mulearn-documentation.ipynb

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    "# $\\mu$-learn\n",
    "\n",
    "$\\mu$-learn (read mooh-learn) is a python package implementing the metodology for data-driven induction of fuzzy sets described in\n",
    "\n",
    "- D. Malchiodi and W. Pedrycz, Learning Membership Functions for Fuzzy Sets through Modified Support Vector Clustering, in F. Masulli, G. Pasi e R. Yager (Eds.), Fuzzy Logic and Applications. 10th International Workshop, WILF 2013, Genoa, Italy, November 19–22, 2013. Proceedings., Vol. 8256, Springer International Publishing, Switzerland, Lecture Notes on Artificial Intelligence, 2013;\n",
    "- D. Malchiodi and A. G. B. Tettamanzi, Predicting the Possibilistic Score of OWL Axioms through Modified Support Vector Clustering, in H. Haddad, R. L. Wainwright e R. Chbeir (Eds.), SAC'18: Proceedings of the 33rd Annual ACM Symposium on Applied Computing, ACM (ISBN 9781450351911), 1984–1991, 2018.\n"
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    "## Install\n",
    "\n",
    "The package can easily be installed:\n",
    "\n",
    "- via `pip`, by running `pip install mulearn` in a terminal;\n",
    "- through `conda`, by running `conda install -c dariomalchiodi mulearn`;\n",
    "- cloning the source repo at https://github.com/dariomalchiodi/mulearn.\n",
    "\n",
    "APIs are described at https://mulearn.readthedocs.io/.\n",
    "\n",
    "\n",
    "## How to use\n",
    "Consider the Iris dataset, whose 150 observations describe each a flower of the Iris species in terms of its sepal and petal width and length, as well as of its class (Setosa, Versicolor, and Virginica), as exemplified here below. We will use the class as _labels_ to be predicted, and the remaining four attributes as the description of each object in the dataset. Referring to the values of the description of an object as a _pattern_, our aim will be that of predicting the class on the basis of the description."
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sepal length</th>\n",
       "      <th>Sepal width</th>\n",
       "      <th>Petal length</th>\n",
       "      <th>Petal width</th>\n",
       "      <th>Class</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
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       "   Sepal length  Sepal width  Petal length  Petal width   Class\n",
       "0           5.1          3.5           1.4          0.2  Setosa\n",
       "1           4.9          3.0           1.4          0.2  Setosa\n",
       "2           4.7          3.2           1.3          0.2  Setosa\n",
       "3           4.6          3.1           1.5          0.2  Setosa\n",
       "4           5.0          3.6           1.4          0.2  Setosa"
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   "source": [
    "import sklearn.datasets as ds\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "iris_X, iris_y = ds.load_iris(return_X_y=True)\n",
    "labels = (\"Setosa\", \"Versicolor\", \"Virginica\")\n",
    "\n",
    "df = pd.DataFrame(iris_X, columns=[\"Sepal length\", \"Sepal width\",\n",
    "                                   \"Petal length\", \"Petal width\"])\n",
    "df['Class'] = iris_y\n",
    "df['Class'] = df['Class'].map(lambda c: labels[c])\n",
    "df.head()"
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    "For sake of visualization, let's extract the first two principal components in the descriptions, so that the patterns we will focus on will be bidimensional vectors, save them in `iris_X_2d`, and generate the corresponding scatter plot, coloring bullets in function of the label of the corresponding pattern. We implement a `gr_dataset` method which computes and shows this plot, in order to regenerate it easily in the subsequent cells."
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca_2d = PCA(n_components=2)\n",
    "iris_X_2d = pca_2d.fit_transform(iris_X)\n",
    "\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "def gr_dataset(fig): \n",
    "    for lab, col in enumerate((\"red\", \"green\", \"blue\")):\n",
    "        fig.add_trace(go.Scatter(x=iris_X_2d[iris_y==lab, 0],\n",
    "                                 y=iris_X_2d[iris_y==lab, 1],\n",
    "                                 mode=\"markers\",\n",
    "                                 marker_color=col,\n",
    "                                 name=labels[lab]))\n",
    "\n",
    "fig = go.Figure()\n",
    "gr_dataset(fig)\n",
    "f = go.FigureWidget(fig)\n",
    "f.show(\"svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's focus on one of the three classes in the dataset, namely Versicolor, and use the mulearn package in order to infer the corresponding fuzzy set. The available class labels refer to a three-classes setting, where 0, 1, and 2 correspond to Setosa, Versicolor, and Virginica, respectively. Therefore, converting each 2 in these labels to 0 has the effect of generating new labels which we will store in `iris_versicolor`, now describing the crisp membership to the Versicolor set. We will exploit these labels in order to learn the membership function to the corresponding fuzzy set $V$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris_versicolor = iris_y.copy()\n",
    "iris_versicolor[iris_versicolor==2] = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The inference of the membership function $\\mu_V$ is done using the main class of the package, called `FuzzyInductor`, starting from the patterns in `iris_X_2d` and the corresponding labels in `iris_versicolor`. This class exposes an interface analogous to that of estimators in Scikit-Learn, thus learning happens through invokation of the `fit` method on an insance of the class, specifying patterns and labels as arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FuzzyInductor(c=1, k=GaussianKernel(), f=ExponentialFuzzifier(), solver=GurobiSolver())"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mulearn import FuzzyInductor\n",
    "\n",
    "fi = FuzzyInductor()\n",
    "fi.fit(iris_X_2d, iris_versicolor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After `fit` has been invoked successfully, the `predict` method of the class is available for computing predictions for the membersip function $\\mu_V$. For instance, in the origin of the considered space we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.76792676])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fi.predict([(0, 0)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which means that $\\mu_V((0, 0))$ is predicted as around 0.7679. Note that even if we wanted to predict the label for a sole pattern, `predict` has been called specifying as input a list containing such pattern, and it has returned an array contaning its membership value. In general, the argument to `predict` can be a list, a tuple, or a numpy array, containing in all cases patterns (described themselves as lists, tuples, or arrays) having a same length. Its return value will be an array of that same length, gathering the inferred membership values.\n",
    "\n",
    "The following cell defines a function `gr_membership_contour`, taking as input the membership function and producing its contour plot, superposed with the scatter plot of the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gr_membership_contour(estimated_membership):\n",
    "    fig = go.Figure()\n",
    "    gr_dataset(fig)\n",
    "    x = np.linspace(-4, 4, 30)\n",
    "    y = np.linspace(-1.5, 1.5, 30)\n",
    "    X, Y = np.meshgrid(x, y)\n",
    "    zs = estimated_membership(np.array((np.ravel(X), np.ravel(Y))).T)\n",
    "    Z = zs.reshape(X.shape)\n",
    "\n",
    "    fig.add_trace(go.Contour(x=x, y=y, z=Z,\n",
    "                             colorscale=[[0, 'rgba(0, 0.1, 0, 0.0)'],\n",
    "                                         [1, 'rgba(0, 0.9, 0, 0.5)']],\n",
    "                             line_smoothing=0.85,\n",
    "                             contours={\"start\": 0, \"end\": 1, \"size\": .2,\n",
    "                                       \"showlabels\": True,\n",
    "                                       \"labelfont\": {\"size\": 12,\n",
    "                                                     \"color\": \"white\"}\n",
    "                                       },\n",
    "                             showscale=False))\n",
    "    go.FigureWidget(fig).show(\"svg\")\n",
    "\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `predict` method can also be used in order to obtain a binary classification, that is computing membership to the crisp set corresponding to $V$. This is done performing an $\\alpha$-cut on the membership function, and the value of $\\alpha$ should be specified through the `alpha` parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fi.predict([(0, 0), (3, 0)], alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hyper-parameters of the learning algorithm, that according to the interface required by Scikit-learn should be specified during object creation, are described here below.\n",
    "\n",
    "### C\n",
    "The argument `c` allows to wheigth the trade-off between the errors in the approximation of the provided dataset and the generalization ability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fi = FuzzyInductor(c=.1)\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fi = FuzzyInductor(c=100)\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fuzzifier\n",
    "\n",
    "This hyper-parameter, regulating how the learnt membership function decreases from 1 to 0, is specified through the `fuzzifier` argument. The corresponding value should be set to an object of one of the classes in the `mulearn.fuzzifier` module. Without being too specific on the inner working of the learning algorithm, the latter finds a mapping $\\Phi$ of the patterns onto a so-called _feature space_ implicitly defined by the chosen kernel (described in the next section). The images of patterns via this mapping have a distance w.r.t. a special point (called _center_) which can be related to to their membership value. In particular, the learning algorithm builds a function $R^2$ associating any possible pattern to the squared distance of its image through $\\Phi$ and the above mentioned center, as well as the value for this distance, called _radius_, which corresponds to a predicted membership of 0.5.\n",
    "\n",
    "The simplest fuzzifier only assumes `0` and `1` as values, thus it corresponds to a crisp set. Basically, it is found by thresholding the values of $R$ using the inferred radius. It is specified via the `mulearn.fuzzifier.CrispFuzzifier` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mulearn.fuzzifier import CrispFuzzifier\n",
    "\n",
    "fi = FuzzyInductor(fuzzifier=CrispFuzzifier())\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.decision_function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the obtained figure can be misleading, because we should obtain only one contour dividing positive and negative predictions. To avoid this behaviour, due to the fact that the plotted function increases instantaneously from 0 to 1, we can slightly modify the `gr_membership_contour` function, adding a parameter to deal with this special configuration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gr_membership_contour(estimated_membership, crisp=False):\n",
    "    fig = go.Figure()\n",
    "    gr_dataset(fig)\n",
    "    x = np.linspace(-3.5, 3.5, 30)\n",
    "    y = np.linspace(-1.5, 1.5, 30)\n",
    "    X, Y = np.meshgrid(x, y)\n",
    "    zs = estimated_membership(np.array((np.ravel(X), np.ravel(Y))).T)\n",
    "    Z = zs.reshape(X.shape)\n",
    "    \n",
    "    contour_desc = {\"start\": 0., \"end\": 1., \"size\": .2,\n",
    "                    \"showlabels\": True,\n",
    "                    \"labelfont\": {\"size\": 12, \"color\": \"white\"}}\n",
    "    if crisp:\n",
    "        contour_desc[\"start\"] = .999\n",
    "        contour_desc[\"end\"] = 1.1\n",
    "        del contour_desc[\"showlabels\"]\n",
    "        del contour_desc[\"labelfont\"]\n",
    "\n",
    "    fig.add_trace(go.Contour(x=x, y=y, z=Z,\n",
    "                             colorscale=[[0, 'rgba(0, 0.1, 0, 0.0)'],\n",
    "                                         [1, 'rgba(0, 0.9, 0, 0.5)']],\n",
    "                             line_smoothing=0.85,\n",
    "                             contours=contour_desc,\n",
    "                             showscale=False))\n",
    "    go.FigureWidget(fig).show(\"svg\")\n",
    "    \n",
    "gr_membership_contour(fi.predict, crisp=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The induction of a fuzzy set is typically done in order to deal with membership degrees not necessarily equal to `0` and `1`. One of the simplest non-Boolean fuzzifier linearly decreases from 1 to 0. It is specified via the `mulearn.fuzzifier.LinearFuzzifier` class, which in its simplest form does not require specific options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mulearn.fuzzifier import LinearFuzzifier\n",
    "\n",
    "fi = FuzzyInductor(fuzzifier=LinearFuzzifier())\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the above mentioned linear decrease is not usually done in feature space, rather than in the space of patterns. This is why the shown contours have an asymmetrical shape.\n",
    "\n",
    "When the no arguments are provided to the fuzzifier constructor, the former is typically built using the inferred $R^2$ and radius. Alternatively, it is possible to tune it according to the data provided to the learning algorithm, by specifying the `profile='infer'` argument to the constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fi = FuzzyInductor(fuzzifier=LinearFuzzifier(profile='infer'))\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `ExponentialFuzzifier` class implements a fuzzifier characterized by an exponential decay of the membership in feature space. The rate of this decay can be set in terms of the radius or fitting the data, precisely using the same syntax of `LinearFuzzifier`. Moreover, the decay can be manually set jointly specifying the `profile` and `alpha` arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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stroke-width: 0px; fill: rgb(0, 0, 255); fill-opacity: 1;\"/></g><g class=\"text\"/></g></g></g><g class=\"overplot\"/><path class=\"xlines-above crisp\" d=\"M0,0\" style=\"fill: none;\"/><path class=\"ylines-above crisp\" d=\"M0,0\" style=\"fill: none;\"/><g class=\"overlines-above\"/><g class=\"xaxislayer-above\"><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"383\" transform=\"translate(184.86,0)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(42, 63, 95); fill-opacity: 1; white-space: pre;\">−2</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"383\" transform=\"translate(309.65999999999997,0)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(42, 63, 95); fill-opacity: 1; white-space: pre;\">0</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"383\" transform=\"translate(434.46,0)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; 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fill-opacity: 1;\"/></g><g class=\"g-gtitle\"/><g class=\"g-xtitle\"/><g class=\"g-ytitle\"/></g></svg>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mulearn.fuzzifier import ExponentialFuzzifier\n",
    "\n",
    "fi = FuzzyInductor(fuzzifier=ExponentialFuzzifier(profile='alpha', alpha=0.1))\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, `QuantileConstantPiecewiseFuzzifier` and `QuantileLinearPiecewiseFuzzifier` implement two fuzzifiers whose decay is automatically inferred using as reference points the quantiles of the squared distances of (images of) points w.r.t. the inferred center in feature space. There reference points are used, respectively, to build a piecewise constant and a piecewise membership function in feature space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mulearn.fuzzifier import QuantileConstantPiecewiseFuzzifier\n",
    "\n",
    "qp = QuantileConstantPiecewiseFuzzifier()\n",
    "fi = FuzzyInductor(fuzzifier=qp)\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mulearn.fuzzifier import QuantileLinearPiecewiseFuzzifier\n",
    "\n",
    "fi = FuzzyInductor(fuzzifier=QuantileLinearPiecewiseFuzzifier())\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once used in order to fit a `FuzzyInductor` object, a fuzzifier can be queried for its so-called _profile_, which is a mapping from the squared distance in feature space to the membership value. This is done thrpugh invocation of its `get_profile` method, specifying as arguments the patterns used in order to learn the membership function. The method returns a triple containing, respectively, the squared distances of all images of the provided patterns w.r.t. the learnt center, an array of synthesized values for such distance, and the corresponding array of memberships. The following cell uses this information in order to plot the inferred profile $\\hat\\mu$, together with the actual memberships of the provided patterns (labeled with $\\mu$ in the picture)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r, r_synth, mu_synth = qp.get_profile(iris_X_2d)\n",
    "\n",
    "fig = go.Figure(data=go.Scatter(x=r_synth, y=mu_synth, name=r'$\\hat\\mu$'))\n",
    "fig.add_trace(go.Scatter(x=r, y=iris_versicolor, mode='markers', name=r'$\\mu$'))\n",
    "fig.show(\"svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we had to save the used fuzzifier in a variable, rather than creating the corresponding object on the fly when instantiating `FuzzyInductor`. This allowed us to subsequently invoke `get_profile`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel\n",
    "\n",
    "The so-called _kernel_ function describes how to compute the inner product of two images of patterns in feature space. Kernels are implemented in the `mulearn.kernel` package: when not explicitly passed to `FuzzyInductor`, a _Gaussian kernel_ with predefined parameter value is used. It is however possible to change this value by explicitly instantiating the `GaussianKernel` class. The closest to zero is the value for the parameter, the bigger flexibility will be used in order to fit the membership function to the provided dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mulearn.kernel import GaussianKernel\n",
    "\n",
    "fi = FuzzyInductor(k=GaussianKernel(0.25))\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The module contains also other kernel implementation: each implicitly defines the feature space. For instance, `LinearKernel` corresponds to having a feature space coinciding with the original pattern space. When used in conjunction with a linear fuzzifier, the contour plot of the inferred membership exhibits a linear decrease."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mulearn.kernel import LinearKernel\n",
    "\n",
    "fi = FuzzyInductor(k=LinearKernel(), fuzzifier=LinearFuzzifier())\n",
    "fi.fit(iris_X_2d, iris_versicolor)\n",
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the peculiar form of the outmost contour only apparently contradicts the linearity previously stated: this is due to the fact that this contour corresponds to a zone of the pattern space in which the membership rapidly decreases from 0.2 to 0, thus showing the 0.1 contour becomes difficult.\n",
    "\n",
    "All kernels implemented in the `mulearn.kernel` are described here below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear kernel\n",
    "\n",
    "Kernel corresponding to the dot product in the original space. This kernel is unique, thus it is instantiated invoking the constructor of the `LinearKernel` class without arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mulearn.kernel import LinearKernel\n",
    "k = LinearKernel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The kernel is computed invoking its `compute` method and specifying as arguments two tuples, lists, or arrays of the same length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k.compute((1, 0, 2), (-1, 2, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3200000000000003"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k.compute([1.2, -0.4, -2], [4, 1.2, .5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different numeric iterables can intertwine as arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3200000000000003"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k.compute((1.2, -0.4, -2), [4, 1.2, .5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Specification of iterables having unequal length causes a `ValueError` to be thrown."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial kernel\n",
    "\n",
    "Kernel corresponding to a dot product after mapping points on a higher-dimensional space through a polynomial (affine) transformation. A hyperplane in this space corresponds to polynomial surfaces in the original space.\n",
    "Implemented via the `PolynomialKernel` class, instantiated in function of the degree of the corresponding transformation. The kernel is computed exactly as with `LinearKernel`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mulearn.kernel import PolynomialKernel\n",
    "\n",
    "k = PolynomialKernel(2)\n",
    "k.compute((1, 0, 2), (-1, 2, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Homogeneous polynomial kernel\n",
    "\n",
    "Kernel corresponding to a dot product after mapping points on a higher-dimensional space through a polynomial (homogeneous) transformation. A hyperplane in this space corresponds to polynomial surfaces in the original space.  Implemented via the `HomogeneousPolynomialKernel` class, instantiated in function of the degree of the corresponding transformation. The kernel is computed exactly as with `LinearKernel`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "81.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mulearn.kernel import HomogeneousPolynomialKernel\n",
    "\n",
    "k = HomogeneousPolynomialKernel(2)\n",
    "k.compute((1, 0, 2), (-1, 2, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian kernel\n",
    "\n",
    "Kernel corresponding to a dot product after mapping points on an infinite-dimensional space. A hyperplane in this space corresponds to the superposition of gaussian densities in the original space.  Implemented via the `GaussianKernel class`, instantiated in function of the standard deviation of the above mentioned densities. The kernel is computed exactly as with `LinearKernel`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11943296826671962"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mulearn.kernel import GaussianKernel\n",
    "\n",
    "k = GaussianKernel(2)\n",
    "k.compute((1, 0, 2), (-1, 2, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hyperbolic tangent kernel\n",
    "\n",
    "Pseudo-kernel corresponding to a dot product based on hyperbolic tangent. Implemented via the `HyprebolicKernel` class, instantiated in function of the scale and offset parameters of the transformation given as argument to the hyperbolic tangent function. The kernel is computed exactly as with `LinearKernel`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999996"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mulearn.kernel import HyperbolicKernel\n",
    "\n",
    "k = HyperbolicKernel(2)\n",
    "k.compute((1, 0, 2), (-1, 2, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Precomputed kernel\n",
    "\n",
    "Custom kernel whose entries are precomputed and stored in a matrix. Implemented via the `PrecomputedKernel` class, instantiated in function of the matrix containing the kernel computations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mulearn.kernel import PrecomputedKernel\n",
    "k = PrecomputedKernel(((9, 1, 4, 4),\n",
    "                       (1, 1, 1, 1), \n",
    "                       (4, 1, 4, 1),\n",
    "                       (4, 1, 1, 4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Specification of non-square matrices as arguments to the constructor causes a `ValueError` to be thrown.\n",
    "\n",
    "The kernel is computed given the indices of the corresponding objects. Note that each index should be enclosed within an iterable in order to be compatible with sklearn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k.compute([1], [1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solvers\n",
    "\n",
    "The `mulearn.optimization` module contains the implementations of solvers used in order to find the solution of a costrained optimization problem. The default solver relies on the gurobi library, which should be already installed and activated in the used system. This library is available for free for academic use. The class `GurobiSolver` implements the logic that solves the above mentioned problem using gurobi.\n",
    "\n",
    "A second solver, based on TensorFlow, is available through the `TensorFlowSolver` class, which can be instantiated in order to provide a value for the `solver` parameter of the `FuzzyInductor` constructor. In this way, the solver based on TensorFlow can be used in all situations in which gurobi is not available, or when the processed dataset is too big to be efficiently handled by gurobi. Note, however, that the implementation of this solver is currently experimental, and might lead to suboptimal solutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=0, dual=-8632.117, prim=-293.435, gap=-36.160110\n",
      "i=10, dual=-12163.816, prim=9085.104, gap=-20663.523438\n",
      "i=20, dual=-6967.269, prim=1021.619, gap=-150.532715\n",
      "i=30, dual=-3221.032, prim=445.536, gap=919.796875\n",
      "i=40, dual=-929.308, prim=438.175, gap=-260.587891\n",
      "i=50, dual=-1681.285, prim=1065.885, gap=-2544.867188\n",
      "i=60, dual=-1058.858, prim=-15.577, gap=799.515625\n",
      "i=70, dual=-794.926, prim=99.331, gap=357.976562\n",
      "i=80, dual=-678.652, prim=210.998, gap=-1.253464\n",
      "i=90, dual=-865.100, prim=636.530, gap=-1313.429688\n",
      "i=100, dual=-703.574, prim=589.960, gap=-1165.632812\n",
      "i=110, dual=-605.386, prim=378.520, gap=-563.523438\n",
      "i=120, dual=-606.433, prim=367.418, gap=-532.941406\n"
     ]
    }
   ],
   "source": [
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "from tensorflow.keras.optimizers import Adam\n",
    "from mulearn.optimization import TensorFlowSolver\n",
    "\n",
    "try:\n",
    "    solver=TensorFlowSolver(optimizer=Adam(learning_rate=0.1))\n",
    "\n",
    "    fi = FuzzyInductor(solver=solver, k=GaussianKernel(0.25))\n",
    "    fi.fit(iris_X_2d, iris_versicolor)\n",
    "    gr_membership_contour(fi.predict)\n",
    "except (ModuleNotFoundError, ValueError):\n",
    "    print('Tensorflow not available')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "\nFor some reason plotly.py was unable to communicate with the\nlocal orca server process, even though the server process seems to be running.\n\nPlease review the process and connection information below:\n\norca status\n-----------\n    state: running\n    executable: /home/malchiodi/share/anaconda3/envs/mulearn/bin/orca\n    version: 1.3.1\n    port: 37355\n    pid: 105533\n    command: ['/home/malchiodi/share/anaconda3/envs/mulearn/bin/orca', 'serve', '-p', '37355', '--plotly', '/home/malchiodi/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/package_data/plotly.min.js', '--graph-only', '--mathjax', 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js']\n\n\n",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mConnectionRefusedError\u001b[0m                    Traceback (most recent call last)",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/connection.py\u001b[0m in \u001b[0;36m_new_conn\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    174\u001b[0m             conn = connection.create_connection(\n\u001b[0;32m--> 175\u001b[0;31m                 \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_dns_host\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mport\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimeout\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mextra_kw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    176\u001b[0m             )\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/util/connection.py\u001b[0m in \u001b[0;36mcreate_connection\u001b[0;34m(address, timeout, source_address, socket_options)\u001b[0m\n\u001b[1;32m     94\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0merr\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 95\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0merr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     96\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/util/connection.py\u001b[0m in \u001b[0;36mcreate_connection\u001b[0;34m(address, timeout, source_address, socket_options)\u001b[0m\n\u001b[1;32m     84\u001b[0m                 \u001b[0msock\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbind\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msource_address\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 85\u001b[0;31m             \u001b[0msock\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconnect\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msa\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     86\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0msock\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mConnectionRefusedError\u001b[0m: [Errno 111] Connection refused",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mNewConnectionError\u001b[0m                        Traceback (most recent call last)",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/connectionpool.py\u001b[0m in \u001b[0;36murlopen\u001b[0;34m(self, method, url, body, headers, retries, redirect, assert_same_host, timeout, pool_timeout, release_conn, chunked, body_pos, **response_kw)\u001b[0m\n\u001b[1;32m    709\u001b[0m                 \u001b[0mheaders\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mheaders\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 710\u001b[0;31m                 \u001b[0mchunked\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mchunked\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    711\u001b[0m             )\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/connectionpool.py\u001b[0m in \u001b[0;36m_make_request\u001b[0;34m(self, conn, method, url, timeout, chunked, **httplib_request_kw)\u001b[0m\n\u001b[1;32m    397\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 398\u001b[0;31m                 \u001b[0mconn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrequest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mhttplib_request_kw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    399\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/connection.py\u001b[0m in \u001b[0;36mrequest\u001b[0;34m(self, method, url, body, headers)\u001b[0m\n\u001b[1;32m    238\u001b[0m             \u001b[0mheaders\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"User-Agent\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_get_default_user_agent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 239\u001b[0;31m         \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mHTTPConnection\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrequest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbody\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbody\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mheaders\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mheaders\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    240\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/http/client.py\u001b[0m in \u001b[0;36mrequest\u001b[0;34m(self, method, url, body, headers, encode_chunked)\u001b[0m\n\u001b[1;32m   1280\u001b[0m         \u001b[0;34m\"\"\"Send a complete request to the server.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1281\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_send_request\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbody\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mheaders\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencode_chunked\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1282\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/http/client.py\u001b[0m in \u001b[0;36m_send_request\u001b[0;34m(self, method, url, body, headers, encode_chunked)\u001b[0m\n\u001b[1;32m   1326\u001b[0m             \u001b[0mbody\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_encode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbody\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'body'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1327\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mendheaders\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbody\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencode_chunked\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mencode_chunked\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1328\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/http/client.py\u001b[0m in \u001b[0;36mendheaders\u001b[0;34m(self, message_body, encode_chunked)\u001b[0m\n\u001b[1;32m   1275\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mCannotSendHeader\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1276\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_send_output\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmessage_body\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencode_chunked\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mencode_chunked\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1277\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/http/client.py\u001b[0m in \u001b[0;36m_send_output\u001b[0;34m(self, message_body, encode_chunked)\u001b[0m\n\u001b[1;32m   1035\u001b[0m         \u001b[0;32mdel\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_buffer\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1036\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1037\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/http/client.py\u001b[0m in \u001b[0;36msend\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m    975\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mauto_open\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 976\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconnect\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    977\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/connection.py\u001b[0m in \u001b[0;36mconnect\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    204\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mconnect\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 205\u001b[0;31m         \u001b[0mconn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_new_conn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    206\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_prepare_conn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mconn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/connection.py\u001b[0m in \u001b[0;36m_new_conn\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    186\u001b[0m             raise NewConnectionError(\n\u001b[0;32m--> 187\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Failed to establish a new connection: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    188\u001b[0m             )\n",
      "\u001b[0;31mNewConnectionError\u001b[0m: <urllib3.connection.HTTPConnection object at 0x7f5a5965c4d0>: Failed to establish a new connection: [Errno 111] Connection refused",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mMaxRetryError\u001b[0m                             Traceback (most recent call last)",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/requests/adapters.py\u001b[0m in \u001b[0;36msend\u001b[0;34m(self, request, stream, timeout, verify, cert, proxies)\u001b[0m\n\u001b[1;32m    449\u001b[0m                     \u001b[0mretries\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax_retries\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 450\u001b[0;31m                     \u001b[0mtimeout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtimeout\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    451\u001b[0m                 )\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/connectionpool.py\u001b[0m in \u001b[0;36murlopen\u001b[0;34m(self, method, url, body, headers, retries, redirect, assert_same_host, timeout, pool_timeout, release_conn, chunked, body_pos, **response_kw)\u001b[0m\n\u001b[1;32m    785\u001b[0m             retries = retries.increment(\n\u001b[0;32m--> 786\u001b[0;31m                 \u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0merror\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_pool\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_stacktrace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexc_info\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    787\u001b[0m             )\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/urllib3/util/retry.py\u001b[0m in \u001b[0;36mincrement\u001b[0;34m(self, method, url, response, error, _pool, _stacktrace)\u001b[0m\n\u001b[1;32m    591\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mnew_retry\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_exhausted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 592\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mMaxRetryError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_pool\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0merror\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mResponseError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcause\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    593\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mMaxRetryError\u001b[0m: HTTPConnectionPool(host='localhost', port=37355): Max retries exceeded with url: / (Caused by NewConnectionError('<urllib3.connection.HTTPConnection object at 0x7f5a5965c4d0>: Failed to establish a new connection: [Errno 111] Connection refused'))",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mConnectionError\u001b[0m                           Traceback (most recent call last)",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/io/_orca.py\u001b[0m in \u001b[0;36mto_image\u001b[0;34m(fig, format, width, height, scale, validate)\u001b[0m\n\u001b[1;32m   1561\u001b[0m         response = request_image_with_retrying(\n\u001b[0;32m-> 1562\u001b[0;31m             \u001b[0mfigure\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfig_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mformat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscale\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscale\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mwidth\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mheight\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mheight\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1563\u001b[0m         )\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/retrying.py\u001b[0m in \u001b[0;36mwrapped_f\u001b[0;34m(*args, **kw)\u001b[0m\n\u001b[1;32m     48\u001b[0m             \u001b[0;32mdef\u001b[0m \u001b[0mwrapped_f\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 49\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mRetrying\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mdargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mdkw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     50\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/retrying.py\u001b[0m in \u001b[0;36mcall\u001b[0;34m(self, fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m    211\u001b[0m                     \u001b[0;31m# get() on an attempt with an exception should cause it to be raised, but raise just in case\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 212\u001b[0;31m                     \u001b[0;32mraise\u001b[0m \u001b[0mattempt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    213\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/retrying.py\u001b[0m in \u001b[0;36mget\u001b[0;34m(self, wrap_exception)\u001b[0m\n\u001b[1;32m    246\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 247\u001b[0;31m                 \u001b[0msix\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreraise\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    248\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/six.py\u001b[0m in \u001b[0;36mreraise\u001b[0;34m(tp, value, tb)\u001b[0m\n\u001b[1;32m    718\u001b[0m                 \u001b[0;32mraise\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 719\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    720\u001b[0m         \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/retrying.py\u001b[0m in \u001b[0;36mcall\u001b[0;34m(self, fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m    199\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 200\u001b[0;31m                 \u001b[0mattempt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mAttempt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mattempt_number\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    201\u001b[0m             \u001b[0;32mexcept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/io/_orca.py\u001b[0m in \u001b[0;36mrequest_image_with_retrying\u001b[0;34m(**kwargs)\u001b[0m\n\u001b[1;32m   1470\u001b[0m     \u001b[0mjson_str\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mjson\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdumps\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrequest_params\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcls\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0m_plotly_utils\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mutils\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mPlotlyJSONEncoder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1471\u001b[0;31m     \u001b[0mresponse\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpost\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mserver_url\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\"/\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mjson_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1472\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/requests/api.py\u001b[0m in \u001b[0;36mpost\u001b[0;34m(url, data, json, **kwargs)\u001b[0m\n\u001b[1;32m    116\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 117\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mrequest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'post'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjson\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mjson\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    118\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/requests/api.py\u001b[0m in \u001b[0;36mrequest\u001b[0;34m(method, url, **kwargs)\u001b[0m\n\u001b[1;32m     60\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0msessions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSession\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0msession\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 61\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0msession\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrequest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     62\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/requests/sessions.py\u001b[0m in \u001b[0;36mrequest\u001b[0;34m(self, method, url, params, data, headers, cookies, files, auth, timeout, allow_redirects, proxies, hooks, stream, verify, cert, json)\u001b[0m\n\u001b[1;32m    528\u001b[0m         \u001b[0msend_kwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msettings\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 529\u001b[0;31m         \u001b[0mresp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0msend_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    530\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/requests/sessions.py\u001b[0m in \u001b[0;36msend\u001b[0;34m(self, request, **kwargs)\u001b[0m\n\u001b[1;32m    644\u001b[0m         \u001b[0;31m# Send the request\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 645\u001b[0;31m         \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0madapter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrequest\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    646\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/requests/adapters.py\u001b[0m in \u001b[0;36msend\u001b[0;34m(self, request, stream, timeout, verify, cert, proxies)\u001b[0m\n\u001b[1;32m    518\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 519\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mConnectionError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrequest\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrequest\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    520\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mConnectionError\u001b[0m: HTTPConnectionPool(host='localhost', port=37355): Max retries exceeded with url: / (Caused by NewConnectionError('<urllib3.connection.HTTPConnection object at 0x7f5a5965c4d0>: Failed to establish a new connection: [Errno 111] Connection refused'))",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-19-92c433c039f3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mgr_membership_contour\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfi\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-6-86473235b3b9>\u001b[0m in \u001b[0;36mgr_membership_contour\u001b[0;34m(estimated_membership)\u001b[0m\n\u001b[1;32m     18\u001b[0m                                        },\n\u001b[1;32m     19\u001b[0m                              showscale=False))\n\u001b[0;32m---> 20\u001b[0;31m     \u001b[0mgo\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFigureWidget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"svg\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m \u001b[0mgr_membership_contour\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfi\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/basedatatypes.py\u001b[0m in \u001b[0;36mshow\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   3395\u001b[0m         \u001b[0;32mimport\u001b[0m \u001b[0mplotly\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mio\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mpio\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3396\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3397\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mpio\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3398\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3399\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mto_json\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/io/_renderers.py\u001b[0m in \u001b[0;36mshow\u001b[0;34m(fig, renderer, validate, **kwargs)\u001b[0m\n\u001b[1;32m    387\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    388\u001b[0m     \u001b[0;31m# Mimetype renderers\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 389\u001b[0;31m     \u001b[0mbundle\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrenderers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_build_mime_bundle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrenderers_string\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    390\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mbundle\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    391\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mipython_display\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/io/_renderers.py\u001b[0m in \u001b[0;36m_build_mime_bundle\u001b[0;34m(self, fig_dict, renderers_string, **kwargs)\u001b[0m\n\u001b[1;32m    295\u001b[0m                         \u001b[0msetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    296\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 297\u001b[0;31m                 \u001b[0mbundle\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto_mimebundle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig_dict\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    298\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    299\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mbundle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/io/_base_renderers.py\u001b[0m in \u001b[0;36mto_mimebundle\u001b[0;34m(self, fig_dict)\u001b[0m\n\u001b[1;32m    132\u001b[0m             \u001b[0mscale\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscale\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m             \u001b[0mvalidate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 134\u001b[0;31m             \u001b[0mengine\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mengine\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    135\u001b[0m         )\n\u001b[1;32m    136\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/io/_kaleido.py\u001b[0m in \u001b[0;36mto_image\u001b[0;34m(fig, format, width, height, scale, validate, engine)\u001b[0m\n\u001b[1;32m    107\u001b[0m             \u001b[0mheight\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mheight\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    108\u001b[0m             \u001b[0mscale\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscale\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 109\u001b[0;31m             \u001b[0mvalidate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mvalidate\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    110\u001b[0m         )\n\u001b[1;32m    111\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mengine\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m\"kaleido\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/io/_orca.py\u001b[0m in \u001b[0;36mto_image\u001b[0;34m(fig, format, width, height, scale, validate)\u001b[0m\n\u001b[1;32m   1592\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0minfo\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1593\u001b[0m \"\"\".format(\n\u001b[0;32m-> 1594\u001b[0;31m                         \u001b[0minfo\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mstatus_str\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1595\u001b[0m                     )\n\u001b[1;32m   1596\u001b[0m                 )\n",
      "\u001b[0;31mValueError\u001b[0m: \nFor some reason plotly.py was unable to communicate with the\nlocal orca server process, even though the server process seems to be running.\n\nPlease review the process and connection information below:\n\norca status\n-----------\n    state: running\n    executable: /home/malchiodi/share/anaconda3/envs/mulearn/bin/orca\n    version: 1.3.1\n    port: 37355\n    pid: 105533\n    command: ['/home/malchiodi/share/anaconda3/envs/mulearn/bin/orca', 'serve', '-p', '37355', '--plotly', '/home/malchiodi/share/anaconda3/envs/mulearn/lib/python3.7/site-packages/plotly/package_data/plotly.min.js', '--graph-only', '--mathjax', 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js']\n\n\n"
     ]
    }
   ],
   "source": [
    "gr_membership_contour(fi.predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=0, dual=0.487, prim=0.068, gap=0.582390\n",
      "i=10, dual=1.947, prim=0.312, gap=0.176922\n",
      "i=20, dual=2.469, prim=0.460, gap=0.037205\n",
      "i=30, dual=2.970, prim=0.492, gap=0.007407\n",
      "i=40, dual=3.470, prim=0.498, gap=0.001460\n"
     ]
    }
   ],
   "source": [
    "Q = [[1, 0], [0, 1]]\n",
    "q = [0, 0]\n",
    "A = [[1, 1]]\n",
    "b = [1]\n",
    "C = [[-1, -1], [1, 0], [0, 1], [-1, 0], [0, -1]]\n",
    "d = [-1, 1, 1, 0, 0]\n",
    "\n",
    "from tensorflow.keras.optimizers import Adam\n",
    "\n",
    "solver=TensorFlowSolver(optimizer=Adam(learning_rate=0.1))\n",
    "\n",
    "obj_val, lagr_val, x, lambda_, gap = \\\n",
    "           solver.solve_lagrange_relaxation(Q, q, A, b, C, d,\n",
    "                                     max_gap=10**-3,\n",
    "                                     verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both `GurobiSolver` and `TensorFlowSolver` have some parameters which can be set during class instantiation. These parameters are described in the package API.\n",
    "\n",
    "## Model selection and assessment\n",
    "\n",
    "As `FuzzyInductor` implements the standard interface of Scikit-learn, several of the tools provided by the latter can be used in conjunction with the induction of a fuzzy membership function. In particular, the use of `GridSearchCV` for model selection and model assessment is available out-of-the-box.\n",
    "\n",
    "Relying on randomized techniquest such as `RandomizedSearchCV` for model selection requires the possibility of specifying a distribution for the involved hyperparameters which are defined through `GaussianKernel` or `ExponentialFuzzifier`. The module `mulearn.distributions` implements two additional classes related to these distributions, namely `GaussianKernelDistribution` and `ExponentialFuzzifierDistribution`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n",
      "{'c': 1, 'k': GaussianKernel(), 'fuzzifier': ExponentialFuzzifier(), 'solver': GurobiSolver(), 'random_state': None, 'chis_': None, 'gram_': None, 'fixed_term_': None, 'train_error_': None}\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import RandomizedSearchCV\n",
    "from scipy.stats import uniform\n",
    "\n",
    "from mulearn.distributions import GaussianKernelDistribution, \\\n",
    "                                  ExponentialFuzzifierDistribution\n",
    "\n",
    "fi = FuzzyInductor()\n",
    "\n",
    "params = {'c': uniform(loc=0, scale=10),\n",
    "          'k': GaussianKernelDistribution(low=0.001, high=10),\n",
    "          'fuzzifier': ExponentialFuzzifierDistribution()}\n",
    "\n",
    "gs = RandomizedSearchCV(fi, params, verbose=0, n_jobs=-1,\n",
    "                                pre_dispatch=10)\n",
    "gs = gs.fit(iris_X_2d, iris_versicolor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
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