tutorials/B_Model_Tutorial_2_General_Mixture_Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a93a8ea3",
   "metadata": {},
   "source": [
    "### General Mixture Models\n",
    "\n",
    "author: Jacob Schreiber <br>\n",
    "contact: jmschreiber91@gmail.com\n",
    "\n",
    "It is frequently the case that the data you have is not explained by a single underlying distribution. Typically this is because there are multiple phenomena occuring in the data set, each with their own underlying distribution. If we want to try to recover the underlying distributions, we need to have a model which has multiple components. An example could be sensor readings where the majority of the time a sensor shows no signal, but sometimes it detects some phenomena. Modeling both phenomena as a single distribution would be silly because the readings would come from two distinct phenomena.\n",
    "\n",
    "A solution to the problem of having more than one single underlying distribution is to use a mixture of distributions instead of a single distribution, commonly called a mixture model. This type of compositional model builds a more complex probability distribution from a set of simpler ones. A common type, called a Gaussian Mixture Model, is composed of Gaussian distributions, but mathematically there is no need for these distributions to all be Gaussian. In fact, there is no need for these distributions to be simple probability distributions.\n",
    "\n",
    "In this tutorial we'll explore how to do mixture modeling in pomegranate, compare against scikit-learn's implementation of Gaussian mixture models, and explore more complex types of mixture modeling that one can do with probabilistic modeling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "199f725d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "numpy        : 1.23.4\n",
      "scipy        : 1.9.3\n",
      "torch        : 1.12.1\n",
      "torchegranate: 0.0.1\n",
      "\n",
      "Compiler    : GCC 11.2.0\n",
      "OS          : Linux\n",
      "Release     : 4.15.0-197-generic\n",
      "Machine     : x86_64\n",
      "Processor   : x86_64\n",
      "CPU cores   : 8\n",
      "Architecture: 64bit\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import seaborn; seaborn.set_style('whitegrid')\n",
    "\n",
    "import torch\n",
    "\n",
    "from torchegranate.gmm import GeneralMixtureModel\n",
    "from torchegranate.distributions import *\n",
    "\n",
    "\n",
    "numpy.random.seed(0)\n",
    "numpy.set_printoptions(suppress=True)\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark -m -n -p numpy,scipy,torch,torchegranate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5f34383",
   "metadata": {},
   "source": [
    "### A simple example: Gaussian mixture models\n",
    "\n",
    "Let's start off with a simple example. Perhaps we have a data set like the one below, which is made up of not a single blob, but many blobs. It doesn't seem like any of the simple distributions that pomegranate has implemented can fully capture what's going on in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "41e8c12a",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(0)\n",
    "\n",
    "X = numpy.concatenate([numpy.random.normal((7, 2), 1, size=(100, 2)),\n",
    "                       numpy.random.normal((2, 3), 1, size=(150, 2)),\n",
    "                       numpy.random.normal((7, 7), 1, size=(100, 2))])\n",
    "\n",
    "plt.figure(figsize=(6, 5))\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.axis(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3de9d63e",
   "metadata": {},
   "source": [
    "It seems clear to us that this data is composed of three blobs. Accordingly, rather than trying to find some complex single distribution that can describe this data, we can describe it as a mixture of three Gaussian distributions. In the same way that we could initialize a basic distribution using the `fit` method, we can initialize a mixture model using it, additionally passing in the type(s) of distribution(s) to use and the number of components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "535e27a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Improvement: 2.6761474609375, Time: 0.0008376s\n",
      "[2] Improvement: 0.5830078125, Time: 0.0006821s\n",
      "[3] Improvement: 0.208740234375, Time: 0.0007272s\n",
      "[4] Improvement: 0.09619140625, Time: 0.0007284s\n"
     ]
    }
   ],
   "source": [
    "model = GeneralMixtureModel([Normal(), Normal(), Normal()], verbose=True).fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51197af4",
   "metadata": {},
   "source": [
    "Now we can look at the probability densities if we had used a single Gaussian distribution versus using this mixture of three Gaussian models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7c76bb0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.arange(-1, 10.1, .1)\n",
    "y = numpy.arange(-1, 10.1, .1)\n",
    "\n",
    "xx, yy = numpy.meshgrid(x, y)\n",
    "x_ = numpy.array(list(zip(xx.flatten(), yy.flatten())))\n",
    "\n",
    "p1 = Normal().fit(X).probability(x_).reshape(len(x), len(y))\n",
    "p2 = model.probability(x_).reshape(len(x), len(y))\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(121)\n",
    "plt.title(\"Single Gaussian\", fontsize=12)\n",
    "plt.contourf(xx, yy, p1, cmap='Blues')\n",
    "plt.scatter(X[:,0], X[:,1], s=10)\n",
    "plt.axis(False)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.title(\"Gaussian Mixture\", fontsize=12)\n",
    "plt.contourf(xx, yy, p2, cmap='Blues')\n",
    "plt.scatter(X[:,0], X[:,1], s=10)\n",
    "plt.axis(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b121c05",
   "metadata": {},
   "source": [
    "It looks like, unsurprisingly, the mixture model is able to better capture the structure of the data. The single Gaussian is so bad that the region of highest density (the darkest blue ellipse) has very few real points in it. In contrast, the darkest regions in the mixture densities correspond to where there are the most points in the clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0908c21",
   "metadata": {},
   "source": [
    "### Initialization and Fitting\n",
    "\n",
    "Initialization of mixture models is similar to that of probability distributions: you can either pass in initialized values, or not. If you already have probability distributions, and optionally already have prior values on which distribution generated the data, you can pass those into initialization and use the model directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fd8c565f",
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = Exponential([1.3, 3.3])\n",
    "d2 = Exponential([2.2, 0.4])\n",
    "\n",
    "model = GeneralMixtureModel([d1, d2], priors=[0.2, 0.8])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dcbe803",
   "metadata": {},
   "source": [
    "Alternatively, if you don't know the values, you can pass in uninitialized distributions and then fit it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bed00021",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Improvement: 1.3780937194824219, Time: 0.0004084s\n",
      "[2] Improvement: 0.4211540222167969, Time: 0.0003901s\n",
      "[3] Improvement: 0.14813995361328125, Time: 0.0003643s\n",
      "[4] Improvement: 0.04771995544433594, Time: 0.0003541s\n"
     ]
    }
   ],
   "source": [
    "d1 = Exponential()\n",
    "d2 = Exponential()\n",
    "\n",
    "X2 = torch.abs(torch.randn(15, 3))\n",
    "\n",
    "model = GeneralMixtureModel([d1, d2], verbose=True).fit(X2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1bbc5d0",
   "metadata": {},
   "source": [
    "You can inspect the learned prior probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5ae58b98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.3427, 0.6573])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.priors"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "011f5250",
   "metadata": {},
   "source": [
    "After training, you can inspect the distribution objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0991595a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.8837, 0.6054, 0.6893]), tensor([0.9316, 0.5709, 0.8068]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1.scales, d2.scales"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d25758f7",
   "metadata": {},
   "source": [
    "### Probability and Log Probability\n",
    "\n",
    "Because mixture models themselves are technically probability distributions, it should be unsurprising that the calculation of probabilities and log probabilities are identical to that of probability distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d08b210b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.8576, -1.0032, -2.6074, -4.4957, -1.0349, -2.9981, -1.7019, -2.8964,\n",
       "        -2.8841, -1.8333, -2.4110, -2.9289, -1.5718, -1.1419, -1.2377])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.log_probability(X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "350c3068",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([-0.7894, -0.8831, -2.6340, -4.4680, -0.9732, -3.2170, -1.6178, -2.8935,\n",
       "         -2.8889, -1.9021, -2.4999, -3.0942, -1.5530, -1.0593, -1.2160]),\n",
       " tensor([-0.8950, -1.0720, -2.5938, -4.5104, -1.0687, -2.9005, -1.7488, -2.8978,\n",
       "         -2.8816, -1.7992, -2.3677, -2.8524, -1.5817, -1.1879, -1.2492]))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1.log_probability(X2), d2.log_probability(X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a1b8107f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.4242, 0.3667, 0.0737, 0.0112, 0.3552, 0.0499, 0.1823, 0.0552, 0.0559,\n",
       "        0.1599, 0.0897, 0.0535, 0.2077, 0.3192, 0.2901])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.probability(X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "44495983",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.4541, 0.4135, 0.0718, 0.0115, 0.3779, 0.0401, 0.1983, 0.0554, 0.0556,\n",
       "         0.1493, 0.0821, 0.0453, 0.2116, 0.3467, 0.2964]),\n",
       " tensor([0.4086, 0.3423, 0.0747, 0.0110, 0.3435, 0.0550, 0.1740, 0.0551, 0.0560,\n",
       "         0.1654, 0.0937, 0.0577, 0.2056, 0.3049, 0.2867]))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1.probability(X2), d2.probability(X2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d032028c",
   "metadata": {},
   "source": [
    "### Prediction\n",
    "\n",
    "A key utility of mixture models, as a clustering method, is that they can make predictions for which component better fits each data point. These methods miror those of scikit-learn. Starting off, if you just want predictions of cluster label for each point you can use the `predict` method. Let's return to the Gaussian mixture model for an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "07010715",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Improvement: 0.216064453125, Time: 0.0008986s\n",
      "[2] Improvement: 0.0286865234375, Time: 0.001328s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = GeneralMixtureModel([Normal(), Normal(), Normal()], verbose=True).fit(X)\n",
    "model.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea3af78d",
   "metadata": {},
   "source": [
    "If you're interested in the underlying probabilities, which are the likelihoods under the probability distributions multiplied by the priors and then normalized (sometimes called the responsibility matrix), you can use `predict_proba` to get these probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7b3d7c41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[3.2331e-10, 5.0367e-06, 1.0000e+00],\n",
       "        [1.3677e-06, 2.1503e-05, 9.9998e-01],\n",
       "        [5.2814e-05, 1.1250e-06, 9.9995e-01],\n",
       "        [3.7857e-05, 1.6255e-03, 9.9834e-01],\n",
       "        [1.1822e-07, 1.1828e-08, 1.0000e+00],\n",
       "        [8.1323e-06, 1.2524e-02, 9.8747e-01],\n",
       "        [3.6977e-06, 5.8397e-09, 1.0000e+00],\n",
       "        [9.9969e-01, 1.0669e-06, 3.0659e-04],\n",
       "        [1.0000e+00, 2.4645e-11, 2.7694e-07],\n",
       "        [9.9968e-01, 1.4797e-12, 3.2161e-04],\n",
       "        [1.0000e+00, 8.9391e-10, 6.9951e-09],\n",
       "        [9.9966e-01, 1.9474e-09, 3.3985e-04],\n",
       "        [9.9987e-01, 1.1254e-07, 1.2672e-04],\n",
       "        [9.9992e-01, 2.5078e-08, 7.5673e-05],\n",
       "        [9.9969e-01, 3.1749e-06, 3.0738e-04],\n",
       "        [1.0000e+00, 1.8341e-10, 2.4478e-08],\n",
       "        [9.9986e-01, 7.4968e-06, 1.2940e-04],\n",
       "        [4.5693e-15, 1.0000e+00, 3.9610e-07],\n",
       "        [2.0310e-08, 9.8980e-01, 1.0201e-02],\n",
       "        [9.1367e-08, 8.6050e-01, 1.3950e-01],\n",
       "        [9.5963e-08, 9.9998e-01, 1.5413e-05],\n",
       "        [1.2553e-08, 9.9989e-01, 1.0525e-04],\n",
       "        [6.6067e-06, 9.9020e-01, 9.7936e-03],\n",
       "        [5.7232e-13, 1.0000e+00, 1.8398e-06]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba(X)[::15]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3d69298",
   "metadata": {},
   "source": [
    "If you'd like to go even deeper, you can get log probabilities -- which are the space where all the calculations are done for numeric stability -- using the `predict_log_proba` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7ac64b1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-2.1852e+01, -1.2199e+01, -4.7684e-06],\n",
       "        [-1.3502e+01, -1.0747e+01, -2.2888e-05],\n",
       "        [-9.8487e+00, -1.3698e+01, -5.3883e-05],\n",
       "        [-1.0182e+01, -6.4219e+00, -1.6649e-03],\n",
       "        [-1.5951e+01, -1.8253e+01,  0.0000e+00],\n",
       "        [-1.1720e+01, -4.3801e+00, -1.2612e-02],\n",
       "        [-1.2508e+01, -1.8959e+01, -3.8147e-06],\n",
       "        [-3.0780e-04, -1.3751e+01, -8.0900e+00],\n",
       "        [-2.3842e-07, -2.4426e+01, -1.5099e+01],\n",
       "        [-3.2187e-04, -2.7239e+01, -8.0422e+00],\n",
       "        [ 0.0000e+00, -2.0835e+01, -1.8778e+01],\n",
       "        [-3.3998e-04, -2.0057e+01, -7.9870e+00],\n",
       "        [-1.2684e-04, -1.6000e+01, -8.9735e+00],\n",
       "        [-7.5579e-05, -1.7501e+01, -9.4891e+00],\n",
       "        [-3.1066e-04, -1.2660e+01, -8.0874e+00],\n",
       "        [ 0.0000e+00, -2.2419e+01, -1.7525e+01],\n",
       "        [-1.3685e-04, -1.1801e+01, -8.9526e+00],\n",
       "        [-3.3019e+01, -4.7684e-07, -1.4742e+01],\n",
       "        [-1.7712e+01, -1.0254e-02, -4.5853e+00],\n",
       "        [-1.6208e+01, -1.5024e-01, -1.9697e+00],\n",
       "        [-1.6159e+01, -1.5259e-05, -1.1080e+01],\n",
       "        [-1.8193e+01, -1.0514e-04, -9.1592e+00],\n",
       "        [-1.1927e+01, -9.8486e-03, -4.6260e+00],\n",
       "        [-2.8189e+01, -1.6689e-06, -1.3206e+01]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_log_proba(X)[::15]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3618610",
   "metadata": {},
   "source": [
    "### Zero-inflated Mixtures\n",
    "\n",
    "A common way to view zero-inflated distributions is as a mixture where one component is a dirac delta distribution with a probability mass entirely on zero and whatever the other distribution is. The zero-inflation is explicitly modeled because sometimes your data will have zeroes that do not come from the primary thing being modeled. Although zero-inflated distributions are explicitly implemented already, one could manually implement one like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "eaac089c",
   "metadata": {},
   "outputs": [],
   "source": [
    "p = numpy.array([30, 1, 3, 7, 8, 7, 4, 3, 2, 1, 2, 1, 1, 1])\n",
    "X = numpy.random.choice(len(p), size=(500, 1), p=p/p.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c9bed3e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([3.3220])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Poisson().fit(X)\n",
    "d.lambdas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "79560b18",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Improvement: 1369.84814453125, Time: 0.0004084s\n",
      "[2] Improvement: 89.228271484375, Time: 0.000468s\n",
      "[3] Improvement: 0.164306640625, Time: 0.0004704s\n",
      "[4] Improvement: 0.0001220703125, Time: 0.0004325s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([5])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = GeneralMixtureModel([DiracDelta([1]), Poisson([1])], verbose=True).fit(X)\n",
    "model.distributions[1].lambdas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "12bbc00a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ezIkTJwgICKB27dpMnjwZcI9czZw5k7fffptOnToRGBhIixYtGDp0aLYdq9yaiiMREbkjpLxU/lr+/v4MHz6c4cOHp/l83bp12bdvX/LHb7755g3beu6553juuedu+Hx4eDifffZZhnIOGzbshq8Xz9OcIxEREZEUVByJiIiIpKDiSERERCQFzTm6XZw7AAdXwaGfIfYIXD4NhgsCC0LeMChRB0o3gLsbg9XP12lFRERyLBVHuZnLBX9+B+v/A0fWpv2a+GiIPgCHf4U1kyEoBKp3gbr9oEDJtPcRERG5g6k4yq1O7YAlL8HJv5elN1vdI0Nlm0DRCMhzl3tbwnl3cXR0A+xfAXFnYf0HsHEG3NcH7h8IQYV8eigiIiI5iYqj3MbpgJ/ehrVTwHCCX16o8wzUfRbyFUt7n9INoFYPcNph/w9/jzStcRdJ2+dD2/+DSm2z9TBERERyKhVHuUl8DCzqCX+tdn9cpT20HAf5wtK3v8UG97SG8FZw8EdYPhyi9sKCJ6F6V3hkMvgF3bodERGR25iuVsstYo/AjKbuwsgWBJ1mQedP0l8YpWQyQfmH4NmfodGrYDLD9nkwqwWcP+rp5CIiIrmKiqPcIOYvmN0aYg9BgdLwzA9QtWPW27X6w0Mj4aml7onap3fC9Afh+JZb7ioicqfZsGED4eHhXLx40ddR0vT+++/Trl27277P7KDiKKeLPQyzH4GLx6FwBei1HIpW9WwfZRq6R5HCqruvbvu07T+n7kREbhNDhw4lPDyc8PBwqlSpQrNmzXj33XeJj49P1/41a9ZkzZo15M2b18tJM6dXr1588sknWWpj8eLFhIeH06pVq+uei4yMJDw8nKZNm2a6z8WLF3PvvfdmKWN2UHGUk8XHwJxOcOkkhN4DPSMzdxotPfKXgKeXuddBssfB3M7w53Lv9CUi4iP3338/a9asYeXKlbz88st88cUXvPvuu+na18/Pj9DQUEwmk5dTZk5wcDAFCxbMcjtBQUHExMSwbdu2VNu//PJLihVLfeGPp/rMDLvd7rW2M1UczZ07l6ZNmxIREUGHDh3YvHnzDV+7YsUKevbsSb169ahVqxZPPPEEv/76a6YD3zEcie6J0tH7IV9x6P415Cni3T7980K3/7mvXHMmwYLucPAn7/YpIpKNrhY4YWFhtG3blrZt2/Ljjz8CkJSUxNixY6lfvz4RERF07dqVHTt2JO977Wm1EydO0K9fP+rUqUONGjV45JFH+PnnnwG4cOECAwcOpF69elSrVo0WLVrw5ZdfJre1b98+evToQbVq1ahbty5vvvkmcXFxyc8PHTqU5557jpkzZ9KoUSPq1q3LqFGjbloQXHuKKzNtAFgsFtq0aZMq7+nTp9m4cSNt2rS5YZ+JiYk88sgjqW7Ke+zYMWrXrs3ChQvZsGEDr7/+OpcuXUoewXv//fcB9814V65cmarte++9l8WLFwNw/PhxwsPDiYyMpHv37kRERPDtt98C7qKtVatWRERE8PDDDzN37tybHl96ZPhqtcjISMaNG8fIkSOpVasW8+fPp0+fPixbtuy6ihJg06ZNNGjQgFdeeYV8+fKxePFi+vfvz8KFC6lcuXKWD+B2Zfp+sHthR/987oLFWyNG17L6Q6fZ8L+n4Y+lMK8rdP8KStfPnv5FJFcyDIMrjivZ1l+gNdAjIzgBAQHJxcKECRNYvnw548ePp3jx4nz88cf07t2bFStWUKBAgev2HT16NHa7nTlz5hAUFMSBAwcICnJf8TtlyhQOHjzIjBkzKFiwIEePHiUhIQGAK1eu0Lt3b2rUqMGiRYuIjo5m+PDhjBkzhvHjxye3v2HDBkJDQ/n00085evQor7zyCpUqVeLxxx9P9/Flto1OnTrRrVs3hg0bRmBgIIsXL+b++++ncOHCN9zH39+f9957j86dO9O4cWOaNGnC4MGDqVu3Lo8//jhJSUm88cYbTJ06le+//x4g+f1Kr/fee4+hQ4fyzjvv4Ofnx8KFC5k6dSojRoygUqVK7N27lzfffJOgoCDat2+fobZTynBxNHv2bDp27Ejnzp0BGDZsGGvWrGHevHkMHDjwutcPGzYs1cevvvoqP/74I6tWrVJxdAOFjq3A/PvngAk6z4a7qmRvAIvNfTXc/H/BgZUwr4t7EnhoxezNISK5gmEY9PiuB79H/Z5tfdYsUpNPH/40SwXSjh07WLJkCfXr1yc+Pp758+czbtw4GjduDMCYMWNYu3YtixYtonfv3tftf/LkSVq2bEl4eDgAJUuWTPVcpUqViIiIAKBEiRLJzy1ZsoTExETefffd5OJgxIgR9OvXj0GDBhESEgJA/vz5GTFiBBaLhXLlytG4cWPWr1+foeIos21UqlSJUqVKsXz5ctq1a8dXX33F0KFDOXbs2C33e/nllxk+fDht2rTh2LFj/Oc//wHco3Z58+bFZDIRGhqa7mNI6amnnqJFixbJH0+bNo2hQ4cmbytZsiQHDhxgwYIF2VccJSUlsXv3bvr27Ztqe8OGDa87N3kjLpeLuLi4NKvwW3E6nRnex+VyYbFYMrxfemUm0824Tu2i9I5/ux8/MBjj7ibg4T7SxWSFTp9g/vwxTCc2Y8ztiKvniutO7V09fk+/D96S2/JC7susvN6VlbzePMacOg/nWqtXr6ZmzZo4HA4cDgfNmjXjzTff5OjRo9jtdmrVqpX8WpvNRrVq1Th48GCabfXo0YO33nqLNWvW0KBBA1q0aME999wDQNeuXXnxxRfZs2cPDRs25KGHHkpu++DBg4SHh6caNalVqxYul4tDhw4lF0fly5dP9fsrNDSUP//8M0PHm5U2OnbsyJdffklYWBjx8fE0btyYOXPm3HK/Xr168eOPP/L5558zY8YMChXy3F0Yqlb954KkmJgYTp06xbBhw1KdynM4HFmeNJ+h4ig2Nhan03ndsFpISAhRUVHpamPWrFlcuXIlzZnwt7Jz584M7xMYGOjVEap9+/Zx5YpnhpJNziTu+fU5bK5ELoTey4F8D8Hvv3uk7cyyVnmD8PMvEHD+KAmzH2Nfg//DsFx/49rMfG58KbflhdyXWXm9KyflNZlMfPrwp7nitFrdunV56623sFqtFClSBJvNBpD8O+zaNg3DuGE/nTt3plGjRqxevZq1a9cyffp0hgwZQvfu3WncuDE//fQTq1evZt26dTz99NN069aNIUOG3LTNlNutVut1zxmGkaHjzUobbdu2ZeLEiXzwwQe0a9fuurZuJDo6mkOHDmGxWDhy5Ei69kkrl8PhuO51KQtKl8sFuEf4qlevnup1ZnPWrjfL1ArZGfniSWnp0qV88MEHTJs27abnLW8kIiIiw6NAV988b7k6nOoJplVjMF/6C7tfAQL/9Rk18hX1WNtZUuEbjFnNCT7/BzWOzcZoN829kCTuv0R37tyZqc+NL+S2vJD7Miuvd2Ul79V9vcFkMhFky/kr7AcGBlK6dOnrtpcqVQqbzcaWLVuS58/a7XZ27drFU089dcP2wsLC6Nq1K127dmXSpEksXLiQ7t27A1CoUCE6dOhAhw4dmD9/PhMmTGDIkCGUL1+er7/+mvj4+ORf9lu3bsVsNlOmTBnPH3QmFShQgKZNm/Ldd9/x1ltvpXu/N954gwoVKvD4448zbNgw6tevT/ny5QH3aFxaI5iFChXi7NmzyR8fPnz4lgMPISEh3HXXXRw7doxHH3003fnSI0PFUcGCBbFYLJw7dy7V9ujo6ORhwBuJjIxk2LBhTJkyhQYNGmQ8Ke4Z9Dnth5fH8hzbBOumAHC02iuUyVc05xxraAX3atyfd8C8cwGEVYMGA1K9JCd+bm4mt+WF3JdZeb0rt+XN6YKCgujatSsTJkwgf/78FCtWjI8//piEhAQ6deqU5j5vv/02DzzwAGXKlOHixYv89ttvlCtXDnBPyK5SpQoVKlQgKSmJ1atXJz/Xtm1bpk6dytChQxkwYAAxMTGMGTOGdu3a3fJ3aXYbP348I0eOTPfl+nPnzuX333/n22+/JSwsjF9++YVBgwaxcOFC/Pz8KF68OPHx8axfv57w8HACAwMJDAykXr16zJ07lxo1auByuXjvvfeSR/Vu5oUXXmDs2LHkyZOHBx54gKSkJHbt2sXFixfp2bNnpo87Q+NOfn5+VKlShbVr16bavm7dOmrWrHnD/ZYuXcrQoUOZNGkSDz74YKaC3tYcifDNc2C4cEU8zvmw+32d6HplH4SW77gf/zACjqz3aRwREU8bNGgQLVu2ZPDgwbRv354jR47w8ccfkz9//jRf73K5GD16NK1bt6Z3797cfffdjBw5EnCPkEyePJlHH32UJ598ErPZzOTJkwH36NXMmTM5f/48nTp14qWXXqJ+/fqp5s3kFAEBAekujA4ePMiECRMYOXIkYWHuK6xHjhzJxYsXmTLF/cd/rVq16NKlCy+//DL169fn448/BmDIkCGEhYXx5JNPMmjQIHr16kVAQMAt++zcuTNjx47lq6++om3btnTv3p2vvvoq1QT4zDAZGTyBGRkZyeDBg3nrrbeoWbMmCxYs4H//+x9Lly6lePHiTJo0iTNnzjBhwgTAXRgNGTKEN954I9UM84CAgHRPmHI6nfz+++/UqFEjU8PIFouFR6b+yu6TnlvyvUqxfCx70UNFzM8T4aexEFwEZ//f+H3f4Uwdq9cZBnz1LOxYAHmLQb81OAMKZPpz4wtZ+VryldyWWXm9K6s/D7N6rAkJCRw6dIi77747Xb+8RHKS9H79ZnjOUevWrYmNjWXatGmcPXuWihUrMn36dIoXLw64J7WdOnUq+fULFizA4XAwevRoRo8enby9ffv2qdZzuGNFH4RfJrofPzwOAgv4NM5NmUzwyGQ4sQWiD8DX/eGJL3ydSkRExKMyNSG7W7dudOvWLc3nri14Pv/888x0cWcwDIh8DZyJ7tNWVTuClyeQZ5l/Hvf8oxnNYP9yTL/9BwIb+TqViIiIx+jear607zs4+CNY/KD1pOQrwHK8ohHuUS7AtGo0QbF7fRxIRETEc1Qc+YojCVYMdz+u/zyElPdtnoy6txdUfgyTy0HZLaPhynlfJxIREfEIFUe+suljiDkIwaHQ6FVfp8k4kwkenYpRoDT+V8647wUnIiJyG8jUnCPJovgY+PnvuVlNh0NAPt/myayA/Lg6zMA862HMuxZBpbZQ5TEAYhJi2Bm1k4MXDnLi0gnOXTlHgjMBu8tOoDWQYFswxYKLUSpfKcILhlOxUEVs5luvaSEiOUNGV2oWyQnS+3Wr4sgX1kyGhAtQpArU7O7rNFlT/F5Ol+9K0QNz2bl8ICsv7uKn0xs4fPFwhpoJtAZSI7QGD5Z8kKalmlI0OIesDi4iqVxdmC8+Pp7AwEAfpxHJmPj4eIBbLjCp4ii7XTgBG2e4Hz/0Fphz/roqNxNvj+ez0BKst5fhoNkFfy5Ifq5s/rLcU+geSuQtwV1BdxFoDcRqtnLFcYWLiRc5cfkERy4eYVf0Li4lXWL9qfWsP7We8RvHUy+sHh0qdqBZqWYaURLJQSwWCwUKFEi+1UNQUFCuuems3LkMwyA+Pp6zZ89SoECBW67zpeIou/38LjgSoFQDqNDc12kyLd4ez7w/5vHJ7k84n3gezBDocvFg/BWaVv4X9Ru8Rn7/tFeVvZbLcHHowiHWnFjDqqOr2Hp2a3KhVDS4KD0q96BjhY654r5NIneCokXdI7sp74UlkhsUKFAg+ev3ZlQcZadzB2DbHPfjh0bmnkv3UzAMg+8OfcekzZM4e8X9g/Euv7voWb0nj0YdI+9P4+C3T6Hms5DO4shsMlOuQDnKFSjHU1We4vil43x94GsW/bmI03GnmbBpArN3zaZ/jf60L98eq1lftiK+ZDKZCAsLo0iRItjtdl/HEUkXm82W7pXh9VsmO/0yAQwnVGgJper5Ok2Gnbh8ghFrR7Dx9EYAiucpTr9q/Sh2oRi1w2tjuQfY/yMc3wjfPA89vslUAVgibwkG1BxAn2p9+Pbgt8zcOZMTl08wev1o5u6Zy7B6w6hTtI6Hj05EMko3v5XblS7lzy4xf8HO/7kfN3ndt1kyyDAMFu9fTIdvOrDx9EYCLAEMqDGAbx77hrZl22Ix/f3D0WyB9h+CNQAO/fzPKFkm+Vv86VyxM0seW8LQ+4ZS0L8gBy8cpNfyXrzx6xtcSLzggaMTERFJTcVRdvl1MhguKN8citX0dZp0i7fH8/qa1xm5biTxjnhqFanF4naLebb6s/hb/K/foXA5aPKG+/GKYXDpTJYz2Cw2ulXqxpL2S3gi/AlMmFjy1xI6ftuRDac2ZLl9ERGRlFQcZYfzx2D7PPfjxrlnscRjF4/RLbIby/5ahsVk4eVaLzOr5SxK5i158x3rPQ9h1d3LFXz3msfy5PfPz/B6w5nTeg6l85XmTPwZeq/ozYRNE0h0JnqsHxERubOpOMoOa6eAywF3PwAl7/N1mnTZdnYb3SK7ceD8AUICQ5jZcibPRDyDJT1LD1is8OgHYLLAnm9g71KPZqsWWo2FbRbSuWJnAD7f8zldlnbh4PmDHu1HRETuTCqOvO3Sadj6mfvxA54bRfGmFYdX0Ht5b2ITY6lSuAoL2yyk9l21M9ZIWDVo+KL78bKBHr/3WpAtiBH1R/BB0w8oFFCIA+cP0C2yG6uOrvJoPyIicudRceRt694HZyKUrAdl7vd1mltavH8xr/3yGkmuJJqUbMKslrMIDQrNXGONh0ChcnD5NPwwwrNBr3ZRsjGLH13MvXfdS5w9jpd+eon/bv8vLsPllf5EROT2p+LIm+LOweZZ7scPvJbj1zWas2cOI9eNxGW46FSxE/9+8N9ZW3jRFgiPvu9+vPVTOPSrZ4Jeo3BgYaa3mE6X8C4ATPt9GgNXDyTOHueV/kRE5Pam4sib1v8H7PHuq9PKN/N1mptauG8h7256F4CeVXoyot6I9M0vupUyDaF2T/fjJS+C/UrW20yDzWxjWL1hjGowCqvZysqjK+nxXQ/OxmsFXxERyRgVR96ScBE2fex+nMNHjZb+tZSxv40FoFfVXrxS+xXP3iup+SjIG+Ze62n1eM+1m4YOFTowu+VsCgcU5s/YP+ke2Z1DFw55tU8REbm9qDjylm2fQ+JFCKkIFVv5Os0NrTq6iuFrhmNg0CW8Cy/XetnzN5EMyA+PTHI/Xvc+nNru2favUaNIDT5v/Tml85XmZNxJenzXg+1R3u1TRERuHyqOvMHpgN8+dD+u/zyYc+bbvO7kOgb9PAin4eTRco/yet3XvXd37XsegcqPuW+f8u2L7vfIi0rmLclnrT6jauGqnE88T+/lvfnl+C9e7VNERG4POfO3dm639xu4cBSCQqBaF1+nSdPuc7t5+aeXsbvsNC/dnFENRmE2efnLodUE9yjSqd9hw4fe7QsoFFCImS1n0rB4QxKcCby46kUiD0V6vV8REcndVBx5mmHAug/cj+/rA7YA3+ZJw+m407yw6gWuOK7QoFgDxt8/PnvudJ/3Lmg+xv34p7ch9ojXuwyyBfF+0/dpW7YtTsPJsLXD+DXWO1fNiYjI7UHFkacdXQ8nt7pvvlqnt6/TXCfeHs+Lq14k6koU5QuUZ1LjSfhZ/LIvQM3uULqh+yq+Za+6i0kvs5ltjG00lk4VO2FgMPPETBb9ucjr/YqISO6k4sjT1v/H/X/1LhAc4tss13AZLoatGcbemL0UCijEB80+II9fnuwNYTZD2ylg8YMDK2HXl9nTrcnMiHoj6BreFYCxG8cyd+/cbOlbRERyFxVHnhR9EP5Y5n5c73nfZknD+9veZ+XRldjMNv6vyf9RPE9x3wQJqfDPrVS+GwLxMdnSrclkYvC9g2kV4r56cPzG8Xy6+9Ns6VtERHIPFUee9Ns0wIAKLSG0oq/TpLLk4BI+3uled2lUg1HULFLTt4Eavgyh90D8OVjxZrZ1azKZePyux+kb0ReA9za/xxd7v8i2/kVEJOdTceQp8TGw7e/TNA0G+DbLNfbF7GP0+tEA9InoQ9tybX2cCLD6QdupgAl+nwN//ZxtXZtMJp6r/hx9q7kLpHEbx2kOkoiIJFNx5ClbPgHHFShaLUfdYPZS0iUG/jyQBGcCDYs3ZEDNHFS4laoLdZ5xP176stduLXIjA2oM4KnKTwEwev1olhxckq39i4hIzqTiyBOcDtg00/24Xv8cc6sQwzAYuW4kRy4eoWhwUcY3Gu/9tYwyqtmIf24t8vOEbO3aZDIx8N6BdAnvgoHB8LXD+f7w99maQUREcp4c9psyl9q3DC4edy/6WKWDr9Mk+3zP5/xw5AesZiuTG0+mQEABX0e6XkB+aP2e+/G6qXB6V7Z2bzKZeL3u63Ss0BGX4WLoL0NZdXRVtmYQEZGcRcWRJ2z4yP1/7adzzKKP285u499b/g3A4DqDiQiN8HGim6jUBu5pAy4HLHkRXM5s7d5sMvNmvTeTF4oc+PNAfj2uhSJFRO5UKo6y6vROOLIWTJZ/5s/4WGxCLIN+HoTDcNCqTCu6hOfMW5ik0noi+OeDE1tg44xs795itjC64WhalG6Bw+Xg5Z9eZuOpjdmeQ0REfE/FUVZdHTWq3A7yFfNtFv6ZZ3Q2/ixl8pXhrQZvee9msp6Urxg8NNL9+MfRcP5Ytkewmq2Mf2A8TUo2IcmVxAurXmBn1M5szyEiIr6l4igr4mNg5//cj+s+69ssf1u4byE/HfsJm9nGxMYTCbIF+TpS+tXuBSXrgj0OIgdly61FrnX1fasbVpd4Rzz9VvZjf+z+bM8hIiK+o+IoK7Z+Co4ECKvu/qXuYwdiDzBx80QAXqn9CvcUusfHiTLIbHavfWS2wZ/fw56vfRLD3+LP1CZTqR5anYtJF+n7Q1+OXcz+kSwREfENFUeZZDacsNG94jT3Pevzy/cTnYkM/nUwic5EGhZvSLdK3XyaJ9OK3AP3v+p+HDkYrsT6JEaQLYj/NPsPFQtW5NyVc/T5oQ+n4077JIuIiGQvFUeZVM++4e/L9wtD1Y6+jsPkzZPZH7ufQgGFGNtwbM5bzygjGr0KhStA3Fn4YaTPYuT3z89HzT+idL7SnLh8gr4/9CUmIXvuAyciIr6Ti3+D+lbbhG/dD3LA5fu/HP+FL/5w3x/s7UZvExIY4tM8WWYLgLZT3I+3fgqH1/gsSkhgCDOaz6BocFEOXThEvx/6cSnpks/yiIiI96k4yoR7TEep5tjlvnz/Xt9evn8+4Twj17lHV56s9CSNijfyaR6PKdMQarlv7cGSl8Ge4LMoYXnCmN58OoUCCrE3Zi8DfhzAFUf23upERESyj4qjTHjKstz9oPKjkL+4T7OM3TCWc1fOUTZ/WV6u/bJPs3hc89GQ5y6I3g+/vufTKHfnv5uPmn9EXltetp7dyiurX8HutPs0k4iIeIeKowwqwCXaW/4+zXOfby/f/+7Qdyw/vByLycI7jd7B3+Lv0zweF1gAWv19v7VfJ8PJ332ZhnsK3cO0h6YRaA1k7Ym1DPl1CM5sXs1bRES8T8VRBj1hWU2Ayc4BSzkoVc9nOc7Gn2Xsb2MB6FutL1VCqvgsi1dVecy9wKbhhK+fA0eST+PUKFKD/2vyf9jMNn448gOj1o/CZbh8mklERDxLxVEGWHDS3foDAEsC2vjs8v2rq2BfTLpI5cKV6VOtj09yZJtHJrtv6nt2N/wyIcvN2Wy2LO3foFgDJj4wEbPJzFcHvmLipokYPliwUkREvEPFUQY0N2+hhOkc0UZefvF7wGc5vtz/JWtOrMHP7Mc7jd7BZs7aL/ucyun6u+AIDoFHJrkf/zoZTmzNdJsWi4VKlbM+ytasdDNGNxgNwJy9c/hw+4dZblNERHIGa2Z2mjt3LjNnziQqKooKFSrwxhtvcO+996b52rNnz/Luu++ya9cujhw5Qvfu3Rk2bFiWQvtKT+v3AHzhbEaSyTfze45fOs7ETe5VsF+s9SLlCpTzSY7sYDGbeGn+Ng6cvQwUZrDf/TRO+pXDs57ipXxTcJgyXhSWL5KHKV1q4nRmfa5Qu/LtiLPHMW7jOKZtn0Yevzx0r9w9y+2KiIhvZbg4ioyMZNy4cYwcOZJatWoxf/58+vTpw7JlyyhW7PobryYlJVGwYEH69+/PJ5984onMPlHZdJi65j+wGxbmOB7CFysJuQwXw9cOJ94RT60itXiy0pM+SJG9Dpy9zO6TFwF4mW6s8N9OGedRmkd9wnuOJ3ycDv5V6V9ctl/m/W3vM2HTBPLY8tC+QntfxxIRkSzI8Gm12bNn07FjRzp37ky5cuUYNmwYRYsWZd68eWm+vkSJEgwfPpzHHnuMvHnzZjmwrzz99+X737nu4wyFfJLh8z2fs+XMFgKtgYxtNBaL2eKTHL4SSz6G23sB0N/yLbVMf/o4kVufiD48XeVpAN5a/xbLDy/3bSAREcmSDBVHSUlJ7N69m0aNUi802LBhQ7Zt2+bRYDlJIS7SzrIOgE8cLX2S4eD5g0zdOhWAQfcOomTekj7J4WvLXffxlbMhFpPBZNt/Ccb3izGaTCZerf0qHSt0xGW4GPrrUNac8N2q3iIikjUZOq0WGxuL0+mkcOHCqbaHhIQQFRXl0WBpycw8EZfLhcWStRGWrpZV+Jvs/O4qy1ajQpYz3czV9lK2a3fZeePXN0hyJdGwWEM6lOvg8X4zK628nnKjz9tI+9PUMe+jjPkMb1o/Z6ijb4bbdrk8f/n9G3Xe4HLSZZYfWc4rP73CtGbTqFWkVpbb9eZ77A3K611ZyZtbjlHE1zI1Idt0zSXshmFct80bdu7cmeF9AgMDqVy5cqb7tOJIvnz/E8fDQOrj3LdvH1eueH70IuWxfn32a/bE7CHIHESnvJ3Yvn17ptq02WxYrZn6lN+y3cx8bm7mZp+3iwQzMKk/8/zG0sW6mlWumqxw1clQ+/v37/fK561zns6cznua7Ze28/zK5xly9xDKBJbxSNuefo+9TXm9K7flFclNMvSbsmDBglgsFs6dO5dqe3R0NCEh3p+iHBERkeFRoKyOELQyb6SoKZazRgGWua5f9DE8PDxL7V/L6XSyc+fO5GPdE72HpbuXAjC8/nCa3N0k842bzFjMni9i7Q4nGC7M5uxbGWKDUYmPnG3ob13CeNsMtiWWJ4qC6d6/QoUKXsv7UcRHPL/qebac3cKU41OY2WImZfOXzXR7135N5HTK611ZyXt1XxG5uQwVR35+flSpUoW1a9fSvHnz5O3r1q2jWbNmHg93LYvFku0/vK5evj/H8RD2NN4ub+WxWCw4cPDmujdxGA6al25Om3JtsjxC98+l8Z5Rp0xB3mxTxSeTwyc7OvOAeQdVzEeYaJvO0/bBXDuydyNms9lrn7tgSzAfNPuAPiv6sCt6F/1W9uPTVp9SIm+JLLXri6//rFBe78pteUVykwyfY+nZsyeDBw+matWq1KxZkwULFnDq1Cm6dOkCwKRJkzhz5gwTJvyzkvHevXsBiIuLIyYmhr1792Kz2ShfvryHDsM7qpsOUMt8gETDyhdO7xd/13p/6/scvHCQwgGFebPemx45dZny0nhPKBcafM16RJ7xYHgor7W856avsWPlJfvzLPUbxoOW7fR0fc9sZyuPZciKPH55+O9D/+Xp75/m4IWD9P2hL58+/CmhQaG+jiYiIreQ4eKodevWxMbGMm3aNM6ePUvFihWZPn06xYu7704fFRXFqVOnUu3z2GOPJT/evXs3S5cupXjx4qxatSpr6b3saav7kuylrvqcI3+29r317FY+2/MZAG81eIuCAek/ZeQL3ii60tWvUYK3Hd0YY/uE161fsMVVkR1GzlgYs0BAAaa3mM5T3z3FsUvH6PtDX2a3nE2BgAK+jiYiIjeRqdm53bp1o1u3bmk+N378+Ou27du3LzPd+FQosTxi/g2A2dl8+f4V5xXGrhuLgcFj5R/jwZIPZmv/uc3nzuY0MO+mlWUTH9im0ibpHS6SvuLK24oEFWFGixk89d1THDh/gP4r+zOjxQzy+OXxdTQREbkB3VvtBp60/oifyckmV0V2GZmfTJsZ807P48TlExTPU5whdYZka9+5k4kh9r4cdYVSyhzFu7bpQM65EWyJvCWY3mI6BfwLsCt6F8/+8CyXki75OpaIiNyAiqM0+GHnX5aVwNXL97PP6mOr+SX2F0yYGNtwrEYY0ukiwTxvf4kkw0IryyZ6WFb4OlIq5QqUY3rz6eT3z8+Oczvou6IvFxIv+DqWiIikQcVRGtqa1xNqushJoxDLXWnfUNcbYhJiGL3Bfaf37pW6c2/R7Ov7drDTKMs7Dvfp3mHWuUSY/vJxotQqFa7EzBYzk0eQ+qzoowJJRCQHUnF0HYPe1mUAfO5ogSNz07Iy3qthMGrdKGISYijhX4LnazyfLf3ebj5xtuR7Zx38TQ6m2aZQgJx1+iq8UDgzW86kUEAh9sbspfeK3sQmxPo6loiIpKDi6BqNzTuoZD7GZSOAuc6m2dbvNwe/YdWxVVjNVvqU6IO/xT/b+r69mBhs78sRVxFKmqP4wDYVCznrlgkVC1ZkVstZFA4ozB8xf/DMimeISYjxdSwREfmbiqNrPGtZAsB8ZxMukj3zfU5cPsH4je6r/PpX60/pwNLZ0u/t6iLB9LW/SpzhTyPLboZa5/k60nXKFSjHrIdnERoYyv7Y/Tyz/BnOXTl36x1FRMTrVBylEGH6iwaWPdgNC7Mc2bOYoMtwMXzNcOLscdQIrcHTlZ/Oln5vd/uMUgy09wegjzWSx8xrfJzoemXzl2VWy1kUCSzCgfMH6LW8F6fjTvs6lojIHU/FUQrPWt33MPvWVZ+TeP9ecQCf7/mczWc2E2gN5J1G7/jkNhy3q+9d9/G+4zEAxttmUDWHTdAGKJO/DLMfnk3R4KIcunCI7t9159CFQ76OJSJyR1Nx9LeSpjO0Mm8AYIajTbb0uS9mH1O3TgXgtTqvUTJfyWzp904y2dGJlc6aBJjsTPebTEFXzpv8XCpfKT57+DPK5CvD6bjTPP390+yJ3uPrWCIidywVR3/rbYnEYjJY7azOH0Ypr/d3xXGFwb8MJsmVROMSjelUoZPX+7wTGZh5xf48B11hFDPFMPLSKEiK83Ws64TlCePTVp9SqVAlYhJi6LW8F5tOb/J1LBGRO5KKI6AgF3nc8jMAHzmzZ9RowqYJ/HXhL0IDQxndcLRHbiorabtEEL3srxFt5KWC8wAs6gUuh69jXadQQCFmtZzFvXfdS5w9jv4r+7PyyEpfxxIRueOoOAJ6WH4g0JTEDtfdrHdV9np/Kw6vYNGfizBh4p3736FQQCGv93mnO2IUpU/SQBLxgz+/x/T9UDByzi1Grsrjl4cPm39Ik5JNSHQm8urqV5n7x1xfxxIRuaPc8cVREAk8ZV0OwEeOtoB3R3BOXT7FW+vfAqBX1V7UC6vn1f7kH1uNiryXZxBgwrxlFqyd4utIafK3+DP5wck8Ef4EBgYTN0/ki1Nf4HTlrPWaRERuV3d8cfSUZQWFTJf5y1WU7111vNqXw+Vg6K9DuZR0iYiQCJ6vqVWws9s6vwbw8Dj3BytHwo7/+TbQDVjNVobVHcYrtV8BYEX0Cgb/OpgER4KPk4mI3P7u6OIomCv0/fvy/fcd7XHi3cvop/0+ja1ntxJsC+bdB97FZrZ5tT+5gXr9cdV1r4HEV8/C3qW+zXMDJpOJXlV7Mb7ReKwmKz8e+5Ge3/fkTNwZX0cTEbmt3dHF0VOWFRQ0XeagK4xvXQ282tcvx39hxs4ZAIyoN4KSeXXZvi8ZzcdAtS5gOGFRT9ifcyc+P1zmYV4r8xr5/fKzK3oXXZd1ZWfUTl/HEhG5bd2xxVEe4unz9w1mvT1qdPzScV7/9XUAuoR3oXXZ1l7rS9LJZIZ2/4HKj4EzCRZ0g0O/+jrVDYUHhzOn1RzKFyhP1JUonv7+aZYcXOLrWCIit6U7tjjKrlGjq1ccXUy6SLWQarxW5zWv9SUZZLFChxlQsRU4EuCLJ+DYRl+nuqGSeUsyp/UcHiz5IEmuJN5Y8waTNk/CkQOXJRARyc3uyOIo5ajRFEcHXF58G8ZvHM/emL0U8C/ApAcn4Wfx81pfcmuhefxxugwslr9HCq1+0PkTKNsE7HEwpyMcWZ+ptp0u7y8NEGwLZkqTKfSJ6APAJ7s/oc+KPkTFR3m9bxGRO4XV1wF84WnLcgqY4jjgKsZSV32v9fPNgW+S1zN694F3KRpc1Gt9SfrkC7RiMZt4af42Dpy9nLzd33iet6znqJa4k4TZ7Xgnzxts8aud7nbLF8nDlC41vRH5OmaTmRdrvUjFQhUZuXYkm89spvOSzkx4YAL3hd2XLRlERG5nd1xxlJd4elsjAZjqxVGj7VHbGb1+NADP1XiOBsW8O+FbMubA2cvsPnkx1bbODOS/tv+jqeV3hl8azcv254l05dx1qB4u8zDhBcN5dfWrHDh/gD4/9OH5Gs/TO6I3ZtMdOSgsIuIRd9xP0D7WpSlGjbzzi+/U5VO8tOolklxJPFjyQfpW6+uVfsSzEvHjWfurLHHWw8/k5H3b+3S2rPZ1rJu6O//dfPHIF7Qr1w6X4eL9be/T94e+nI477etoIiK51h1VHN1FDH0s7lGjiY7HvTJqFG+P54VVLxCdEE14wXDevf9d/RWfi9ix8pJ9APMcTbCYDCbapvOc5Rsg591q5KpAayBjG41ldIPRBFgC2HBqAx2/7cjyw8t9HU1EJFe6o35rv2pdRKApiU2uiiz3wmrYTpeTIb8OYV/sPgoHFOb9pu8TZAvyeD/iXS7MvO7ozUeORwAYbFvAJNuH+GH3cbKba1+hPQvbLqRy4cpcTLrIoJ8HMWzNMC4nXb71ziIikuyOKY5KOw7T2fIzAOPs/8Ib91CbsnUKq4+txs/sx5SmUwjLE+bxPiS7mBjn6MZwe08chpmOll+Z4/cOhbh461196O78dzOn9Rz6RPTBbDLz7cFv6fBtB9acWOPraCIiucadURwZBn3jp2M2GSx11mWrUdHjXcz/Yz6zd88GYEzDMVQPre7xPiT7zXE252n7EC4aQdxn3sfXfm9SwXTc17Fuyma28WKtF5ndcjbF8xTnVNwp+q/sz+u/vk5sQqyv44mI5Hh3RnG052tqOHaQaNgY7+jq8eaX/rWUtze8DcBz1Z/TCti3mTWuCNonjeKw6y5KmaP42u9NHjNn70iMzZbx+/DVuqsWix9dzJOVnsSEiaV/LeWxbx4j8q9IDCPnzqESEfG12784SoqD5cMA+K+zLceNIh5tfvWx1QxfMxyAf93zL/pV7+fR9iVnOGgU57Gk0ax1ViHYlMj/+U3jXet0AkgE/llc0hssFguVKlfJ1L5BtiCG3DeEOa3dtx6JSYhhyK9D6PNDHw7EHvBw0n9kppgTEckpbvt1jkzrP4CLJzhtvov/Oh71aNubTm9i4OqBOA0nbcu2Zch9QzCZPD+XSXKG8+Slu/11XnB9xUvWxTxhXU1N836es79EvsCwNBeX9ISrC0w6nc5Mt1EttBoL2yzk410f8/GOj9lwagOdlnSi6z1d6V+jP/n88nkwMVSqXOWfVcg9yOkysJg9/z2mYk5EUrrtiyPOHwFMTA/qS2K8527dkWg5wgurPkhey2hUw1G6ZP8O4MLMFGdHNhr3MMX2HyqaT7DEbziRsX3AVSPNxSVzCpvFRv/q/WlTtg3vbXqPVcdWMWfvHCIPRfJ8jedpX6E9NrNnigSb1eLxQtGbq5DntmJORLzrti+OjFYTofFgNsw9CR660sgSeJizwZ9i2K9wX9H7eK/xex77pSK5w3pXFVonjmOybRoPWHbS8ex/YPYWijufZjeeHYXxtJJ5SzKl6RTWnVjH+E3jOXThEGN+G8Pnez5nQM0BNC/d3COFfk4uFK+V24o5EfGu2744wi8YAvMBJz3SnCV4P4ElPsMw2alVpBZTmkzB3+LvkbYldzlHfp6yD+FfrlW86TePgGO/8T5bmWTpyExna5x4fiTCkxoUb8CXYV+ycN9Cpu+YzuGLhxn08yAqF67MSzVfon6x+nfUaeLcVMyJiHfpPFAGWPPuIrDEJ5jMdgLslfmw+Yfk8cvj61jiQwZm5jofYtzds6FcU/xJ4g3bPJb4DaeeeY+v492SzWyjW6VuRHaI5LnqzxFkDWJP9B6eXfks3SK78dPRn3Rlm4jccVQcpZM131YCin+ByezEfjGC0Ph+BFoDfR1LcohY213w5GL+HfwSF4wgKpuPMN9vLNNs/0cJ01lfx7ulYFsw/Wv057uO3/FkpSfxt/iz89xOXvzpRTou6ch3h77D6cr8hHARkdxExdEtGfgV/pHA4gsxmVzYz9cm4UQXTF48I6krZ3Ipk4mV/s15MHEynzma4zRMtLZs5Ee/1xhsnU9+cv5tPAoFFGLIfUP4vuP39Krai2BbMPtj9zP4l8G0Xtya2btmcyHxgq9jioh4lYqjmzHZCSi2AP8iPwCQFN2IhFMdwctzSbx15Yxkj1jyMcLRk9ZJ41jjrIK/yc5z1m9Z4/8SA60LKcAlX0e8pZDAEF6p/QrLOy7n+RrPU8C/ACfjTjJ5y2Qe+t9DjFo/in0x+3wdU0TEK27/CdmZZLJFE1hiLpaAkxiGmcTT7bCfr5stfXvjypkHw0N5reU9HmtPbm2fUYon7W/wkHMrr1oXUdl8hBesX9PT8j2fOFvyieNhzpH/lu1cXWDSF5ea5/fPT7/q/Xi6ytN8d+g75u6dy77YfSz6cxGL/lxElcJVaF++Pa3KtvL4WknXSn4fPHxpvP4QEZFrqThKgzXPbgKK/Q+TJQGXI5iEE11xxpfP1gyevnKmXGiwx9qSjDCx0lWbH5Nq0ty8hZeti6lsPsIA6zf0sSxjiasBsx0t2W3cfcMW8gVavbLAZEYuNQ+wBtC+QnseK/8YW85s4Ys/vuCnoz+xO3o3u6N3M3HzRJqVasYjZR/hviL3eaXg8Nb7oD8cRORaKo5SMiXhf9dS/ApuBMAZX4orJ7phOG79173IzRiYWeGqww9JtWlu3sJz1m+pYT5IJ8svdLL8wkZXOHMczVnuupdE0l6sNCdcam4ymbi36L3cW/ReYhJiWHpwKV8d+IoD5w8QeSiSyEOR5PPLR7NSzbhiLQ6E4enT0PrDQUS8TcXR3yzBfxJQ9CvMfrEYhomk6AdIimqO3iLxpKtF0oqkOtQwHeBp6/c8Yt7AfeZ93Oe3j4tGIMuc9fjSeT+bjXAg564zVCigED2q9KB75e7sjt7NkoNLWHFkBeeunOOrA19BMOSpGIDjcjiOy5VwXK4IriBfxxYRuaU7/je/yXoR/yLfYcu/DQCXvQAJJzvjjC930/00/0Gy6nejPC/bB/AO3fiX9Uc6WX6hhOkcXa0/0dX6E0ddoXznuo/4+JbgquHruDdkMpmoGlKVqiFVGVxnMJtObeKHoz+w6I9IXJbL2PJvx5Z/O4ZhxnmlFM648jjjyuJMKAXGHf8jSERyoDv3J5MpCb9Ca/EL+QmTOQnDMGGPrU9iVEtw3XrFa81/EE85S0H+z9GJKY4O3GfaR0fLL7S2bKCUOYpnzcvg2DKYNJYBjlp8aa7CBlclLpH1ERhvFPgWs4V6xetRr3g91m96gD9id2PNsxdrnr1YAs5gDTqMNegwhILhsuG8UhpnXFkc8eVwXSnOnfwjSURyjjvvJ5EpCVuBjfiFrMZsdRc1zvhSJJxpiyuhZIab0/wH8RQDMxuMSmxwVGKk4ykeNG+npWUTLWzbCYo7Syu+p5Xf9zgMM9uNcqxxRbDOWYXtRlkSyPgtbLxd4Jsw47pSmqQrpUmKehiTLQZr8H4sQQexBP+F2XoZa/ABrMEH8AcMlxVXYhjOKyVwJpTAdaUkrqQQtOKIiGS3O6Y4cpjO4xeyEr+Cv2GyxgPgSipEYlRzHBerox/AkpNcIYDvXHX5zlWX9pVC+Pd9l1n6v5lUvrKFsubT1Dbtp7Z5Py9ZF2M3LOwxSrPVVYFtrgrsMspw2CiKK51f09lV4Bv2QtjP1/17SQwDs99ZLMF/YQk6gCXoEGZrPJbAY1gCj/2zj9MfZ0IxXIlFOeGswObTLpymnL+Ypojkbrd9cXT4wmGm/j6Vk3lX45/PBbiLoqToB7Gfr423F3QUySqnyQblm/HfYD92X7hIcaJoaNlFI/Mu7jP/QVFTLNVNf1Hd/Bc9WQ5AgmFjn1GSP1yl+MMoyR9GKfa5ShJDXnLGJG8TrqS7cCXdhT22PmBgskVjCTyOJeA45sDjWAJOYLIkYg0+BMGH+NO5np7LP4N8EByUB1diEVxJRXAlFcKwF8KVVAiXvXC6TouLiNxMpoqjuXPnMnPmTKKioqhQoQJvvPEG99577w1fv3HjRsaPH8/+/fspUqQIvXv3pmvXrpkOnRFTfp/CT8d+AhM44ktjj2mI41JVNFIkudUJQlnobMJCZxPAoBjR1Db/SS3zfmqaD1DRdJwgU2JywZTSJSOQo0YRjhh34RdVFjbXo7r9MnGmQM4YBblCgG8OChOGPQSHPQTHxRp/b3Ni9o/CHHACi/8ZioZcICAoipNxJzFbL7tPiwf/dV1LLkewu1iy58dw5MNw5MPlyIthz4fhyI/Lke/vAionFIkikhNluDiKjIxk3LhxjBw5klq1ajF//nz69OnDsmXLKFas2HWvP3bsGH379qVz585MnDiRrVu3MmrUKAoVKkTLli09chA382zEs1QLrcbCn/Px53HN55HbjYmThHDSFcISVwMAzLgoZTrDPaZjVDIf5R7TUSqZjlDKHEVe0xWqmI5QhSMQsxGWzucd4OqUpYtGIGeNgpwxCnKagkQZBYk18nCePJw33P9iyUOskYcL5CEJb94H0IIrsSiuxKI4gOphYUztVItWU39gX8xBzP5nMPtFY7ZFY/aLwWSLwWyNx2yNA2tcqtNz1zJcNnfh5Axiu70gr/9aitiAOPxCLBjOYAxn0N//AjFc/uDy//t/G/rDSuT2l+HiaPbs2XTs2JHOnTsDMGzYMNasWcO8efMYOHDgda+fP38+YWFhDBs2DIBy5cqxc+dOZs2alS3F0T2F7qFKaBW++ulXwLcL6IlkBxdmDhthHDbC+N51X/J2f5IoYYqitOkMpU1neDD0Mo1D4zh2cA+FnFEEmxLJZ7pCPtMVynMyXX3FGf5cJJg4I4A4Aog3Ash7PD8sKs4LcZc4bjUTRwCJhh+J2EjERhJWkoy//+ef/xMNm/v/vz+2G1acmHFhxoGZQGdeSLxEoAGWhDCcCcVxYCLVCJA5AbMtxl0sWS9isl7EbL2IyXoJk+2C+7ElAZPZjskvGogmxjjG0r92gD/4h976mA2nH4bhD053wWS4/P4pngwrhmEFw8p5/2Cm/b4TP4sf/hZ//Mx+yY/9Lf74WdwfW81WLCYLVrM19WOTFYvZct3zZkPFmYi3Zag4SkpKYvfu3fTt2zfV9oYNG7Jt27Y09/n9999p2LBhqm33338/X375JXa7PV13oDcMI7n/jK4D5HK55xlVKhqMvwenF5UpHIjT6VS7ater7Xq+7RDOU4nzQN4KITRqVpEpX27nr7OXCSCBQq4YCrpiKeSKpaArhoKu8wQbl8hnXCYPl8njukRe4zLBRhwWXAQAASQACf90kQjOP7bTHPDoWbrD4JwI/wPI88/mqwWUEwsuTLhMZlxYcDnMuBxmDEwYJncBZWAiwQQxZjMxFhOXzCYSbGbs/hZOOZxcMMFlM1wym7hkdj9OMMMVkwnX1RrMDGD/+9+NJ4cnAbN3/uLBN8DNZMDjwfdSufLkDP88dDqdwD8/U0UkbSYjA98lZ86c4YEHHmDevHnUqlUrefuHH37IV199xfLly6/bp2XLlrRv355+/folb9u6dStdu3bl119/pUiRIrfsNykpiZ07d6Y3poiI3ERERAR+fmnfpkZEMjkh22RKPZHRMIzrtt3q9WltvxGr1UpERARmsznd+4iISGqGYeByubBab/sLlUWyJEPfIQULFsRisXDu3LlU26OjowkJCUlzn5CQEKKiolJti4mJwWq1UqBAgXT1azab9VeOiIiIZIsMzezz8/OjSpUqrF27NtX2devWUbNmzTT3qVGjBuvWrUu1bc2aNVStWjVd841EREREslOGL3vo2bMnixYtYtGiRRw8eJB33nmHU6dO0aVLFwAmTZrE4MGDk1/fpUsXTp48ybhx4zh48CCLFi3iyy+/pFevXp47ChEREREPyfCJ59atWxMbG8u0adM4e/YsFStWZPr06RQvXhyAqKgoTp06lfz6kiVLMn36dMaNG8fcuXMpUqQIw4YNy5bL+EVEREQyKkNXq4mIiIjc7rSamIiIiEgKKo5EREREUlBxJCIiIpKCiiMRERGRFG774mju3Lk0bdqUiIgIOnTowObNm30dKU0fffQRHTt2pGbNmtSvX5/nnnuOv/76y9ex0u2jjz4iPDyct99+29dRbujMmTMMGjSIunXrUr16ddq1a8euXbt8HStNDoeDf//73zRt2pRq1arRrFkzPvjgg+R7Bfrapk2b6NevH40aNSI8PJyVK1emet4wDN5//30aNWpEtWrV6N69O/v37/dR2pvntdvtTJw4kbZt21KjRg0aNWrE4MGDOXPmTI7Me60RI0YQHh7OJ598kn0BRW5zt3VxFBkZybhx4+jfvz9ff/01tWvXpk+fPpw8mb47jmenjRs30q1bNxYuXMjs2bNxOp0888wzxMfH+zraLe3YsYMFCxYQHh7u6yg3dOHCBbp27YrNZmPGjBksW7aMoUOHki9fPl9HS9OMGTOYP38+I0aMIDIyktdee42ZM2fy+eef+zoaAPHx8YSHhzNixIg0n58xYwazZ89mxIgRLFq0iJCQEHr27Mnlyze+Uas33SxvQkICe/bsoX///ixevJgPPviAw4cP079/fx8kdbvV+3vVypUr2b59e7ruUSkiGWDcxjp16mSMGDEi1baHH37YeO+993yUKP2io6ONihUrGhs3bvR1lJu6fPmy0aJFC2Pt2rXGk08+aYwdO9bXkdI0ceJEo2vXrr6OkW59+/Y1Xn/99VTbBgwYYAwaNMhHiW6sYsWKxg8//JD8scvlMho2bGh89NFHydsSExON2rVrG/PmzfNFxFSuzZuW7du3GxUrVjROnDiRTalu7EZ5T58+bdx///3Gn3/+aTRp0sSYPXt29ocTuU3dtiNHSUlJ7N69m0aNGqXa3rBhQ7Zt2+ajVOl36dIlAPLnz+/jJDc3evRoGjduTIMGDXwd5aZWrVpF1apVefHFF6lfvz6PPfYYCxcu9HWsG6pduza//fYbhw4dAuCPP/5gy5YtNG7c2MfJbu348eNERUWl+t7z8/OjTp06ueJ7D+Dy5cuYTKYcO7Locrl47bXXeOaZZ6hQoYKv44jcdm7bWzPHxsbidDopXLhwqu1p3Qg3pzEMg3HjxlG7dm0qVqzo6zg3tGzZMvbs2cOiRYt8HeWWjh07xrx58+jZsyf9+vVjx44djB07Fj8/Px577DFfx7tOnz59uHTpEq1atcJiseB0OnnllVdo06aNr6Pd0tXvr7S+93LiKe1rJSYm8t5779GmTRvy5Mnj6zhpmjFjBlarlR49evg6isht6bYtjq4ymUypPjYM47ptOc3o0aP5888/+eKLL3wd5YZOnTrF22+/zaxZs/D39/d1nFsyDIOqVavy6quvAlC5cmUOHDjAvHnzcmRxFBkZybfffsukSZMoX748e/fuZdy4cRQpUoT27dv7Ol66pPW9l9PZ7XZeeeUVDMPgrbfe8nWcNO3atYvPPvuMxYsX5/ifZSK51W1bHBUsWBCLxcK5c+dSbY+OjiYkJMRHqW5tzJgxrFq1ijlz5lC0aFFfx7mh3bt3Ex0dTYcOHZK3OZ1ONm3axNy5c9m5cycWi8WHCVMLDQ2lXLlyqbaVLVuW5cuX+yjRzU2YMIG+ffvyyCOPABAeHs7Jkyf56KOPcnxxFBoaCsC5c+dSTRTO6d97drudl19+mePHj/Ppp5/m2FGjzZs3Ex0dTZMmTZK3OZ1O3n33XT777DNWrVrlw3Qit4fbtjjy8/OjSpUqrF27lubNmydvX7duHc2aNfNhsrQZhsGYMWP44Ycf+PzzzylZsqSvI91UvXr1WLJkSaptr7/+OmXLlqVPnz45qjACqFWrVvL8nasOHz6cfMPknCYhIeG6UQGLxZIrRl9KlChBaGgoa9eupXLlyoB7DuCmTZsYNGiQj9Ol7WphdOTIET777DMKFizo60g31K5du+vm+D3zzDO0a9cu1R8rIpJ5t21xBNCzZ08GDx5M1apVqVmzJgsWLODUqVN06dLF19GuM2rUKJYuXcq0adMIDg5OnreRN29eAgICfJzuenny5LluPlRQUBAFChTIkfOknnrqKbp27cqHH35Iq1at2LFjBwsXLmT06NG+jpamJk2a8OGHH1KsWLHk02qzZ8+mY8eOvo4GQFxcHEePHk3++Pjx4+zdu5f8+fNTrFgxevTowUcffUSZMmUoXbo0H330EQEBAT6bM3WzvEWKFOHFF19kz549fPTRRzidzuTvv/z58+Pn55ej8hYrVuy64s1msxESEkLZsmWzO6rIbclk5IY/RbNg7ty5zJw5k7Nnz1KxYkVef/116tSp4+tY17nRGkHjxo3LNX8Ndu/enXvuuYdhw4b5OkqafvrpJyZPnszhw4cpUaIEPXv25PHHH/d1rDRdvnyZKVOmsHLlSqKjoylSpAiPPPIIzz//vE9+WV9rw4YNaU4Gbt++PePHj8cwDD744AMWLFjAhQsXqF69OiNGjPBZ4XyzvAMGDLjhaPJnn31G3bp1vR3vOrd6f6/VtGlTevTowdNPP50N6URuf7d9cSQiIiKSEbftOkciIiIimaHiSERERCQFFUciIiIiKag4EhEREUlBxZGIiIhICiqORERERFJQcSQiIiKSgoojERERkRRUHImIiIikoOJIREREJAUVRyIiIiIpqDgSERERSeH/AWXc871ZHvCJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.arange(0, len(p)+0.1, 0.1)\n",
    "y1 = d.probability(x.reshape(-1, 1))\n",
    "y2 = model.distributions[1].probability(x.reshape(-1, 1))\n",
    "\n",
    "\n",
    "plt.figure(figsize=(6, 3))\n",
    "plt.hist(X[:,0], density=True, bins=numpy.arange(0, len(p), 1))\n",
    "plt.plot(x, y1, label=\"Poisson\")\n",
    "plt.plot(x, y2, label=\"Poisson in Mixture\")\n",
    "plt.legend(loc=(1.05, 0.4))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56cffd0c",
   "metadata": {},
   "source": [
    "Alternatively, we can use the ZeroInflated wrapper to do this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "77784dff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d0 = Poisson()\n",
    "d = ZeroInflated(d0).fit(X)\n",
    "\n",
    "y3 = d0.probability(x.reshape(-1, 1))\n",
    "\n",
    "plt.figure(figsize=(6, 3))\n",
    "plt.hist(X[:,0], density=True, bins=numpy.arange(0, len(p), 1))\n",
    "plt.plot(x, y1, label=\"Poisson\")\n",
    "plt.plot(x, y2, label=\"Poisson in Mixture\")\n",
    "plt.plot(x, y3, label=\"Poisson in ZIP\")\n",
    "plt.legend(loc=(1.05, 0.4))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a85dfcfe",
   "metadata": {},
   "source": [
    "The ZeroInflated wrappers extends to multivariate distributions in a way that the mixture model implementation doesn't. Simply, using a DiracDelta by itself will give a zero probability to all examples that have one or more non-zero values. Because we want each feature to be scored independently, in that all zeroes in the matrix have some probability of belonging to the DiracDelta component, we need to modify the internals slightly. Here is the result of using that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "f4e3a7d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([3.1120, 2.9900, 3.0660]),\n",
       " tensor([3.3898, 3.2569, 3.3397]),\n",
       " tensor([5.4776, 5.2811, 5.5329]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = numpy.array([30, 1, 3, 7, 8, 7, 4, 3, 2, 1, 2, 1, 1, 1])\n",
    "X = numpy.random.choice(len(p), size=(500, 3), p=p/p.sum())\n",
    "\n",
    "d = Poisson().fit(X)\n",
    "\n",
    "model = GeneralMixtureModel([DiracDelta([1, 1, 1]), Poisson([1.0, 1.0, 1.0])]).fit(X)\n",
    "model.distributions[1].lambdas\n",
    "\n",
    "ZIP = ZeroInflated(Poisson()).fit(X)\n",
    "\n",
    "d.lambdas, model.distributions[1].lambdas, ZIP.distribution.lambdas"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}