LightGBM_Reproduce_Poisson_Loss.ipynb

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      "name": "LightGBM_Reproduce_Poisson_Loss.ipynb",
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      "authorship_tag": "ABX9TyP6V/4uZT1BRvHnWVjHMbWJ",
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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/sasha-kap/Programming/blob/master/LightGBM_Reproduce_Poisson_Loss.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CXNckn2NB_ke"
      },
      "source": [
        "import lightgbm as lgb\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xdWrUVty9HQ4",
        "outputId": "cc14de43-3608-4a2c-9047-6438701fff8d"
      },
      "source": [
        "print(f\"The LightGBM version is {lgb.__version__}.\")"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The LightGBM version is 2.2.3.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GXx2LKN2TPaU"
      },
      "source": [
        "#### Define objective and evaluation functions\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vYd6T_JhA24o"
      },
      "source": [
        "def poisson_loss(y_true, y_pred):\n",
        "    \"\"\"Custom objective function that reproduces LightGBM's built-in Poisson\n",
        "    objective.\n",
        "\n",
        "    Parameters:\n",
        "    -----------\n",
        "    y_true : array-like of shape = [n_samples]\n",
        "        The target values\n",
        "    y_pred : array-like of shape = [n_samples]\n",
        "        The predicted values.\n",
        "        Predicted values are returned before any transformation, e.g. they are\n",
        "        raw margin instead of probability of positive class for binary task.\n",
        "\n",
        "    Returns:\n",
        "    --------\n",
        "    grad : array-like of shape = [n_samples]\n",
        "        The value of the first order derivative (gradient) of the loss with\n",
        "        respect to the elements of y_pred for each sample point.\n",
        "    hess : array-like of shape = [n_samples]\n",
        "        The value of the second order derivative (Hessian) of the loss with\n",
        "        respect to the elements of y_pred for each sample point.\n",
        "\n",
        "    Notes:\n",
        "    ------\n",
        "    0.7 is the default value of poisson_max_delta_step parameter used for\n",
        "    Poisson regression to safeguard optimization\n",
        "    (https://lightgbm.readthedocs.io/en/latest/Parameters.html)\n",
        "\n",
        "    This 0.7 value enters the hessian in this manner in the library's C++ code\n",
        "    (https://github.com/microsoft/LightGBM/blob/master/src/objective/regression_objective.hpp#L446)\n",
        "    \"\"\"\n",
        "    # loss here is the negative log-likelihood for Poisson regression\n",
        "    loss = np.exp(y_pred) - y_true * y_pred\n",
        "    grad = np.exp(y_pred) - y_true\n",
        "    hess = np.exp(y_pred + 0.7)\n",
        "\n",
        "    return grad, hess"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QS_PcTkVVjkD"
      },
      "source": [
        "def poisson_eval_metric(y_true, y_pred):\n",
        "    \"\"\"Custom evaluation function that reproduces the results of LightGBM's\n",
        "    built-in Poisson evaluation metric (negative log-likelihood).\n",
        "\n",
        "    Parameters:\n",
        "    -----------\n",
        "    y_true : array-like of shape = [n_samples]\n",
        "        The target values\n",
        "    y_pred : array-like of shape = [n_samples]\n",
        "        The predicted values.\n",
        "        Predicted values are returned before any transformation, e.g. they are\n",
        "        raw margin instead of probability of positive class for binary task.\n",
        "\n",
        "    Returns:\n",
        "    --------\n",
        "    eval_name : str\n",
        "        The name of evaluation function (without whitespace)\n",
        "    eval_result : float\n",
        "        The eval result\n",
        "    is_higher_better : bool\n",
        "        Is eval result higher bettr, e.g., AUC is is_higher_better\n",
        "    \"\"\"\n",
        "    return 'poisson_metric', np.mean(np.exp(y_pred) - y_true * y_pred, axis=0), False"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N46eWx4NWRcD"
      },
      "source": [
        "#### Create dataset for model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "zcESJSEnhHuW",
        "outputId": "fdb6863d-a8e8-44ea-e6bf-b723e8033596"
      },
      "source": [
        "n = 1000\n",
        "\n",
        "rng = np.random.RandomState(42)\n",
        "\n",
        "x1 = rng.uniform(0, 4, n)\n",
        "x2 = rng.uniform(0, 1.5, n)\n",
        "x3 = rng.normal(0, 3, n)\n",
        "\n",
        "mu = np.exp(1 - 0.2 * x1 - 0.3 * x2 - 0.01 * x3)\n",
        "y = rng.poisson(mu, size=n)\n",
        "\n",
        "df = pd.DataFrame({'y': y, 'x1': x1, 'x2': x2, 'x3': x3})\n",
        "df.head()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "      <th>0</th>\n",
              "      <td>3</td>\n",
              "      <td>1.498160</td>\n",
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              "   y        x1        x2        x3\n",
              "0  3  1.498160  0.277699 -2.633948\n",
              "1  1  3.802857  0.812851 -2.480641\n",
              "2  2  2.927976  1.309419 -0.679437\n",
              "3  0  2.394634  1.098337  1.102097\n",
              "4  1  0.624075  1.209842  2.740754"
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          "metadata": {},
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    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nVDYb5BtPzgL",
        "outputId": "729016b1-f9b5-4536-b079-65792738c001"
      },
      "source": [
        "df['y'].value_counts().sort_index()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    241\n",
              "1    341\n",
              "2    221\n",
              "3    126\n",
              "4     45\n",
              "5     19\n",
              "6      7\n",
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          "metadata": {},
          "execution_count": 6
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lJ0RjE1gWf0Z"
      },
      "source": [
        "#### Run Poisson regression with built-in Poisson objective and evaluation functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2Xjs83WVhdId",
        "outputId": "ff392e4a-f5a6-4657-ed17-4a6ea8a9ad24"
      },
      "source": [
        "model = lgb.LGBMRegressor(\n",
        "    objective='poisson',\n",
        "    learning_rate=0.1,\n",
        "    n_estimators=100\n",
        ")\n",
        "\n",
        "# using LightGBM's scikit-learn API\n",
        "# to make the results match, the init_score is set to the log of the mean of\n",
        "# the target values.\n",
        "model.fit(\n",
        "    df[['x1', 'x2', 'x3']].to_numpy(),\n",
        "    df['y'].to_numpy(),\n",
        "    init_score=np.repeat([np.log(np.mean(df['y']))], len(df['y'])),\n",
        "    eval_set=[(df[['x1', 'x2', 'x3']], df['y'].to_numpy())],\n",
        "    eval_metric='poisson',\n",
        "    eval_names=['Train'],\n",
        "    verbose=20,\n",
        ")"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[20]\tTrain's poisson: 0.879023\n",
            "[40]\tTrain's poisson: 0.819204\n",
            "[60]\tTrain's poisson: 0.77684\n",
            "[80]\tTrain's poisson: 0.74138\n",
            "[100]\tTrain's poisson: 0.71657\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LGBMRegressor(boosting_type='gbdt', class_weight=None, colsample_bytree=1.0,\n",
              "              importance_type='split', learning_rate=0.1, max_depth=-1,\n",
              "              min_child_samples=20, min_child_weight=0.001, min_split_gain=0.0,\n",
              "              n_estimators=100, n_jobs=-1, num_leaves=31, objective='poisson',\n",
              "              random_state=None, reg_alpha=0.0, reg_lambda=0.0, silent=True,\n",
              "              subsample=1.0, subsample_for_bin=200000, subsample_freq=0)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "id": "3UDXNbPxnewX",
        "outputId": "44ebfd0e-9067-4c17-faa5-9b9a208cfd15"
      },
      "source": [
        "# Plot Poisson evaluation metric against boosting iterations\n",
        "lgb.plot_metric(model, metric='poisson', figsize=(8,6))\n",
        "plt.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SB5vZIGAQQGpqKoWFhRVW2MCcQzw8YR8DXxjD7zrFEGZWYa9dnZWUlFRoO8v/Uht7T21cOdTOVZ+XIaAYaFBqOcO/7gjn3Fr8ZwLMLA641Dm3zb+t2P/vcjMrBNoBy8ocPwQYApCbm+sKCgoq9AeIqLuae96fw5yDGfy6T06FvnZ1VVhYSEW3s/w3tbH31MaVQ+1c9Xl5OWAKkGNm2WYWBQwA/quXv5mlmNnhGu4DXvavr21m0Yf3AboD8z2s9aiu6NiAi9ul87dRiylctKGy315ERMRTnoUA59wB4FbgS2ABMMw5N8/MHjGzw739C4BFZrYYqAs87l/fHJhqZrPwdRj8k3Ou0kOAmfHExa3IrRvPHe/O1PwBIiISVDztE+CcGwmMLLPuwVLPhwPDj3LcBKCVl7WVV42ocF74WQcuePZbfvXWdN67uSsxkeGBLktEROS0acbAcshKieXpK9oyp3g7g0fMC3Q5IiIiFUIhoJz65NXl1t5NGDplDUMnrw50OSIiIqdNIeAk/OaspvTMSeHBj+cxu2hboMsRERE5LQoBJyE8zPj7gHakxkdz8xvT2FyyN9AliYiInDKFgJOUFBvFCz/rwKYf93H70Bkc0I2GRESkmlIIOAWtMhJ57KKWfLd0M3/RjYZERKSaUgg4RVd0bMBV+Q15YewyPp+zLtDliIiInDSFgNPw0AV5tG1Qi7vem8Xi9TsDXY6IiMhJUQg4DdER4Tz/s/bUjI7gmn9/z+rNmlFQRESqD4WA01Q/sQZv3NCZvQcOcdVLk1i3fXegSxIRESkXhYAK0KxeAq9f35ltu/Zz9b++Z+NODR0UEZGqTyGggrTOqMUr13Vi7fbdXPPv79m2a1+gSxIRETkuhYAK1CkriX/9vCPLN/7IwFemsGvfgUCXJCIickwKARWsZ04q/7iqHXOKtnHb25pMSEREqi6FAA/0bVGPh/u3ZNTCDTw4Yh7OuUCXJCIi8j8iAl1AsLqmSyZrt+3m+cJlpNeqwS29mwS6JBERkf+iEOCh352dy7ptu/nzl4tIqxXDxe0yAl2SiIjIEQoBHgoLM568rA3rd+zl7uGzqVUjit7N6gS6LBEREUB9AjwXFRHGC9d0ILdePIPemMoXc3WfARERqRoUAipBYo1I3rqxC63SE7nl7Rl8PLM40CWJiIgoBFSWxBqRvHFDPp2yanPHuzMZOnl1oEsSEZEQpxBQiWKjI3j1us70yknl3g/m8Op3KwJdkoiIhDCFgEoWExnOkJ93oG+Lugz+ZD5Dxi0LdEkiIhKiFAICIDoinGevas95revzxMiFPDdmaaBLEhGREKQhggESGR7G33/alsgw489fLmLfgUPc0ScHMwt0aSIiEiIUAgIoIjyMp65oS0R4GH8ftYQDhw5x19m5CgIiIlIpFAICLDzMePLS1kSGh/HcmGVs2LGXxy5uSXREeKBLExGRIKcQUAWEhRlPXNySlLgo/jF6KSs2/cgL13QgJS460KWJiEgQU8fAKsLMuPPsXP5xZTvmrt1O/2e/Y97a7YEuS0REgphCQBVzQZs03vtFNw4eclz2/ERNMywiIp5RCKiCWmUkMuLW7uTWi+eXb03XpEIiIuIJhYAqqk5CDEMHdeGs5r5Jhf44cgGHDrlAlyUiIkFEIaAKi4kM5/mfdeCaLpm8OG45vxk2k30HDgW6LBERCRIaHVDFhYcZj/RvQb3EGP785SI27tzL81d3ILFmZKBLExGRas7TMwFm1s/MFpnZUjO79yjbM81slJnNNrNCM8sotW2gmS3xPwZ6WWdVZ2bc0rsJT13ehikrt3D+s+OZW6yRAyIicno8CwFmFg48B5wD5AFXmllemd3+ArzunGsNPAL80X9sEvAQkA90Bh4ys9pe1VpdXNohg3d/0ZUDBx2XPD+Bd6fodsQiInLqvDwT0BlY6pxb7pzbBwwF+pfZJw8Y7X8+ptT2vsDXzrktzrmtwNdAPw9rrTbaN6zNp7f1ID87iXven8Pv3pvFnv0HA12WiIhUQ16GgHRgTanlIv+60mYBl/ifXwzEm1lyOY8NWclx0bx6XWduP6MJ700r4qdDJrH1x32BLktERKqZQHcMvAt41syuBcYBxUC5/6w1s0HAIIDU1FQKCws9KLHqah8Ft7WL5vlZ2zjvr99wV6cYkmK8HfBRUlIScu1c2dTG3lMbVw61c9XnZQgoBhqUWs7wrzvCObcW/5kAM4sDLnXObTOzYqCgzLGFZd/AOTcEGAKQm5vrCgoKyu4S9AqA7p02c+NrU3lqJrx+Q0cap8Z59n6FhYWEYjtXJrWx99TGlUPtXPV5+WfjFCDHzLLNLAoYAIwovYOZpZjZ4RruA172P/8SONvMavs7BJ7tXydH0aVRMkMHdWHP/oNc8cJEjRwQEZFy8SwEOOcOALfi+/JeAAxzzs0zs0fM7EL/bgXAIjNbDNQFHvcfuwV4FF+QmAI84l8nx9AyPZH3bu5KTGQ4A4ZM0j0HRETkhDztE+CcGwmMLLPuwVLPhwPDj3Hsy/znzICUQ6PUOIb/sis3vzmdm9+czrXdsvj9uc2JitDEkCIi8r/07RBk6ifW4L1fdOW67lm8OmEll78wgTVbdgW6LBERqYIUAoJQVEQYD13Qguevbs/yjT9y3jPjGb1wfaDLEhGRKkYhIIid06o+n97egwZJNbnxtam8olsSi4hIKQoBQS4zOZb3bu7Kmc3r8vAn83no47kcOKg7EYqIiEJASKgZFcELP+vATT2zeW3iKm56fSolew8EuiwREQkwhYAQER5m3H9eHo9f3JJxSzZx2fMTWLqhJNBliYhIACkEhJir8zN55dpOrN+xh/P/MZ43Jq3CORfoskREJAAUAkJQr6apfHlHLzpnJ/OHj+Zy/atT2Lhzb6DLEhGRSqYQEKLqJMTw2nWdGHxBHhOWbabf38ZpGKGISIhRCAhhZsa13bP55LYe1EmI4fpXp/LHkQvYr9EDIiIhQSFAaFo3ng9/1Y2r8xvy4rjl/PTFiazdtjvQZYmIiMcUAgSAmMhwHr+4Ff+4sh2L15dw7jPjGbVAlwdERIKZQoD8lwvapPHJbT1IS6zBDa9N5bfvzmTLj/sCXZaIiHhAIUD+R3ZKLB/8qhu3ndGEEbPW0uevY/loRrGGEoqIBBmFADmqmMhw7jw7l09v70HDpJrc8e5MBr4yhc271WlQRCRYKATIcTWrl8D7v+zG4AvymLZyC3/4bjdfzvsh0GWJiEgFUAiQEwoP8w0l/Oz2ntSpGcYv3pjGQx/PZc/+g4EuTUREToNCgJRbVkos93eJ4fruvhsRXfr8BJZv1P0HRESqq3KHADMLN7M0M2t4+OFlYVI1RYYZD16Qx0s/70jxtt2c/49veXfKanUaFBGphsoVAszsNmA98DXwmf/xqYd1SRXXJ68uI2/vSZuMWtzz/hx+8cY0Npfo/gMiItVJec8E/BrIdc61cM618j9ae1mYVH1ptWrw1o353H9ucwoXbaTv38YzZtGGQJclIiLlVN4QsAbY7mUhUj2FhRk39WrER7d0Jyk2kutemcJvh81kw449gS5NREROIKKc+y0HCs3sM+DIOV/n3F89qUqqnby0BEbc2oNnRi3hpfEr+HLuD9x6Rg7X98giOiI80OWJiMhRlPdMwGp8/QGigPhSD5EjYiLDubtfM776TS+6Nk7h/75YSN+nxzFqwXp1HBQRqYLKdSbAOfcwgJnF+Zc1LkyOKSsllpcGdmTs4o088sk8bnhtKr2apvKH85qTU1fZUUSkqijv6ICWZjYDmAfMM7NpZtbC29KkuvtJ01S+uKMXD56fx8zVW+n39/EMHjGPbbt0QyIRkaqgvJcDhgC/dc5lOucygTuBf3lXlgSLyPAwru+RTeHvenNl5wa8PnElBX8pZMi4ZezepxkHRUQCqbwhINY5N+bwgnOuEIj1pCIJSkmxUTx2USs+u70nrdITeWLkQno+OYaXv12h6YdFRAKkvCFguZn9wcyy/I8H8I0YEDkpzesn8MYN+bx3c1dy6sTxyKfzKfhzIe9MXs2hQ+o8KCJSmcobAq4HUoEP/I8U/zqRU9IpK4l3BnXh7ZvySa9dg/s+mMPlL05k0Q87A12aiEjIKO/ogK3A7eC7hwC+ywM7vCxMQkO3xil0vTmZ96cX8/hn8znvmfH84ieNuO2MHGIiNb+AiIiXyjs64G0zSzCzWGAOMN/MfudtaRIqzIzLOmQw6s4CLmybxnNjltH3b+MYMWstB3WJQETEM+W9HJDn/8v/IuBzIBu4xrOqJCQlxUbx1yva8vaN+USFh3H7OzPo+7dxfDyzWGFARMQD5Q0BkWYWiS8EjHDO7Qf0W1k80a1JCl/e0Ytnr2pHmMGvh87k7KfH8vmcdZp5UESkApU3BLwIrMQ3LHCcmWUCJ+wTYGb9zGyRmS01s3uPsr2hmY0xsxlmNtvMzvWvzzKz3WY20/94ofw/kgSDsDDj/NZpfPHrXvzz6vZEhIXxy7emc9PrU1m7bXegyxMRCQrlCgHOuWecc+nOuXOdzyqg9/GO8XcgfA44B8gDrjSzvDK7PQAMc861AwYA/yy1bZlzrq3/cXN5fyAJLmFhxrmt6vPZ7T24/9zmfLt0E2f9dSyvT1ypIYUiIqepvB0Df+3vGGhm9m8zmw6ccYLDOgNLnXPLnXP7gKFA/zL7OCDB/zwRWHsStUsIiQgP46Zejfjqjp/QPrM2D348j8temMC8tbrDtYjIqbLyXGM1s1nOuTZm1hf4BfAH4A3nXPvjHHMZ0M85d6N/+Rog3zl3a6l96gNfAbXxXWro45ybZmZZ+O5TsBjfZYcHnHPjj/Ieg4BBAKmpqR2GDRtWrh9aTl1JSQlxcXEBrcE5x4S1Bxi6cB8l++GMhhFckhNFbKQFtK6KUhXaONipjSuH2tl7vXv3nuac63iqx5drngDg8G/Xc/F9+c8zs4r4jXsl8Kpz7ikz6wq8YWYtgXVAQ+fcZjPrAHxkZi3Kzk3gnBuC774G5ObmuoKCggooSY6nsLCQqtDOvYFbd+3nr18v4o1Jq5ixOYy7++ZyRccGhIVV7zBQVdo4mKmNK4faueorb8fAaWb2Fb4Q8KWZxQOHTnBMMdCg1HKGf11pNwDDAJxzE4EYIMU5t9c5t9m/fhqwDGhazlolRCTWjOTh/i359LaeNE6N5d4P5nD+P76lcNEGjSIQESmH8oaAG4B7gU7OuV1AFHDdCY6ZAuSYWbaZReHr+DeizD6rgTMBzKw5vhCw0cxS/R0LMbNGQA66V4EcQ15aAsN+0ZW/D2jLzr37ufaVKQwYMolpq7YGujQRkSrtuCHAzJr5n7b1/9vIzNoDmZzgUoJz7gBwK/AlsADfKIB5ZvaImV3o3+1O4CYzmwW8A1zrfH/C9QJmm9lMYDhws3Nuy8n/eBIqzIz+bdMZ9dsCHunfgmUbf+TS5ydw0+tTWbqhJNDliYhUSSfqE/BbfB3vnjrKNscJRgg450YCI8use7DU8/lA96Mc9z7w/glqE/kfURFh/LxrFpe2z+CV71bw4tjl9P3bOK7q3JBf98khJS460CWKiFQZJ/prfpD/3+POCSBS1cRGR3DrGTlc2bkhfx+1hLe+X82HM4r5ZUFjbuiRrZsTiYhQ/nkCIs3sdjMb7n/c6p9GWKRKS46L5pH+Lfnyjl50aZTMn79cxJlPjeWz2ZqCWESkvB0Dnwc64JvR75/+5897VZRIRWtSJ46XBnbk7ZvyiY+J4Ja3p/PTIZM02ZCIhLTyzhPQyTnXptTyaH9nPpFqpVvjFD67vSdDp6zmqa8Wc/4/vuWnHRtw25k5pNeqEejyREQqVXnPBBw0s8aHF/zD9g56U5KIt8LDjKvzMxlzVwHXdcvm/elFFPx5DPd9MIc1W3YFujwRkUpT3jMBvwPGmNnhsfpZnHieAJEqLbFGJA9ekMcNPbN5oXAZ705Zw3tT13Bp+wxuO7MJGbVrBrpEERFPlfdMwHf4bid8CNjifz7Rq6JEKlN6rRo8elFLxt5dwNX5DflwZjFn/GUsT4xcwPZd+wNdnoiIZ8obAl4HsoFHgX8AjYA3vCpKJBDqJ9bg4f4tKbyrgAvapPGv8cvp9ecxvDR+OXsP6HCP8LQAACAASURBVOqXiASf8oaAls65G51zY/yPm4AWXhYmEihptWrw1BVt+Oy2nrTOSOSxzxbQ569jGTlHwwpFJLiUNwRMN7MuhxfMLB+Y6k1JIlVDXloCb9yQz+vXdyY2KoJfvTWdK16cyKw12wJdmohIhShvCOgATDCzlWa2El9/gE5mNsfMZntWnUgV0KtpKp/d3pMnLm7Fik0/0v+57/jNuzM1kkBEqr3yjg7o52kVIlVceJhxVX5DLmhTn38WLuPf365gxKy1XNwunV8VNKZRalygSxQROWnlCgHOuVVeFyJSHcTHRHJPv2b8vGsmQ8Yt5+3vV/PB9CLOa53GbWc0oWnd+ECXKCJSbuW9HCAipdRPrMFDF7Tg23vOYFCvxoxesJ5+fxvH4BHz2L5bwwpFpHpQCBA5Danx0dx7TjO+vecMrs7P5PWJKznzqULem7qGQ4c0kkBEqjaFAJEKUDs2ikcvasmIW3vQMKkmvxs+m8temMD4JRs1rFBEqiyFAJEK1DI9keE3d+PPl7Vm9ZbdXPPvyZz19DjenLSKXfsOBLo8EZH/ohAgUsHCwozLOzbgu3t789TlbYiJDOOBj+bS5YlRPPnFQvUZEJEqo7xDBEXkJEVHhHNphwwuaZ/OtFVbefm7FTw/dhnvTF7N7WfmcHV+JlERyuEiEjj6DSTiMTOjY1YS/7y6A5/c2oO8tAQe/mQ+Zz/tm4pYHQhFJFAUAkQqUcv0RN68IZ9XrutEdEQ4v3prOn3/No5hU9foJkUiUul0OUCkkpkZvXPr0CsnlRGzihkybgV3D5/NX75cxLXds8jcrzMDIlI5FAJEAiQ8zLi4XQYXtU3n26WbGDJuOU9+sYiYcJi9fwHX98imbkJMoMsUkSCmECASYGZGz5xUeuakMn/tDh55bwL/Gr+cV75byaUd0hnUqzHZKbGBLlNEgpD6BIhUIXlpCdzcJobCu3pzRacM3p9ezBlPFXLzG9OYtmpLoMsTkSCjMwEiVVDD5Jo8dlErbj8zh1e/W8lb36/mi3k/0L5hLQb1asRZefUID7NAlyki1ZzOBIhUYXXiY7i7XzMm3HsGgy/IY2PJXm5+czpnPFXIm5NWsWe/RhSIyKlTCBCpBmKjI7i2ezaFd/Xmuavak1gjkgc+mkuP/xvNs6OXsG3XvkCXKCLVkC4HiFQj4WHGea3rc26rekxavoUXxy3jL18t5rkxy7ioXRpX52fSMj0x0GWKSDWhECBSDZkZXRsn07VxMgvW7eCV71bw4Yxi3pm8hjYZiVydn8n5bepTM0r/i4vIselygEg117x+Ak9e1obvf9+HwRfksWvfQe5+fzadHx/FfR/MYeaabbqdsYgclf5MEAkSiTUiubZ7NgO7ZTFl5VaGTlnNhzOKeGfyaprVi+fyjg24pF06tWOjAl2qiFQRCgEiQcbM6JydROfsJAZf2IJPZq1l2JQ1PPrpfP7vi4X0a1GPAZ0b0LVRMmYaZigSyhQCRIJYQkwkV+dncnV+JgvW7eDdKWv4YHoRI2atJSu5Jld0asBl7TOoo+mJRUKSp30CzKyfmS0ys6Vmdu9Rtjc0szFmNsPMZpvZuaW23ec/bpGZ9fWyTpFQ0Lx+AoMvbMHk+/vw9E/bUCchhie/WETXP43mxtem8s389Rw4eCjQZYpIJfLsTICZhQPPAWcBRcAUMxvhnJtfarcHgGHOuefNLA8YCWT5nw8AWgBpwDdm1tQ5p5lRRE5TTGQ4F7fL4OJ2GSzfWMKwqUUMn1bENwvWkxofzSXt0rm0QwZN68YHulQR8ZiXlwM6A0udc8sBzGwo0B8oHQIckOB/ngis9T/vDwx1zu0FVpjZUv/rTfSwXpGQ0yg1jnvPacadZzdlzMINvDetiH9/u4IXxy2ndUYil3XIoH+bdBJrRga6VBHxgHk1dMjMLgP6Oedu9C9fA+Q7524ttU994CugNhAL9HHOTTOzZ4FJzrk3/fv9G/jcOTe8zHsMAgYBpKamdhg2bJgnP4v8R0lJCXFxcYEuI6gFuo137HVMXHeA74oPsHrnIaLCoEtaBGc2jCAzITxgdVWkQLdxqFA7e693797TnHMdT/X4QHcMvBJ41Tn3lJl1Bd4ws5blPdg5NwQYApCbm+sKCgq8qVKOKCwsRO3srarQxhf6/51bvJ03J63io5nFjCvaQ4fM2lzTJZN+LesRE1l9A0FVaONQoHau+rwMAcVAg1LLGf51pd0A9ANwzk00sxggpZzHiojHWqYn8qdLW3PfOc15b9oa3py0ijvenUmtTyK5pF0GV3ZuQI76DohUW16ODpgC5JhZtplF4evoN6LMPquBMwHMrDkQA2z07zfAzKLNLBvIASZ7WKuIHEdizUhu7NmI0XcW8NaN+XRvksIbk1Zy1tPjuPT5CbwzeTXbd+8PdJkicpI8OxPgnDtgZrcCXwLhwMvOuXlm9ggw1Tk3ArgT+JeZ/QZfJ8Frna+TwjwzG4avE+EB4BaNDBAJvLAwo3uTFLo3SWFzyV7en17E0ClruO+DOTz08TzObF6Hi9ql0zu3DlERmpVcpKrztE+Ac24kvmF/pdc9WOr5fKD7MY59HHjcy/pE5NQlx0UzqFdjburZiDnF2/lwRjGfzFrL53N/ICUumut7ZPGzLpkkxGhkgUhVFeiOgSJSzZkZrTNq0TqjFvef25zxSzfxyncrefKLRTw/Zhk/65rJdd2zqBOvWQlFqhqFABGpMBHhYfTOrUPv3DrMLd7OC2OX8eLYZfz72xX0zk3l3Fb1ObN5XeKi9atHpCrQ/4ki4omW6Yk8e1V7Vm76kVcnrGTknHV8OW890RFh/KRpKpe0T+esvHqEh+kmRiKBohAgIp7KSoll8IUtePD8PKat3spns9fx+dx1fDV/PVnJNbmpVyMubZ9RrecdEKmu1H1XRCpFWJjRKct3e+MJ957J81e3J7FGJPd/OJce/zeaf4xawqaSvYEuUySk6EyAiFS68DDjnFb16deyHpOWb2HIuGU89fVinhm9hH4t63N1fkPys5Mw06UCES8pBIhIwJgZXRsn07VxMks3lPD296sZPm0Nn8xaS+PUWK7Kz+Sy9hm6gZGIR3Q5QESqhCZ14njwgjwm39+Hpy5vQ0KNSB79dD6dn/iGu96bxYzVW/HqhmcioUpnAkSkSomJDOfSDhlc2iGD+Wt38Nb3q/hoRjHDpxWRVz+ByzpkcGHbNFLiogNdqki1pzMBIlJl5aUl8PjFrfj+/j48fnFLwsLgkU/nk//EKK57ZTIjZq1lz37NKC5yqnQmQESqvLjoCK7Oz+Tq/EyWrN/JBzOK+WhGMbe/M4O46AjOblGX/m3T6d44mYhw/W0jUl4KASJSreTUjeeefs343dm5TFq+mY9nrmXk3HV8ML2YlLgozmtVnwvbptO+YS2NLhA5AYUAEamWwsKMbk1S6NYkhYf7t6Bw0UZGzCrmnSlreG3iKjJq1+DCNmn0b5tObr34QJcrUiUpBIhItRcTGU6/lvXo17IeO/bs56t56xkxay0vjlvOPwuX0aZBLW7skc05LevpcoFIKQoBIhJUEmIiuaxDBpd1yGBTyV4+nbWW1yau4rZ3ZpBeqwbXdc8ibb+GGoqAQoCIBLGUuGiu7Z7Nz7tmMWrhBl4av5zHPltAdDiM3T6bKzo1UN8BCWkKASIS9MLCjLPy6nJWXl1mF23jzx9+zyez1/Lu1DU0qRPHTzs24NIOGSTFRgW6VJFKpYtjIhJSWmfU4oZW0Uy+vw9/uqQV8TERPD5yAV3+OIq73pvFnKLtgS5RpNLoTICIhKS46AgGdG7IgM4NWfTDTt6YtJIPpvtmJmzXsBbXdMnk3Fb1dYtjCWo6EyAiIS+3XjyPXdSKSb8/k4cuyGP7rv38dtgsOj3+Dfd/OIdZa7bpvgUSlHQmQETELyEmkuu6ZzOwaxbfr9jCsKlrGD6tiLe+X02zevH8tFMDLmmnuxpK8FAIEBEpIyzsP7c4frh/C0bMXMuwqWt4+JP5/OnzhZzXuj5X5zekfcPaGlkg1ZpCgIjIcSTERPKzLpn8rEsmc4u38/bk1Xw8o5gPphfTtG4cl3XI4KJ26dSJjwl0qSInTX0CRETKqWV6Ik9c3IrJ9/fhj5e0IjY6gidGLqTrH0dz/atTGDlnne5qKNWKzgSIiJyk2OgIruzckCs7N2TphhLen17EB9OLGL1wA/ExEZzTsh4XtU0nv1Ey4WG6XCBVl0KAiMhpaFInjnv6NeOus3P5bukmPppZzGez1zFsahF1E6I5p2V9ejerQ352koYbSpWjECAiUgHCw4xeTVPp1TSV3RcdZNTC9Xw0Yy3vTF7NqxNWEhMZRrfGKfTOTeWcVvVJiYsOdMkiCgEiIhWtRlQ457dO4/zWaezZf5CJyzczdtFGChdtYPTCDTz8yXzOaFaHyzs2oCA3lUjd2VACRCFARMRDMZHh9M6tQ+/cOkALFq/fyfvTinh/ejFfzV9PSlwU57WqT0FuHbo0SqZGlC4ZSOVRCBARqURN68Zz37nNuatvLmMXbeS9aWt4d+oaXpu4iqiIMPKzk/hJ01TObVWftFo1Al2uBDmFABGRAIgMD6NPXl365NVlz/6DTFm5hbGLNjJ28UYe+2wBj322gM7ZSVzYJo1zW9XXHQ7FEwoBIiIBFhMZTs+cVHrmpPIAsHLTj3wyay0fz1rLAx/NZfCIeXRrkkLfFnU5q3ld6iRoYiKpGAoBIiJVTFZKLLedmcOtZzRhwbqdjJi1li/mruP+D+fywEdzadegFn1b1KNvi3pkpcQGulypxjwNAWbWD/g7EA685Jz7U5ntTwO9/Ys1gTrOuVr+bQeBOf5tq51zF3pZq4hIVWNm5KUlkJeWwD39clm8voSv5v3Al/N/4I+fL+SPny8kt248fVvWo2+LuuTVT9C9DOSkeBYCzCwceA44CygCppjZCOfc/MP7OOd+U2r/24B2pV5it3OurVf1iYhUJ2ZGbr14cuvFc9uZORRt3cVX89bzxbwfeHb0Ep4ZtYTslFguapvOxe3SaZhcM9AlSzXg5ZmAzsBS59xyADMbCvQH5h9j/yuBhzysR0QkaGTUrsn1PbK5vkc2m0v28vX89Xw0s5inv1nM098spmNmbS5ql06/lvU0MZEck5chIB1YU2q5CMg/2o5mlglkA6NLrY4xs6nAAeBPzrmPvCpURKQ6S46LZkDnhgzo3JDibbv5aEYxH84o5oGP5vLgx3PplJXEOS3r0a9lfeolqlOh/Ic557x5YbPLgH7OuRv9y9cA+c65W4+y7z1AhnPutlLr0p1zxWbWCF84ONM5t6zMcYOAQQCpqakdhg0b5snPIv9RUlJCXFxcoMsIampj74VCGzvnKCpxTP3hAFPXH6C4xPe7PjsxjLap4bStE07D+DBP+xCEQjsHWu/evac55zqe6vFengkoBhqUWs7wrzuaAcAtpVc454r9/y43s0J8/QWWldlnCDAEIDc31xUUFFRE3XIchYWFqJ29pTb2Xii18TX+f5dtLOGLuT/wzYL1fLRsGx8u3U9aYgxnNK9Dr5xUujZOJj4mskLfO5TaubryMgRMAXLMLBvfl/8A4KqyO5lZM6A2MLHUutrALufcXjNLAboDT3pYq4hIUGucGsctvZtwS+8mbNy5lzELN/DNgvV8ML2YNyetJiLMaN+wNj1zUuiRk0Kr9EQidE+DoOdZCHDOHTCzW4Ev8Q0RfNk5N8/MHgGmOudG+HcdAAx1/31dojnwopkdAsLw9Qk4VodCERE5Canx0VzRqQFXdGrAvgOHmLZqK+OXbGTcko089fVinvp6MfExEXRplEyPJr5Q0CglVsMPg5Cn8wQ450YCI8use7DM8uCjHDcBaOVlbSIiAlERYXRtnEzXxsnc3a8Zm0v2MmHZZr5buolvl27i6/nrAWiYVJPeuan0bua70VFMpG50FAw0Y6CIiByRHBfNBW3SuKBNGgCrN+9i7JKNFC7ccORGRzGRYXTOTqZHk2S6N0mheb0EwsJ0lqA6UggQEZFjaphck2uSM7mmSyZ79h9k0vLNFC7ayLdLN/HEyIUAJMVG0a1xMr1yUumRk6K7H1YjCgEiIlIuMZHhFOTWoSC3DgA/bN9z5LLBt0s38ensdQA0qRNHjyYpxO06QIude0mN12RFVZVCgIiInJJ6iTFc2iGDSztk4Jxj0fqdfLtkE+OWbOKdyavZe+AQz878huyUWDpk1qZTVm06ZNamUUqcLh9UEQoBIiJy2syMZvUSaFYvgRt7NmLfgUO8/ukYDiVlMXnFVkYtWM/waUUAJNaIpH3DWv5gkESbBrXU0TBAFAJERKTCRUWE0aRWOAW9GjOol28Gw+WbfmTaqq1MX7WVaau2MmbRRt++4WG0aZBI5+wkOmcn0yGzNnHR+nqqDGplERHxnJnRODWOxqlxXNHRN5nstl37mLpyK5NXbmHyii28MHY5z41ZRniY0SItgc5ZSXTOTqJTVhK1Y6MC/BMEJ4UAEREJiFo1o+iTV5c+eXUB+HHvAWas3sb3Kzbz/YotvD5pFS99uwKAnDpxdMxKonN2bbo1TqFugm6EVBEUAkREpEqIjY6gh3/aYoA9+w8yu2g7U1ZuYcrKLXw6ay3vTF4NQKv0RM5sXoc+zevSIi1BsxmeIoUAERGpkmIiw/39BJIAOHjIsfCHHRQu2sioBev5+6gl/O2bJdRNiKZjVhIdM2vTMTOJ5vXjdd+DclIIEBGRasHXVyCRFmmJ3NK7CZtK9jJ64QbGLd7I9FVb+cw/T0GNyHA6ZNYmPzuJLo2TaZ2RSHSERh8cjUKAiIhUSylx0VzRscGRjoZrt+1mmn/kwfcrtvDU14vha4iOCKN9Q/88BVlJtGtYi4QKvm1ydaUQICIiQSGtVg3SatU4ct+DrT/uY/LKLUxavpnJK7bw7JilHHJgBrl148n3D0nslF2bOvGh2dFQIUBERIJS7dgo+raoR98W9QAo2XuAmau3MXXVFqat2sp704p4beIqABqlxJLfKIkujXx3VAyVUKAQICIiISGuzOiD/QcPMX/tDr5f4TtT8OnsdbwzeQ3gu/9Bt8bJtGtYi1bptWiUEhuUUx0rBIiISEiKDA+jTYNatGlQi0G9GnPwkGPe2u1MWLaZics2M3xaEa/7zxTERoXTIi2RNg0S6ZBZm/aZwXEJQSFAREQE3+iD1hm1aJ1Ri5t/0pgDBw+xdGMJc4q2M6d4O7OLtvPaxFX8a7xvAqMGSTXo0LA2LdMTyUtLIK9+ArVqVq+ZDRUCREREjiIiPOzITZEu949A2HvgIPPW7jhy/4MJyzbz0cy1R45Jr1WD5vUTaJWeSKuMBFqmJ1bpMwYKASIiIuUUHRFO+4a1ad+wNjf29K3buHMvC9btYP66Hcxfu4O5a7czauF6nPNtr5sQTat03/wGLdMTaZmeQL2EmCoxy6FCgIiIyGlIjY8mNT6VXk1Tj6wr2XuAecW+ywhzi7czb+0ORi/cwCF/MKgTH01+o2Tys5PIz06iSZ24gIQChQAREZEKFhcd4fuSb5R8ZN2ufQdYsG4nc4u3+yc02swns3yXEpJjo+jSOJnujVPo1jiZzOSalRIKFAJEREQqQc2oCDpk1qZDZm0GdsvCOceqzbv4fsVmJi3fwoRlm45MfZyWGEO3Jin0zEmhe5MUUuKiPalJIUBERCQAzIyslFiyUmL5aaeGOOdYselHJizbzIRlm/hmwXqGTysCoHn9BHrmpHBjj2zqVOBtlBUCREREqgAzo1FqHI1S4/hZl8wj8xaMX7KJb5ds4tUJKxnUq1GFvqdCgIiISBVUet6CW3o3Yc/+g8REVuzdEHXDZRERkWqgogMAKASIiIiELIUAERGREKUQICIiEqIUAkREREKUQoCIiEiIUggQEREJUQoBIiIiIUohQEREJER5GgLMrJ+ZLTKzpWZ271G2P21mM/2PxWa2rdS2gWa2xP8Y6GWdIiIiocizaYPNLBx4DjgLKAKmmNkI59z8w/s4535Tav/bgHb+50nAQ0BHwAHT/Mdu9apeERGRUOPlmYDOwFLn3HLn3D5gKND/OPtfCbzjf94X+No5t8X/xf810M/DWkVEREKOlzcQSgfWlFouAvKPtqOZZQLZwOjjHJt+lOMGAYMAUlNTKSwsPO2i5fhKSkrUzh5TG3tPbVw51M5VX1W5i+AAYLhz7uDJHOScGwIMAcjNzXUFBQUelCalFRYWonb2ltrYe2rjyqF2rvq8vBxQDDQotZzhX3c0A/jPpYCTPVZEREROgZchYAqQY2bZZhaF74t+RNmdzKwZUBuYWGr1l8DZZlbbzGoDZ/vXiYiISAXx7HKAc+6Amd2K78s7HHjZOTfPzB4BpjrnDgeCAcBQ55wrdewWM3sUX5AAeMQ5t8WrWkVEREKRp30CnHMjgZFl1j1YZnnwMY59GXjZs+JERERCnGYMFBERCVEKASIiIiFKIUBERCREKQSIiIiEKIUAERGREKUQICIiEqIUAkREREKUQoCIiEiIUggQEREJUQoBIiIiIUohQEREJEQpBIiIiIQohQAREZEQpRAgIiISohQCREREQpRCgIiISIhSCBAREQlRCgEiIiIhSiFAREQkRCkEiIiIhCiFABERkRClECAiIhKiFAJERERClEKAiIhIiFIIEBERCVEKASIiIiFKIUBERCREmXMu0DVUCDPbCSwKdB0hIAXYFOgigpza2Htq48qhdvZernMu/lQPjqjISgJskXOuY6CLCHZmNlXt7C21sffUxpVD7ew9M5t6OsfrcoCIiEiIUggQEREJUcEUAoYEuoAQoXb2ntrYe2rjyqF29t5ptXHQdAwUERGRkxNMZwJERETkJARFCDCzfma2yMyWmtm9ga4nGJhZAzMbY2bzzWyemf3avz7JzL42syX+f2sHutbqzszCzWyGmX3qX842s+/9n+d3zSwq0DVWd2ZWy8yGm9lCM1tgZl31Wa5YZvYb/++KuWb2jpnF6LN8+szsZTPbYGZzS6076mfXfJ7xt/dsM2t/otev9iHAzMKB54BzgDzgSjPLC2xVQeEAcKdzLg/oAtzib9d7gVHOuRxglH9ZTs+vgQWllv8PeNo51wTYCtwQkKqCy9+BL5xzzYA2+Npbn+UKYmbpwO1AR+dcSyAcGIA+yxXhVaBfmXXH+uyeA+T4H4OA50/04tU+BACdgaXOueXOuX3AUKB/gGuq9pxz65xz0/3Pd+L7pZmOr21f8+/2GnBRYCoMDmaWAZwHvORfNuAMYLh/F7XxaTKzRKAX8G8A59w+59w29FmuaBFADTOLAGoC69Bn+bQ558YBW8qsPtZntz/wuvOZBNQys/rHe/1gCAHpwJpSy0X+dVJBzCwLaAd8D9R1zq3zb/oBqBugsoLF34C7gUP+5WRgm3PugH9Zn+fTlw1sBF7xX3Z5ycxi0We5wjjnioG/AKvxfflvB6ahz7JXjvXZPenvw2AIAeIhM4sD3gfucM7tKL3N+YaWaHjJKTKz84ENzrlpga4lyEUA7YHnnXPtgB8pc+pfn+XT478m3R9f4EoDYvnfU9jigdP97AZDCCgGGpRazvCvk9NkZpH4AsBbzrkP/KvXHz695P93Q6DqCwLdgQvNbCW+y1hn4Lt2Xct/ShX0ea4IRUCRc+57//JwfKFAn+WK0wdY4Zzb6JzbD3yA7/Otz7I3jvXZPenvw2AIAVOAHH8v1Ch8nVFGBLimas9/bfrfwALn3F9LbRoBDPQ/Hwh8XNm1BQvn3H3OuQznXBa+z+1o59zVwBjgMv9uauPT5Jz7AVhjZrn+VWcC89FnuSKtBrqYWU3/747DbazPsjeO9dkdAfzcP0qgC/D/7d1PiJVVGMfx7w+jjBKjaBsWGEKBU2BkWbiIFuGiXDQQbYzoD1RQRIibaBEM1CZoFRRtRIgiaxHWqhqMcEhHjf5siiAiaRFDJUVMT4tzxm7DqI2ODc77/cAwvPe977nvHS7Mb8458zwzI8sGC1oRxYKS3EVbW10FvFZVzy/zLZ33kmwBJoGj/LNevYu2L+AN4CrgO+Deqpq/aUWLlGQr8HRVbUtyDW1m4HLgEHB/Vf2xnPd3vksyRtt8eSHwDbCD9keQn+UlkuQ5YJz2n0WHgAdp69F+ls9Ckj3AVlpHxmPAs8BeFvjs9gD2Mm0p5jiwo6pO2WBoRYQASZK0eCthOUCSJJ0BQ4AkSQNlCJAkaaAMAZIkDZQhQJKkgTIESAOR5Nf+fV2S+5Z47F3zjj9ZyvElnRuGAGl41gGLCgEjVd9O5l8hoKpuWeQ9SVoGhgBpeCaA25JM9x7wq5K8kGSq9yB/GFoBoySTSd6lVX8jyd4kn/W+8Q/1xyZo3eOmk+zuj83NOqSP/XmSo0nGR8b+MMmbSb5KsrsXOiHJRJIv+r28+L//dKQBOV26l7Ty7KRXJwTov8xnqmpTkouA/Uk+6M+9Ebi+qr7txw/0ymQXA1NJ3qqqnUkeq6qxBV5rOzAGbKRVPJtK8nE/dwNwHfADsB+4NcmXwD3AhqqqJJct+buXdIIzAZLupNUbn6aVhb4CWN/PHRgJAABPJDkMfEprVLKeU9sC7Kmq2ao6BnwEbBoZ+/uq+guYpi1TzAC/A68m2U4rfSrpHDEESArweFWN9a+rq2puJuC3E09q/Q3uADZX1UZaLfjVZ/G6ozXkZ4ELeu/5m2id/rYB+85ifEmnYQiQhucXYM3I8fvAo711NEmuTXLJAtetBX6uquNJNgA3j5z7c+76eSaB8b7v4ErgduDAyW4syaXA2qp6D3iStowg6RxxT4A0PEeA2T6t/zrwEm0q/mDfnPcTcPcC1+0DHunr9l/TlgTmvAIcSXKwt0Oe8zawGTgMFPBMVf3YQ8RC1gDvJFlNm6F46szeoqT/wi6CkiQNlMsBkiQNlCFAkqSBMgRIkjRQhgBJkgbKECBJDp5+uAAAABlJREFU0kAZAiRJGihDgCRJA2UIkCRpoP4G5FHb2eSc78UAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z-dEBTmwXF2Q"
      },
      "source": [
        "#### Run Poisson regression utilizing custom Poisson objective and evaluation functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M41PavJsPLRg",
        "outputId": "12f45425-1c74-4b48-86e6-e9cab347cbbd"
      },
      "source": [
        "model = lgb.LGBMRegressor(\n",
        "    objective=poisson_loss,\n",
        "    learning_rate=0.1,\n",
        "    n_estimators=100\n",
        ")\n",
        "\n",
        "# using LightGBM's scikit-learn API\n",
        "# to make the results match, the init_score is set to the log of the mean of\n",
        "# the target values.\n",
        "model.fit(\n",
        "    df[['x1', 'x2', 'x3']].to_numpy(),\n",
        "    df['y'].to_numpy(),\n",
        "    init_score=np.repeat([np.log(np.mean(df['y']))], len(df['y'])),\n",
        "    eval_set=[(df[['x1', 'x2', 'x3']], df['y'].to_numpy())],\n",
        "    eval_metric=poisson_eval_metric,\n",
        "    eval_names=['Train'],\n",
        "    verbose=20,\n",
        ")"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[20]\tTrain's poisson_metric: 0.879023\n",
            "[40]\tTrain's poisson_metric: 0.819204\n",
            "[60]\tTrain's poisson_metric: 0.77684\n",
            "[80]\tTrain's poisson_metric: 0.74138\n",
            "[100]\tTrain's poisson_metric: 0.71657\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LGBMRegressor(boosting_type='gbdt', class_weight=None, colsample_bytree=1.0,\n",
              "              importance_type='split', learning_rate=0.1, max_depth=-1,\n",
              "              min_child_samples=20, min_child_weight=0.001, min_split_gain=0.0,\n",
              "              n_estimators=100, n_jobs=-1, num_leaves=31,\n",
              "              objective=<function poisson_loss at 0x7fe082c19050>,\n",
              "              random_state=None, reg_alpha=0.0, reg_lambda=0.0, silent=True,\n",
              "              subsample=1.0, subsample_for_bin=200000, subsample_freq=0)"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "id": "i68xD41DoHl6",
        "outputId": "c2ac6ea2-ac54-415f-baf0-d9c6dd478d2f"
      },
      "source": [
        "# Plot Poisson evaluation metric against boosting iterations\n",
        "lgb.plot_metric(model, metric='poisson_metric', figsize=(8,6))\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}