_comb to predict ADn.1\n",
      "Running kernel to predict ADn.1\n",
      "Running mb to predict ADn.2\n",
      "Running xgb_run to predict ADn.2\n",
      "Running lin_comb to predict ADn.2\n",
      "Running kernel to predict ADn.2\n",
      "Running mb to predict ADn.3\n",
      "Running xgb_run to predict ADn.3\n",
      "Running lin_comb to predict ADn.3\n",
      "Running kernel to predict ADn.3\n",
      "Running mb to predict ADn.4\n",
      "Running xgb_run to predict ADn.4\n",
      "Running lin_comb to predict ADn.4\n",
      "Running kernel to predict ADn.4\n",
      "Running mb to predict ADn.5\n",
      "Running xgb_run to predict ADn.5\n",
      "Running lin_comb to predict ADn.5\n",
      "Running kernel to predict ADn.5\n",
      "Running mb to predict ADn.6\n",
      "Running xgb_run to predict ADn.6\n",
      "Running lin_comb to predict ADn.6\n",
      "Running kernel to predict ADn.6\n",
      "Running mb to predict ADn.7\n",
      "Running xgb_run to predict ADn.7\n",
      "Running lin_comb to predict ADn.7\n",
      "Running kernel to predict ADn.7\n",
      "Running mb to predict ADn.8\n",
      "Running xgb_run to predict ADn.8\n",
      "Running lin_comb to predict ADn.8\n",
      "Running kernel to predict ADn.8\n",
      "Running mb to predict ADn.9\n",
      "Running xgb_run to predict ADn.9\n",
      "Running lin_comb to predict ADn.9\n",
      "Running kernel to predict ADn.9\n",
      "Running mb to predict ADn.10\n",
      "Running xgb_run to predict ADn.10\n",
      "Running lin_comb to predict ADn.10\n",
      "Running kernel to predict ADn.10\n",
      "Running mb to predict ADn.11\n",
      "Running xgb_run to predict ADn.11\n",
      "Running lin_comb to predict ADn.11\n",
      "Running kernel to predict ADn.11\n",
      "Running mb to predict ADn.12\n",
      "Running xgb_run to predict ADn.12\n",
      "Running lin_comb to predict ADn.12\n",
      "Running kernel to predict ADn.12\n",
      "Running mb to predict ADn.13\n",
      "Running xgb_run to predict ADn.13\n",
      "Running lin_comb to predict ADn.13\n",
      "Running kernel to predict ADn.13\n",
      "Running mb to predict ADn.14\n",
      "Running xgb_run to predict ADn.14\n",
      "Running lin_comb to predict ADn.14\n",
      "Running kernel to predict ADn.14\n",
      "Running mb to predict ADn.15\n",
      "Running xgb_run to predict ADn.15\n",
      "Running lin_comb to predict ADn.15\n",
      "Running kernel to predict ADn.15\n",
      "Running mb to predict ADn.16\n",
      "Running xgb_run to predict ADn.16\n",
      "Running lin_comb to predict ADn.16\n",
      "Running kernel to predict ADn.16\n",
      "Running mb to predict Pos.0\n",
      "Running xgb_run to predict Pos.0\n",
      "Running lin_comb to predict Pos.0\n",
      "Running kernel to predict Pos.0\n",
      "Running mb to predict Pos.1\n",
      "Running xgb_run to predict Pos.1\n",
      "Running lin_comb to predict Pos.1\n",
      "Running kernel to predict Pos.1\n",
      "Running mb to predict Pos.2\n",
      "Running xgb_run to predict Pos.2\n",
      "Running lin_comb to predict Pos.2\n",
      "Running kernel to predict Pos.2\n",
      "Running mb to predict Pos.3\n",
      "Running xgb_run to predict Pos.3\n",
      "Running lin_comb to predict Pos.3\n",
      "Running kernel to predict Pos.3\n",
      "Running mb to predict Pos.4\n",
      "Running xgb_run to predict Pos.4\n",
      "Running lin_comb to predict Pos.4\n",
      "Running kernel to predict Pos.4\n",
      "Running mb to predict Pos.5\n",
      "Running xgb_run to predict Pos.5\n",
      "Running lin_comb to predict Pos.5\n",
      "Running kernel to predict Pos.5\n",
      "Running mb to predict Pos.6\n",
      "Running xgb_run to predict Pos.6\n",
      "Running lin_comb to predict Pos.6\n",
      "Running kernel to predict Pos.6\n",
      "Running mb to predict Pos.7\n",
      "Running xgb_run to predict Pos.7\n",
      "Running lin_comb to predict Pos.7\n",
      "Running kernel to predict Pos.7\n",
      "Running mb to predict Pos.8\n",
      "Running xgb_run to predict Pos.8\n",
      "Running lin_comb to predict Pos.8\n",
      "Running kernel to predict Pos.8\n",
      "Running mb to predict Pos.9\n",
      "Running xgb_run to predict Pos.9\n",
      "Running lin_comb to predict Pos.9\n",
      "Running kernel to predict Pos.9\n",
      "Running mb to predict Pos.10\n",
      "Running xgb_run to predict Pos.10\n",
      "Running lin_comb to predict Pos.10\n",
      "Running kernel to predict Pos.10\n",
      "Running mb to predict Pos.11\n",
      "Running xgb_run to predict Pos.11\n",
      "Running lin_comb to predict Pos.11\n",
      "Running kernel to predict Pos.11\n",
      "Running mb to predict Pos.12\n",
      "Running xgb_run to predict Pos.12\n",
      "Running lin_comb to predict Pos.12\n",
      "Running kernel to predict Pos.12\n",
      "Running mb to predict Pos.13\n",
      "Running xgb_run to predict Pos.13\n",
      "Running lin_comb to predict Pos.13\n",
      "Running kernel to predict Pos.13\n",
      "Running mb to predict Pos.14\n",
      "Running xgb_run to predict Pos.14\n",
      "Running lin_comb to predict Pos.14\n",
      "Running kernel to predict Pos.14\n"
     ]
    }
   ],
   "source": [
    "methods = ['mb', 'xgb_run', 'lin_comb', 'kernel']\n",
    "final_data = {}\n",
    "for g in np.sort(combination.keys()):\n",
    "    features = combination[g]['features']\n",
    "    targets = combination[g]['targets'] \n",
    "    results = test_features(features, targets, methods)        \n",
    "    final_data[g] = results\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "- Let's plot the result for this dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VcYmI1Gfp1gwlIiJpSMlCRERCKVmIiEgoJQsREQmlZCEiIqGULEREJFTadZ0V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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e07365dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pyplot import *\n",
    "\n",
    "methods_to_plot = ['mb', 'xgb_run', 'lin_comb', 'kernel']\n",
    "labels = {  'mb':'MB \\n 60 bins', \n",
    "            'lin_comb':'Linear', \n",
    "            'nn':'NN', \n",
    "            'xgb_run':\"$\\mathbf{XGB}$\",\n",
    "            'h1':\"Linear \\n (cos$\\\\theta$, sin$\\\\theta$)\",\n",
    "            'kernel':\"$6^{rd}$ order \\n kernel\"}\n",
    "labels_plot = [labels[m] for m in methods_to_plot]\n",
    "mean_pR2 = list()\n",
    "sem_pR2 = list()\n",
    "for model in methods_to_plot:\n",
    "    PR2_art = final_data['ADn'][model]['PR2']\n",
    "    mean_pR2.append(np.mean(PR2_art))\n",
    "    sem_pR2.append(np.std(PR2_art)/np.sqrt(np.size(PR2_art)))        \n",
    "bar(np.arange(np.size(mean_pR2)), mean_pR2, 0.4, align='center',\n",
    "        ecolor='k', alpha=1, color='#EE6C4D', ec='w', yerr=np.array(sem_pR2), label = 'Antero-dorsal nucleus')\n",
    "plot(np.arange(np.size(mean_pR2)), mean_pR2, 'k.', markersize=5)\n",
    "mean_pR2 = list()\n",
    "sem_pR2 = list()\n",
    "for model in methods_to_plot:\n",
    "    PR2_art = final_data['Pos'][model]['PR2']\n",
    "    mean_pR2.append(np.mean(PR2_art))\n",
    "    sem_pR2.append(np.std(PR2_art)/np.sqrt(np.size(PR2_art)))\n",
    "bar(np.arange(np.size(mean_pR2))+0.405, mean_pR2, 0.4, align='center',\n",
    "        ecolor='k', alpha=1, color='#3D5A80', ec='w', yerr=np.array(sem_pR2), label = 'Post-subiculum')\n",
    "plot(np.arange(np.size(mean_pR2))+0.41, mean_pR2, 'k.', markersize=5)\n",
    "plot([-1, len(methods_to_plot)], [0,0],'--k', alpha=0.4)\n",
    "legend(loc='upper center', ncol=2, frameon = False)\n",
    "xlim(-0.5,)\n",
    "ylim(-0.2, 0.9)\n",
    "xticks(np.arange(np.size(mean_pR2))+0.205, labels_plot)\n",
    "ylabel(\"$Pseudo-R^2$\")\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## II. ANALYSING SPLIT POSITIONS\n",
    "\n",
    "Using the same dataset, we will now look at the positions of splits within the tuning curve of one neuron from ADn and one neuron from PoSub."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 1. Extracting tree thresholds from XGB\n",
    "\n",
    "By default, XGB returns a list of tree as strings. To extract the split positions, one needs to parse the string first. That is the purpose of the function extract_tree_threshold that takes as input the booster. \n",
    "Here, we also define fisher_information which takes as input the tuning curve.\n",
    "\n",
    "This section requires graphviz.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def extract_tree_threshold(trees):\n",
    "    \"\"\" Take BST TREE and return a dict = {features index : [splits position 1, splits position 2, ...]}\n",
    "    \"\"\"\n",
    "    n = len(trees.get_dump())\n",
    "    thr = {}\n",
    "    for t in xrange(n):\n",
    "        gv = xgb.to_graphviz(trees, num_trees=t)\n",
    "        body = gv.body\t\t\n",
    "        for i in xrange(len(body)):\n",
    "            for l in body[i].split('\"'):\n",
    "                if 'f' in l and '<' in l:\n",
    "                    tmp = l.split(\"<\")\n",
    "                    if thr.has_key(tmp[0]):\n",
    "                        thr[tmp[0]].append(float(tmp[1]))\n",
    "                    else:\n",
    "                        thr[tmp[0]] = [float(tmp[1])]\n",
    "    for k in thr.iterkeys():\n",
    "        thr[k] = np.sort(np.array(thr[k]))\n",
    "    return thr\n",
    "\n",
    "\n",
    "def fisher_information(x, f):\n",
    "    \"\"\" Compute Fisher Information over the tuning curves\n",
    "        x : array of angular position\n",
    "        f : firing rate\n",
    "        return (angular position, fisher information)\n",
    "    \"\"\"\n",
    "    fish = np.zeros(len(f)-1)\n",
    "    slopes_ = []\n",
    "    tmpf = np.hstack((f[-1],f,f[0:3]))\n",
    "    binsize = x[1]-x[0]\t\n",
    "    tmpx = np.hstack((np.array([x[0]-binsize-(x.min()+(2*np.pi-x.max()))]),x,np.array([x[-1]+i*binsize+(x.min()+(2*np.pi-x.max())) for i in xrange(1,4)])))\t\t\n",
    "    for i in xrange(len(f)):\n",
    "        slope, intercept, r_value, p_value, std_err = scipy.stats.linregress(tmpx[i:i+3], tmpf[i:i+3])\n",
    "        slopes_.append(slope)\n",
    "    fish = np.power(slopes_, 2)\n",
    "    fish = fish/(f+1e-4)\n",
    "    return (x, fish)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's define new combinations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "combination = {\n",
    "    'ang':{\n",
    "        'ADn':{\n",
    "            'features' \t:\t['ang'],\n",
    "            'targets'\t:\t['ADn.8']\n",
    "                },\n",
    "        'Pos':\t{\n",
    "            'features' \t:\t['ang'],\n",
    "            'targets'\t:\t['Pos.9']\n",
    "                },\n",
    "        },\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 2. Learning XGB examples\n",
    "\n",
    "Each booster is saved in the dictionnary bsts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning ADn.8 from feature ang\n",
      "Learning Pos.9 from feature ang\n",
      "['ang']\n"
     ]
    }
   ],
   "source": [
    "params = {'objective': \"count:poisson\", #for poisson output\n",
    "    'eval_metric': \"logloss\", #loglikelihood loss\n",
    "    'seed': 2925, #for reproducibility\n",
    "    'silent': 1,\n",
    "    'learning_rate': 0.01,\n",
    "    'min_child_weight': 2,\n",
    "    'max_depth': 5}        \n",
    "\n",
    "num_round = 30\n",
    "bsts = {}\n",
    "for i in combination.iterkeys():    \n",
    "    bsts[i] = {}\n",
    "    for j in combination[i].iterkeys():        \n",
    "        features = combination[i][j]['features']\n",
    "        targets = combination[i][j]['targets']\n",
    "        print(\"Learning \"+targets[0]+\" from feature \"+features[0])\n",
    "        X = data[features].values\n",
    "        Yall = data[targets].values\n",
    "        for k in xrange(Yall.shape[1]):\n",
    "            dtrain = xgb.DMatrix(X, label=Yall[:,k])\n",
    "            bst = xgb.train(params, dtrain, num_round)\n",
    "            bsts[i][j] = bst\n",
    "\n",
    "print(bsts.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 3. Tuning curves\n",
    "\n",
    "By default, tuning curves are built over 60 angular bins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def tuning_curve(x, f, nb_bins, tau = 40.0):\n",
    "    bins = np.linspace(x.min(), x.max()+1e-8, nb_bins+1)\n",
    "    index = np.digitize(x, bins).flatten()    \n",
    "    tcurve = np.array([np.sum(f[index == i]) for i in xrange(1, nb_bins+1)])\n",
    "    occupancy = np.array([np.sum(index == i) for i in xrange(1, nb_bins+1)])\n",
    "    tcurve = (tcurve/occupancy)*tau\n",
    "    x = bins[0:-1] + (bins[1]-bins[0])/2.\n",
    "    return (x, tcurve)\n",
    "\n",
    "X = data['ang'].values\n",
    "example = [combination['ang'][k]['targets'][0] for k in ['ADn', 'Pos']]\n",
    "tuningc = {}\n",
    "for k in example:\n",
    "    Y = data[k].values\n",
    "    tuningc[k.split(\".\")[0]] = tuning_curve(X, Y, nb_bins = 60)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "- Let's plot the two tuning curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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3UgdiTCXzN60GVbyJ5/VZmanpc2l/+n78DatK2u3UVK+eGoGf7MtAjKlk/vpmEMEbN7XP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\nBGCqnv/qK5DNWP1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4frR8IZAF5nRRZrfbEXa1OwcYF8V2cbR+KPAk0C96/lng/wApYF3e\n++sBF3h/x+eI1h9/TjiO5b3R8i3Ab6PlO4C7o+VphHNgdY49BWzLe34V0AqMzVs3OPpZC7wCDAFG\nAZuiz+YBz3SK7wvAJ+P+e7BH3z7KfhyAqXpHNRzmDoR104QzVAK8HpiWV/1SH511DwZ+Ep35KyfG\ns7wW+DaAqr4iIsu6KbOn7fKrejap6kvR8mXAdODZKJ4U8DwwlfCAvDja3+Hoc/T0mV8DvC1avhP4\nRt5r90b7aRaREV28dxhwoNO6F1V1c97zT4jIX0TLDcBkYDTwuKrui+K7O1rfYVf0WUyCWAIw5UyA\nSzWcBfbESpH/JBy9+nYRGQc83sP7iQ6GXyJMFh/obrsuHOm0zUOqemOnWC7o4f3d6amNo/00cR0D\nOk8IdjxOEbkK+DPC761dRB7nRBVXT3HWRvs2CWJtACZuPR2UHgI+fnxDkZnR4kBOzAeV33vlKcL6\n8Y4D8wwAVb1XVWer6pzoTL3L7U4T2wvAPBFpit5XF12BrAZGicjcaH191BjbGsXZleeA90TL7wWe\nLqB8os9yAHCiaVG6MgjYHx38zyO8coFwZtbXisiQaFTpOzu9bwqwvJt9miplCcDEraez4Y8DF4nI\nMhFZDnw4Wv8vwNdFZBEn/w3/N2E10QrgdmAhXetpO+1qWVX3ADcDP4+qjJ4DpkZXJ+8CvisiSwmT\nVg3hVcn0jkbgTuXfBtwSbX8jJ5Jc5++iu+/mIeCKbl57AEhFn+1rhNVUqOqO6LO+QJhwOs8pMw94\nuJt9miplU0EYU2FEZDbwCVV9f5H2N4uwAbgo+zOVw64AjKkwqroEePxsBoJ1MhT4hyLty1QQuwIw\nxpiEsisAY4xJKEsAxhiTUJYAjDEmoSwBGGNMQlkCMMaYhPr/U6zJKIbiHhIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e10a11fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "title_ = ['Antero-dorsal nucleus', 'Post-subiculum']\n",
    "colors_ = ['#EE6C4D', '#3D5A80']\n",
    "figure()\n",
    "limts = [(1.5,5),(0.7, 3.6)]\n",
    "\n",
    "e = 'ADn'\n",
    "i = 0\n",
    "plot(tuningc[e][0], tuningc[e][1], color = colors_[i], linewidth = 1.5)\n",
    "xlabel('Head-direction (rad)', labelpad = 0.0)\n",
    "ylabel('Firing rate (Hz)', labelpad = 2.1)\n",
    "locator_params(axis='y', nbins = 3)\n",
    "locator_params(axis='x', nbins = 4)\n",
    "title(title_[i], fontsize = 12)\n",
    "xlim(0, 2*np.pi)\n",
    "    \n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cpD+rzsMTP6uOPJKfDOwyxuQaY2qBN4FZHbh/5UYaHJ2H/qw6j84e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\nQ1SYUhnPvVcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e0737bd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure()\n",
    "e = 'Pos'\n",
    "i = 1\n",
    "plot(tuningc[e][0], tuningc[e][1], color = colors_[i], linewidth = 1.5)\n",
    "xlabel('Head-direction (rad)', labelpad = 0.0)\n",
    "ylabel('Firing rate (Hz)', labelpad = 2.1)\n",
    "locator_params(axis='y', nbins = 3)\n",
    "locator_params(axis='x', nbins = 4)\n",
    "title(title_[i], fontsize = 12)\n",
    "xlim(0,2*np.pi)\n",
    "\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 4. Extracting tree structure\n",
    "\n",
    "HEre, 'thresholds' is the dictionnary that contains the position of splits for the only feature we use: f0 (the head-direction). However, the function is generic enough to take multi-dimensional bosster as argument (e.g. f0, f1, f2, ...)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['ang']\n",
      "['ADn', 'Pos']\n",
      "['f0']\n",
      "628 splits\n"
     ]
    }
   ],
   "source": [
    "thresholds = {}\n",
    "for i in bsts.iterkeys():\n",
    "    thresholds[i] = {}\n",
    "    for j in bsts[i].iterkeys():\n",
    "        thresholds[i][j] = extract_tree_threshold(bsts[i][j])\n",
    "\n",
    "print(thresholds.keys())\n",
    "print(thresholds['ang'].keys())\n",
    "print(thresholds['ang']['ADn'].keys())\n",
    "print(len(thresholds['ang']['Pos']['f0'])), \"splits\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "- Let's plot the tuning curves and the splits.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xBg7B27kVVQ07HFNglgBM2fN27QBV6/2TI2fgMLT9EGrTQpQ9SwCm7Hk7NoM4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\niLIEYIwxEWUJwBhjIsoSgDHGRNT/B0FTUmlh6KghAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0dffdcc510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e = 'ADn'\n",
    "i = 0\n",
    "plot(tuningc[e][0], tuningc[e][1], color = colors_[i], linewidth = 1.5)\n",
    "xlabel('Head-direction (rad)', labelpad = 0.0)\n",
    "ylabel('Firing rate (Hz)', labelpad = 2.1)\n",
    "locator_params(axis='y', nbins = 3)\n",
    "locator_params(axis='x', nbins = 4)\n",
    "title(title_[i], fontsize = 12)\n",
    "xlim(0, 2*np.pi)\n",
    "\n",
    "[axvline(l, alpha = 1, color = 'grey', linewidth = 0.5) for l in np.unique(thresholds['ang'][e]['f0'])]\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rjDEsX5fD/IUrWJW9g8AAYdqEocw+ZaKzjTegY23uyl7xMZH0iI9m5XoNeW/X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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0dffbaee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure()\n",
    "e = 'Pos'\n",
    "i = 1\n",
    "plot(tuningc[e][0], tuningc[e][1], color = colors_[i], linewidth = 1.5)\n",
    "xlabel('Head-direction (rad)', labelpad = 0.0)\n",
    "ylabel('Firing rate (Hz)', labelpad = 2.1)\n",
    "locator_params(axis='y', nbins = 3)\n",
    "locator_params(axis='x', nbins = 4)\n",
    "title(title_[i], fontsize = 12)\n",
    "xlim(0,2*np.pi)\n",
    "\n",
    "[axvline(l, alpha = 1, color = 'grey', linewidth = 0.5) for l in np.unique(thresholds['ang'][e]['f0'])]\n",
    "\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 5. Fisher Information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "adn_fisher = fisher_information(tuningc['ADn'][0], tuningc['ADn'][1])\n",
    "pos_fisher = fisher_information(tuningc['Pos'][0], tuningc['Pos'][1])\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "- Let's plot the Fisher information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PSvk94I/A20KIwwHVDVoRc0YTAIY+C6DLQgtA+n14d27CPu8wS3zvziXHAuD5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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0dffbbb6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e = 'ADn'\n",
    "i = 0\n",
    "plot(tuningc[e][0], tuningc[e][1], color = colors_[i], linewidth = 1.5)\n",
    "xlabel('Head-direction (rad)', labelpad = 0.0)\n",
    "ylabel('Firing rate (Hz)', labelpad = 2.1)\n",
    "locator_params(axis='y', nbins = 3)\n",
    "locator_params(axis='x', nbins = 4)\n",
    "title(title_[i], fontsize = 12)\n",
    "\n",
    "\n",
    "[axvline(l, alpha = 1, color = 'grey', linewidth = 0.5) for l in np.unique(thresholds['ang'][e]['f0'])]\n",
    "\n",
    "twinx()\n",
    "plot(adn_fisher[0], adn_fisher[1], '-', color = '#25393C', label = 'Fisher \\n Information', linewidth = 2.0)\n",
    "yticks([])\n",
    "xlim(0, 2*np.pi)\n",
    "legend(loc = 'best')\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tTh6grdMSztBHDf6G4M/0Fvm4mEiyM5Ko6qe9gS35WlFd5R0DFR7HFZEXAFLK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\nkIm3sYWJ4uNi3XbNcWOSOXv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7nj1et9lbdPighBK816TMH3a72rB58v1VFGVnJPGH+6/h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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0dffbcbb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure()\n",
    "e = 'Pos'\n",
    "i = 1\n",
    "plot(tuningc[e][0], tuningc[e][1], color = colors_[i], linewidth = 1.5)\n",
    "xlabel('Head-direction (rad)', labelpad = 0.0)\n",
    "ylabel('Firing rate (Hz)', labelpad = 2.1)\n",
    "locator_params(axis='y', nbins = 3)\n",
    "locator_params(axis='x', nbins = 4)\n",
    "title(title_[i], fontsize = 12)\n",
    "xlim(0,2*np.pi)\n",
    "\n",
    "[axvline(l, alpha = 1, color = 'grey', linewidth = 0.5) for l in np.unique(thresholds['ang'][e]['f0'])]\n",
    "\n",
    "twinx()\n",
    "plot(pos_fisher[0], pos_fisher[1], '-', color = '#25393C', label = 'Fisher \\n Information', linewidth = 2.0)\n",
    "yticks([])\n",
    "xlim(0, 2*np.pi)\n",
    "legend(loc = 'best')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Et voila!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## III. Miscellaneous\n",
    "\n",
    "### 1. Accessing the gain\n",
    "\n",
    "By default, XGB returns the average gain over one feature for all the trees. By multiplying by the number of splits for each feature, you get the total gain.\n",
    "\n",
    "- Let's define a new combination with head-direction and x,y positions and all the neurons from each group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'ADn': {'features': ['ang', 'x', 'y'], 'targets': ['ADn.0', 'ADn.1', 'ADn.2', 'ADn.3', 'ADn.4', 'ADn.5', 'ADn.6', 'ADn.7', 'ADn.8', 'ADn.9', 'ADn.10', 'ADn.11', 'ADn.12', 'ADn.13', 'ADn.14', 'ADn.15', 'ADn.16']}, 'Pos': {'features': ['ang', 'x', 'y'], 'targets': ['Pos.0', 'Pos.1', 'Pos.2', 'Pos.3', 'Pos.4', 'Pos.5', 'Pos.6', 'Pos.7', 'Pos.8', 'Pos.9', 'Pos.10', 'Pos.11', 'Pos.12', 'Pos.13', 'Pos.14']}}\n"
     ]
    }
   ],
   "source": [
    "combination = {\n",
    "    'ADn':    {\n",
    "            'features'  :   ['ang', 'x', 'y'],\n",
    "            'targets'   :   [i for i in list(data) if i.split(\".\")[0] == 'ADn']\n",
    "        },\n",
    "    'Pos':    {\n",
    "            'features'  :   ['ang', 'x', 'y'],\n",
    "            'targets'   :   [i for i in list(data) if i.split(\".\")[0] == 'Pos']\n",
    "        },  \n",
    "}\n",
    "print combination"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "- Let's learn the booster for each combination."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADn ADn.0\n",
      "ADn ADn.1\n",
      "ADn ADn.2\n",
      "ADn ADn.3\n",
      "ADn ADn.4\n",
      "ADn ADn.5\n",
      "ADn ADn.6\n",
      "ADn ADn.7\n",
      "ADn ADn.8\n",
      "ADn ADn.9\n",
      "ADn ADn.10\n",
      "ADn ADn.11\n",
      "ADn ADn.12\n",
      "ADn ADn.13\n",
      "ADn ADn.14\n",
      "ADn ADn.15\n",
      "ADn ADn.16\n",
      "Pos Pos.0\n",
      "Pos Pos.1\n",
      "Pos Pos.2\n",
      "Pos Pos.3\n",
      "Pos Pos.4\n",
      "Pos Pos.5\n",
      "Pos Pos.6\n",
      "Pos Pos.7\n",
      "Pos Pos.8\n",
      "Pos Pos.9\n",
      "Pos Pos.10\n",
      "Pos Pos.11\n",
      "Pos Pos.12\n",
      "Pos Pos.13\n",
      "Pos Pos.14\n"
     ]
    }
   ],
   "source": [
    "params = {'objective': \"count:poisson\", #for poisson output\n",
    "    'eval_metric': \"poisson-nloglik\", #loglikelihood loss\n",
    "    'seed': 2925, #for reproducibility\n",
    "    'silent': 1,\n",
    "    'learning_rate': 0.1,\n",
    "    'min_child_weight': 2, \n",
    "    'n_estimators': 30,\n",
    "    # 'subsample': 0.5, \n",
    "    'max_depth': 5, \n",
    "    'gamma': 0.5}        \n",
    "\n",
    "num_round = 30\n",
    "bsts = {}\n",
    "for k in combination.keys():\n",
    "    features = combination[k]['features']\n",
    "    targets = combination[k]['targets'] \n",
    "    X = data[features].values\n",
    "    Yall = data[targets].values \n",
    "    bsts[k] = {}\n",
    "    for i in xrange(Yall.shape[1]):\n",
    "        print k, targets[i]\n",
    "        dtrain = xgb.DMatrix(X, label=Yall[:,i])\n",
    "        bst = xgb.train(params, dtrain, num_round)\n",
    "        bsts[k][targets[i]] = bst\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "- Let's retrieve the gain from the booster and plot for each features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IL+/j+4dGxPciYk1E/GtEHF3+UmtP64qV1S5BwMqVK6pdQt3zGBy4XkM8IgYAfwOcDZwE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\noFHj/8wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0dff9fa9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gain = {}\n",
    "for i in ['ADn', 'Pos']:\n",
    "    gain[i] = {}\n",
    "    for j in bsts[i].iterkeys(): # for each neuron\n",
    "        gain[i][j] = bsts[i][j].get_score(importance_type = 'gain')\n",
    "\n",
    "\n",
    "labels = ['ADn', 'PoSub']\n",
    "x = np.arange(3, dtype = float)\n",
    "for g, i in zip(gain.iterkeys(), xrange(2)):\n",
    "    tmp = []\n",
    "    for k in gain[g].iterkeys():\n",
    "        tmp.append([])\n",
    "        for f in ['f0', 'f1', 'f2']:\n",
    "            if f in gain[g][k].keys():\n",
    "                tmp[-1].append(gain[g][k][f])\n",
    "            else:\n",
    "                tmp[-1].append(0.0)                \n",
    "    tmp = np.array(tmp)\n",
    "    tmp = tmp/np.vstack(tmp.sum(1))\n",
    "    mean = tmp.mean(0)\n",
    "    sem = np.std(tmp, 0)/np.sqrt(np.size(tmp))\n",
    "    bar(x, mean, 0.4, yerr = sem, align='center',\n",
    "        ecolor='k', alpha=.9, color=colors_[i], ec='w', label = labels[i], capsize = 1)\n",
    "    plot(x, mean, 'o', alpha = 1, color = 'black', markersize = 2)\n",
    "    x += 0.41\n",
    "#     ylim(0,18)\n",
    "    xlim(-0.5, 2.95)\n",
    "\n",
    "xticks(np.arange(3)+0.205, ('Angle','x pos', 'y pos'), rotation = 45, ha='right')\n",
    "locator_params(axis='y', nbins = 3)\n",
    "legend()\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "- Bonus : a function to extract the split order :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def extract_tree_order(trees, n_feat):\n",
    "    # return array (len(trees), n_feat) \n",
    "    n = len(trees.get_dump())\n",
    "    propor = np.zeros((n,n_feat))       \n",
    "    for t in xrange(n):\n",
    "        gv = xgb.to_graphviz(trees, num_trees=t)\n",
    "        body = gv.body      \n",
    "        for i in xrange(len(body)):\n",
    "            for l in body[i].split('\"'):\n",
    "                if 'f' in l and '<' in l:\n",
    "                    feat = l.split(\"<\")[0]\n",
    "                    propor[t,int(feat[1:])] += 1\n",
    "    \n",
    "    propor = np.cumsum(propor, 0)           \n",
    "    propor = propor/np.vstack(np.sum(propor, 1))\n",
    "    return propor"
   ]
  }
 ],
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