doc/source/examples/ale_regression_california.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Accumulated Local Effects for predicting house prices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we will explain the behaviour of regression models on the California housing dataset. We will show how to calculate accumulated local effects (ALE) for determining the feature effects on a model and how these vary on different kinds of models (linear and non-linear models)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import fetch_california_housing\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "from alibi.explainers import ALE, plot_ale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fetch and prepare the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row in the dataset represents a whole census block (the smallest geographical unit for which the US census publishes data), thus the feature values for each datapoint are averages within the block. For a complete description of the dataset please refer to the [scikit-learn documentation page](https://scikit-learn.org/stable/datasets/real_world.html#california-housing-dataset)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = fetch_california_housing(as_frame=True)\n",
    "feature_names = data.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MedInc</th>\n",
       "      <th>HouseAge</th>\n",
       "      <th>AveRooms</th>\n",
       "      <th>AveBedrms</th>\n",
       "      <th>Population</th>\n",
       "      <th>AveOccup</th>\n",
       "      <th>Latitude</th>\n",
       "      <th>Longitude</th>\n",
       "      <th>MedHouseVal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.3252</td>\n",
       "      <td>41.0</td>\n",
       "      <td>6.984127</td>\n",
       "      <td>1.023810</td>\n",
       "      <td>322.0</td>\n",
       "      <td>2.555556</td>\n",
       "      <td>37.88</td>\n",
       "      <td>-122.23</td>\n",
       "      <td>4.526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.3014</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6.238137</td>\n",
       "      <td>0.971880</td>\n",
       "      <td>2401.0</td>\n",
       "      <td>2.109842</td>\n",
       "      <td>37.86</td>\n",
       "      <td>-122.22</td>\n",
       "      <td>3.585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.2574</td>\n",
       "      <td>52.0</td>\n",
       "      <td>8.288136</td>\n",
       "      <td>1.073446</td>\n",
       "      <td>496.0</td>\n",
       "      <td>2.802260</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.24</td>\n",
       "      <td>3.521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.6431</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5.817352</td>\n",
       "      <td>1.073059</td>\n",
       "      <td>558.0</td>\n",
       "      <td>2.547945</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "      <td>3.413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.8462</td>\n",
       "      <td>52.0</td>\n",
       "      <td>6.281853</td>\n",
       "      <td>1.081081</td>\n",
       "      <td>565.0</td>\n",
       "      <td>2.181467</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "      <td>3.422</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   MedInc  HouseAge  AveRooms  AveBedrms  Population  AveOccup  Latitude  \\\n",
       "0  8.3252      41.0  6.984127   1.023810       322.0  2.555556     37.88   \n",
       "1  8.3014      21.0  6.238137   0.971880      2401.0  2.109842     37.86   \n",
       "2  7.2574      52.0  8.288136   1.073446       496.0  2.802260     37.85   \n",
       "3  5.6431      52.0  5.817352   1.073059       558.0  2.547945     37.85   \n",
       "4  3.8462      52.0  6.281853   1.081081       565.0  2.181467     37.85   \n",
       "\n",
       "   Longitude  MedHouseVal  \n",
       "0    -122.23        4.526  \n",
       "1    -122.22        3.585  \n",
       "2    -122.24        3.521  \n",
       "3    -122.25        3.413  \n",
       "4    -122.25        3.422  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.frame.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = data.data.to_numpy(), data.target.to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Shuffle the data and define the train and test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit and evaluate models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and evaluate a linear regression model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5411287478470682"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(y_test, lr.predict(X_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and evaluate a random forest model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf = RandomForestRegressor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RandomForestRegressor()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RandomForestRegressor</label><div class=\"sk-toggleable__content\"><pre>RandomForestRegressor()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "RandomForestRegressor()"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2538208780210583"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(y_test, rf.predict(X_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Effects: Motivation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we develop an intuition for calculating feature effects. We start by illustrating the calculation of feature effects for the linear regression model.\n",
    "\n",
    "For our regression model, the conditional mean or the prediction function $\\mathbb{E}(y\\vert x)=f(x)$ is linear:\n",
    "\n",
    "$$\n",
    "f(x) = w_0 + w_1x_1 + \\dots + w_kx_k.\n",
    "$$\n",
    "\n",
    "Because the model is additive and doesn't include feature interactions, we can read off individual feature effects immediately: the effect of any feature $x_i$ is just $w_ix_i$, so the effect is a linear function of $x_i$ and the sign of the coefficient $w_i$ determines whether the effect is positive or negative as $x_i$ changes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose we don't know the true effect of the feature $x_i$ which is usually the case when using a more complex model. How might we approach the problem of estimating the effect? Let's focus on one feature - median income (`MedInc`). The following is a scatterplot of model predictions versus the feature:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "FEATURE = 'MedInc'\n",
    "index = feature_names.index(FEATURE)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X_train[:, index], lr.predict(X_train));\n",
    "\n",
    "ax.set_xlabel('Median income in $10,000\\'s');\n",
    "ax.set_ylabel('Predicted value in $100,000\\'s');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, there is a strong positive correlation as one might expect. However the feature effects for `MedInc` cannot be read off immediately because the prediction function includes the effects of all features not just `MedInc`. What we need is a procedure to block out the effects of all other features to uncover the true effect of `MedInc` only. This is exactly what the ALE approach does by averaging the differences of predictions across small intervals of the feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate Accumulated Local Effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we initialize the ALE object by passing it the predictor function which in this case is the `clf.predict` method for both models. We also pass in feature names and target name for easier interpretation of the resulting explanations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr_ale = ALE(lr.predict, feature_names=feature_names, target_names=['Value in $100,000\\'s'])\n",
    "rf_ale = ALE(rf.predict, feature_names=feature_names, target_names=['Value in $100,000\\'s'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now call the `explain` method on the explainer objects which will compute the ALE's and return an `Explanation` object which is ready for inspection and plotting. Since ALE is a global explanation method it takes in a batch of data for which the model feature effects are computed, in this case we pass in the training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr_exp = lr_ale.explain(X_train)\n",
    "rf_exp = rf_ale.explain(X_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting `Explanation` objects contain the ALE's for each feature under the `ale_values` attribute - this is a list of numpy arrays, one for each feature. The easiest way to interpret the ALE values is by plotting them against the feature values for which we provide a built-in function `plot_ale`. By calling the function without arguments, we will plot the effects of every feature, so in this case we will get 8 different subplots. To fit them all on the screen we pass in options for the figure size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ALE for the linear regression model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ALE plots show the main effects of each feature on the prediction function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ale(lr_exp, n_cols=4, fig_kw={'figwidth':14, 'figheight': 7});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the feature effects plots are linear because we used a linear model. The interpretation of the ALE plot is that, given a feature value, the ALE value corresponding to that feature value is the difference to the mean effect of that feature. Put differently, the ALE value is the relative feature effect on the prediction at that feature value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of the median income"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the ALE plot for the feature `MedInc` (median income) in more detail:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ale(lr_exp, features=['MedInc']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ALE on the y-axes of the plot above is in the units of the prediction variable which, in this case, is the value of the house in \\$100,000's.\n",
    "\n",
    "The median income here is in units of \\$10,000's.\n",
    "\n",
    "The main interpretation of the ALE plot is qualitative—fixing the feature value and looking at the ALE plot as a function at that point, the tangent at that point (or the slope of linear interpolation between the closest bin endpoints) shows how sensitive the target prediction is with respect to small changes of the feature value. Since we have a linear regression model, the tangent/slope is the same across the whole feature range so the feature sensitivity is identical at any point in the feature range. We can calculate it by taking the slope of the linear interpolation between any two points of the ALE plot:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4476000685169465\n"
     ]
    }
   ],
   "source": [
    "slopes = np.array([((v[-1]-v[0])/(f[-1]-f[0])).item() for v, f in zip(lr_exp.ale_values, lr_exp.feature_values)])\n",
    "slope_med_inc = slopes[feature_names.index('MedInc')]\n",
    "print(slope_med_inc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This value can be interpreted that, at any point in the feature range of `MedInc`, the effect of changing it by some amount $\\delta$ will result in a change in the prediction by approximately $0.4476\\cdot\\delta$. In other words, at any point an additional median income of \\$10,000 would result in an uplift of the predicted house value by ~44,760 dollars."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "Note\n",
    "    \n",
    "This interpretation doesn't mean that for any single datapoint the effect will be the same uplift. Rather, the effect is true *on average* for datapoints close to the feature value of interest, i.e. in a bin of size $\\delta$.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also say a few more quantitative things about this plot.\n",
    "The ALE value for the point `MedInc=6 ($60,000)` is ~1 which has the interpretation that for areas with this median income the model predicts an up-lift of ~\\$100,000 *with respect to the average effect of* `MedInc`. This is because the ALE plots are centered such that the average effect of the feature across the whole range of it is zero.\n",
    "\n",
    "On the other hand, for neighbourhoods with `MedInc=4 ($40,000)`, the ALE value is ~0 which indicates that the effect of the feature at this point is the same as the average effect of the feature. For even lower values of `MedInc`, below \\$40,000, the feature effect becomes less than the average effect, i.e. a smaller median income in the area brings the predicted house value down with respect to the average feature effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of the crime level"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An additional feature of the ALE plot is that it shows feature deciles on the x-axis. This helps understand in which regions there is low data density so the ALE plot is interpolating. For example, for the `AveOccup` feature (average number of household members), there appears to be an outlier in the data at over ~1,200 which causes the plot to linearly interpolate over a large range where there is no data. Note that this can also be seen by the lack of markers on the plot within that large range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ale(lr_exp, features=['AveOccup']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For linear models this is not an issue as we know the effect is linear across the whole range of the feature, however for non-linear models linear interpolation in feature areas with no data could be unreliable. This is why the use of deciles can help assess in which areas of the feature space the estimated feature effects are more reliable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linearity of ALE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is no surprise that the ALE plots for the linear regression model are linear themselves—the feature effects are after all linear by definition. In fact, the slopes of the ALE lines are exactly the coefficients of the linear regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.47600069e-01,  9.56752596e-03, -1.24755956e-01,  7.94471254e-01,\n",
       "       -1.43902596e-06, -3.44307993e-03, -4.18555257e-01, -4.33405135e-01])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.47600069e-01,  9.56752596e-03, -1.24755956e-01,  7.94471254e-01,\n",
       "       -1.43902596e-06, -3.44307993e-03, -4.18555257e-01, -4.33405135e-01])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slopes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(lr.coef_, slopes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus the slopes of the ALE plots for linear regression have exactly the same interpretation as the coefficients of the learnt model—global feature effects. In fact, we can calculate the ALE effect of linear regression analytically to show that the effect of feature $x_i$ is $\\text{ALE}(x_i) = w_ix_i-w_i\\mathbb{E}(x_i)$ which is the familiar effect $w_ix_i$ relative to the mean effect of the feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ALE for the random forest model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at the ALE plots for the non-linear random forest model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kk3Xb9jSZHjOgJ93bERjyG8hO5DaQvchvIHhBn0E/KDO70cwWmNmCzZs3Bx1OqB0+sFeT6U9NGBxQJED7kN9A9iK/gexFfgPp06kC3cy6bHA559wDzrnJzrnJAwcO7KqXzUgrN+2KPzZJxd0LggsGGYv8BrIX+Q1kL/IbyA6tFuhm9lbC4z82mz0vbRGhU2bMXatlG3bGp/PzjOvP0SryG8he5DeQvchvIPu1dQa9Z8Ljic3mWRpiwSF4YcmGJtNHDe3N9edoC/kNZC/yG8he5DeQ5doq0F0n57WbmT0maY6k8WZWbWbXpWK9uahnYdNeTSdz9hxtI7+B7JXW/Ca3gUCR30CWa+talb5mdom8Ir6vmV3qt5ukPql4cefcValYT66rqKrV35Z+3KSN689xEOQ3kL3Smt/kNhAo8hvIcm0V6K9L+lzC488mzHsjbRGhw+5/fVWTQ6YR4/7nOCjyG8he5DeQvchvIMu1WqA75/6ltXlmdll6wkFnVKxpervKoX26cf052kR+A9mL/AayF/kNZL/O3gf91ymNAp02Y+5abd1T36TtqMNS0kMZuYv8BrIX+Q1kL/IbyAKdLdAZJTIEZsxdqx/+ZUmL9pvOODyAaJBFyG8ge5HfQPYiv4Es0NY16G1JySjP6LwZc9fq1pmLW7SfPm4A3dtxqMhvIHuR30D2Ir+BLNBqgW5mi5U80U3S4LRFhHZpft/zRmyZ0R7kN5C9yG8ge5HfQPZr6wz6Z5K0maQRkr6XnnDQXjv21idtP//ooV0cCTIU+Q1kL/IbyF7kN5Dl2hrFvarxsZmdIGmapM9LWi3p6fSHhtbMmLtW71Zvb9JWkGf60eeO1rQpIwOKCpmE/AayF/kNBKeiqlbllTWaOqZ/Wi45JL+B7NdWF/cjJF3l/9si6QlJ5pw7q4tiQyuSdW+nOEdHkN9A9iK/gdSqa4hp57567dzXoJ37GrRjX7127qvXjr2Nj73/12zZrdc/3CxJKsyPaPr1U1NepJPfQPZrq4v7+5LelPQZ59xKSTKzb3VJVGjTxKG99eaKLfHp08cNoDhHR5HfQPYivwFfLOa0c39DvKDemVBQewV3vXYk/L9jb8v2ffWxg75OcZG3Sx3zrw6vb4ipvLImHWfRyW8gy7VVoF8q6UpJs83sRUmPi9s3hEJx94Im01PG9A8oEmQw8hvIXuQ3soJzTnvro15BvbdpIR0vtJMU1Intu+oa5A4ygm63goiKuxWouFu+evv/D+vbXb2753vtRfnq3d1rL+5WoN6N//vzexXlKy9iqqiq1dUPlau+IaaC/Iimpmf/jPwGslxb16DPkjTLzHpKukjSNyUNMrP7JM10zr3UJRGihbmVNU2mS3oUBhQJMhX5DWQv8hth0dg1PFnhvKO1Qnt/0zPdDbG2q+v8iB0onLvnq7ioQCP79WhRUPdOKKgTC/HibgUqzI+k5P2WlZZo+vVT030N+iyR30BWO+h90J1zuyXNkDTDzErkDUTxXUlsAAJw1/PL9UZC93ZJWrp+eytLA20jv4HsRX7jUDR2DW/zDHVC1/EdzbqO79hbr/0N7esaXtztwBnqQcXdNHZg0zPUzQvqPgnt3QvyZBaeE8hlpSVpKcybI7+B7HXQAj2Rc65W0gP+PwTgj+VVLdq49zlSgfwGshf5nVsau4Y3none0fya69auxU5o37m/4aCv09g1/ECX7wINK+keP2Pd/Mx2YiGe2DUch4b8BrJLhwp0BGvG3LXaXRdt0X7ZpOEBRAMAANKhriHWZkG942CF9r4GRdvRNfxAsewV1KMG9PAL7oT27gkFeEJ7KruGA0DYpfsWioko0DPI3a980KLtptPHdElXKgAAcHDRmNOufS27fHsF9YGz08muxW4suA/WNdxM6lV04Cx1724FGtK7m8YNaj6YWctC22srULeCSKi6hgNAujnnVBeNaW9dVHv8f/vqGx83xNv31kcPLFPfoLU1e/TS0o2KOqei/Ihm3JD6WygmokDPEBVVtdq0s65JW1Ge6ZYLJgQUEQAA2WduZY1e+2CzjhxSrOH9uvvFc/NrsRPuib23aSG+qx1dw7sX5DUpnPt0L9Dwku7eQGbdml6TXVxUEH/c+H+vwnxF6BoOIAs1RGPaUx/VvoQiem99g/e/XzzH2+saWhbU/vKJxXbicw/Wu6i5wryIzKSofzuI+mjabqEYR4GeIcqbjdwuSceO6Nv1gQAAkGWiMafyyho98MYqvf7hljaXLcizFgOXjRrQI35muvnAZs1vyVXcLV8FeXQNB5CZYjGnfQ0Hit742eeEInlvvC0WL6L3+PP3xh+3LLr31kVVFz344JKJ8iKmHgV56l6Ypx6FeepW4P3fozBf/XsVqUdhnronzO9RmN9kunuB3xZ/7Lf70/l5ka66hWIcBXqGWLFxZ4u2W87n7DkAAJ21YuNOPb1wnWa9s04f79jX5JrqiEmXThquaVNGNim06RoOIMycc9rfEEsohA8UzO0tkvf47fsSz1bXe+376jtWQEtqUSR3L8xXj4I8De5d4LUVJLS3KKi99u4FBwrnHoV56lGQr26FEf8Md3q3yV1xC8VEFOgZovkZ9H49Crj2HACADqioqtWr72/U3rqo5q+p1eJ125UXMZ1xxEB9/zMT1L9nof7lkfnxsyRXnTRSk0byWwsgteqjsWbdshuSFMmNBXFil+4DhXXLZRsL6gZ1sBe3CvMjftHbWAB7BXHfHoU6rG/Ts82NRXSLorvgQHviWexsOajZVbdQlCjQM4drmmnF3QoCCgQAgNRK9+i41bV79Mg/1ujhf6yO77iOGdBDt3/mKH32uMM0sLgovmxXniUBEIyDbXNiMdfi2uXEQcTiRXLCWermRXJi8dxkILL6qOqjHaug8yPWpIt2YwHcqyhfAxu7cScUyd1bFND5TbptH1jGK8S53WG4UKBngBlz1+rjZgPE9e1BgQ4AyHyvvr9RNzxaIeecCvMjmn598tFxK6pq9W9PLFJ17R51L8zT2IG91LMoX/17FerM8YNUH41pybodOnZYH004rLcWrd2m5xav1/pt+1S1dU+TdUVMuqxshK49bXSL1+nKsyQAuoZzTht37NeKTTv16vub9OjbVYo6p4hJowf0lJklXDcd7XA3bjPFzz5397tfNxbJfboXNL3+uUWR3LSw7l7QclluaZhbKNBD7q7nl+v+NypbtF9x4sgAogEAILUWrd0WH1W3viH56LgVVbW67L6349O79ke1qHp7fPov725odf0Rk645uVSTR5Xo3//0XpcN8gOgYxLPakve5Z0lPQpVu6cu/n/jGe9kZ8C9ti06YlBvFRVEtGLTLq3YuFMfbtypFZt2aee+lndYiDnv34QhvVopklu5/jnejdt7TlF+dnTjRjhQoIfYOb98TSs2727RXlyUp2lTKNABAJnvjPGDdM/slYo5tVo4JxbnBxMx6cghxVq+YaecJJM0uHc3fe64YRrWtwfd14GQqaiq1fdnLtbyjw8MiGzW4upOSV5X77PGD9TsDzYrGnOKmGlSaV/t2teg9z/2cj5Rv56FGjeoly46/jAdMbhYYwf10r76qL4yfWH8YN0vPn8c2wOECgV6SF18z1tJi3NJunpKaRdHAwBAepSVlui600brwTdX61MTBreYP+qW5w66jvw8U8RM0ai3w/1PU0fpzmeXtjhbTvd1IFxmzF2rW2cubtGerDiXpIaY08vLN8Wno85pzZbd6laQFy/OTdIXThyh/3fueA3oVZR0PYw1gTCjQA+hiqraJl33Eo0b2FO3XMDt1QAA2eOkUf314Jur9dx7G/TK8o3x69DHtFGcnzSqRH17FGpgcZEunTRckprscI8fUswOOBBiFVW1SYvz5kySk9c7pjAvou9fOEE/eX55/ADc/f88WZKa3Kf6C5NHtFqcSxysQ7hRoIfQNb+fm7R9eN9uevnbZ3ZtMAAApNmHm7yurU5SXf2B69BbG6bp+OF99ORNp7RoT9zhZgccCLffvb6qzfl5EdMNp41WcfeCFtegTzisT4sDcJwVR7agQA+Zu55frt110Rbtp48boEevmxJARAAApFdJj8L441iz6WRmfe20NEcEIN1eWraxRVvvbnmaOmZAvGdMa4V2sgNwHJRDtqBAD5kH31rdom3cwJ4U5wCArLVkfdPLuma+U93qYKhr7rqwK0ICkEZjb215+UqeSe/dcV4A0QDhQoEesMTbRHzjsYXxW80kols7AGSWZLcAkrx78c7+YJPeWbtNZ44fxNkeX/ObE81fU6sZc9cGEguA9Gvo2G3GgZxCgR6g5vd1TebEUey8AUAYtbxn7xYdO7yvanfX6TtPvaf6aEx5EdMZRwzU/oaY1m/bq49q96g+6mSSHnyzMj4YWq6beFifFm3tGTwKQOY5+vYXk7YfM6zldgDIRRToAbrhD/MPuswt5zNiO4DwalmkHjhr3Na8VL/2wV4v6bzR/XTk0N6as6pGFVW1KhtVoohJ76zdppPH9NfUMf31zkfbmjxv9vub1LdHgVZu2qUnF3ykJJ2emmiIOZVX1mjc4GJNGNpb/XsVasGaWjlJ9Q0HBkPLdbV76oIOAUAX2ZVkrCWJsSWARoEW6GZ2nqTfSMqT9JBz7q4g4+lqW/fUtzn/p5ccw44bMlau53fYdbS4fXvVFk08rLd27WvQ/DW1mjC0txpiMf3k2eWqj8YUiUgmUzTmlJ9n+nzZcD1VUa2GqGsyryDPdOsFE5SfF9GHH+/U5FElKsyPaPG67Tr58AGaOrqf3q3erjmrtmjSyBLVRWOau3qrjh3WR0cO7a131tbqHyu3qC4a0/OLP1Y05hQx7wzs0vXbFXMHuks7eY8HFRdp0879OkgtLb1+4OF/v7qyU5+rSTrl8P6av6ZWDbGYCvMjevS6KfFteUVVbZNbATV+3pkm1fnd3s/hp5cccygvA6Adgvj9Ht63W7pfAsgYgRXoZpYn6V5J50iqljTfzP7inFsWVExdqaKqts35w/p2a3WAHCDscj2/g9KeovvEUSX6cOMu3fGXpWqIOeVFTJNG9tXCtdsUjbkmxa0k9SjM055WznYkisYOPKs+6jRj3kdJ59VFne7464GvwaPlVfHH985u+5Y7rYk5acWmnfGz2YmFuJN3FjtZcW6SRg3oqTVbdreYb5JG9Ouhj7buaTEvYtLlZcP0l3c3qL7B68YuM0WjXtH9b58eLyl5j4Gy0pKMvxVQOvK7rLQkfq/jtvC7CKRXOvK7tTE5Er11y9mdXT2QdYI8g36SpJXOuUpJMrPHJV0kqdUNQE1NjR555JGuiS7N7qvsK+/jb7477Dmh26asea/ISTmd3+n00d58rdlToFE96jWie4M+2puv1bsLFHOmN2t6KCopImlszzqt3F2omJJtZRpLIVM0FlPFmhrFZJJMB0pZb5n8WJ2/xsTyyWRyGtezTqv2FCrmvCUk7xZZeSadUrJH/6jt0eKMdsSkw3vW6cNdhS3WKTmVFERVW5+XdN6gwgZtqsuPT0f8JfJM+lT/bXpxY7GijbGYV7jnmXRy8Ra9uCf5vIn5G/SRJZ93bOHHWp9kXkRS8eYluvowxf8W0oHHi2c/I0nqKWlxlZTsSuq25mWAtOT36B69Vbmn8XshNf/7S45tBJB+Kc3vD3YW6PF13rXleSZ9ceQ2SX104FeD3AaaC7JAHybpo4Tpakkt7iVmZjdKulGShg0b1jWRdYGNdY07oNKBnRCnQnP69ODdmtx3f0CRASmR8vxOLEwltShSE6czXbIifM2eAhXI6eUtveIF45Cieq3fX+A/68A42DFJH+4uik83L7rH9NivtXsLFXVOeSadN3iXX9y6hELUm3f6gN2tzvvEgD36hPa0+ncZV1yXdJ4kVe4uTLrOU/vvafX1Tuq3Nz7Pi3un9kYj8dcbXBRtNZZ0zJPU5PuWDd+9dkrL7/c1I3fojvf7q+mY7s3HdweQZinN75W7i/xfIFPUOf2+qljkNdA2c+6gV+Wl54XNLpd0nnPuen/6nyVNcc59rbXnTJ482S1YsKCrQkybo29/scUAGcVFeVr8I+79iI4xswrn3OSg42gu1fldUVWrz9//dtKzsUcMLtaHG3fKOakwP6IffnaiavfUhb77cPMuf3NWbdGr729SxEwP/2O1f+226aihxVqyfoeSbaqL8iPan3CvmryISc6pID+i2y88Snc+tyxpF+zp10+V1P4B3dIx2FtnX689XSWzRa7kd6JRt7S8N3Ii7oGObJEr+V1RVasv/G6OojGnwryI6qLJ769GbiNbpCK3gzyDvk7SiITp4X5bVktWnEtSzyIG1EdWSWl+l1fWJL2+OOakj7buic/b3xDTbf6tmQryI/rF5ceqe0G+lm7Yrk+MHSCZpbzY6+hga2+t2KyYk/7ntZVqiDqZSQN6FWrTzpajWEdjTis27WpSnEf8IxSFeRHd/tmJuvPZpfEBx27/TNODE+OH9m6zsG5+bXTz6fbM66zOvl7zeQhETv5+AzkipfldVlqiP157kr4yY6FMUt0eboAOHEyQVeF8SePMbLS8xL9S0rQA40m7c375Wqu3lrj4+Ozpvg8oxfk9dUx/dSuIJD0bfNuFR+nOZ5eqriHmXcnmF7N1DTF9/fFF8XXc/cqK+OOISZ88cpBe/3CzP7J4RP9+3njtq49q6pgBbRbaJ4zoq7cra/Tq+xtV3+D02Ly13kjiEdNRQ3vHRxKXml5F3bMwT7uT5L9z3iBmB64KlyKJZ8I/c5AifEhxqwcZ0lFYAwro95tRnoEukfL8PmXsAP3bOUfo9meWJp3P2XOgqcAKdOdcg5l9TdLf5N3G4WHnXPLMzQLffPwdrdi8O+m8cQN76pYLuN85skeq87v5yNdS07PBjUVqSY9C3fnXpaqLxpQfMZ00ur/+sXJLi5GhY056Zfmm+PT+hph+/Oxyf+pD5UdMDQe7wXUz3tnunU3ui5145Xdxt/x4gd68CP/Op49MWREOpFs6f7/bGsmdUZ6B9EtXfu/clzNjdACHLNB+1c655yU9H2QMXWHG3LWatWh90nnHD++jWV87rYsjAtIv1fnd3m7PicWsJC2o2pr0zPst5x2pn77wvhr86+ESz3oP7l2kddv2tYih+a23TN513y7J2e7mr/f1s4+gCEfWSNfv9+q7LjzodegA0isd+d34mwzg4LjwuQv88C9LkrafPm6AHr2uxcCYAA5B82K2rTPvxwzve+DMe0Lx/NWzxrVaaN90xuHtLrSbvx5FOHBwP73kGN06M0NvQAcgqbLSEt10+hjd/0Zl0KEAoUeBnmbX/H6u6qMtO+z17Z5PcQ50gc6ceU9loc0AZ0DHTJsyUrfNXNykq3sed2UCMt4tF0zQyP49mxyA4/pzoCUK9DSaMXet3lixJem8RT88t4ujAdCWZIU1hTYQjNV3XajDv/ecos4rzlf9JzvxQDaYNmWkpk0ZGXQYQKhRoKfR/8xekbT94uMP6+JIAADILBTlAIBcFAk6gGx1zi9fU3WSQaZ6Febp7itPCCAiAAAAAECYcQY9DY647XnVJbnuXJKW3HleF0cDAAAAAMgEFOgpdsRtz8m/1XELfbrzcQMAAAAAkqOLewod+f3nWy3OJem7503oumAAAAAAABmFAj1Fzvnla9rXkLxbe37E9NNLjmHUSgAAAABAq+hznSIrN+9O2j5uYE+9/O0zuzYYAAAAAEDG4Qx6GvXtnk9xDgAAAABoFwr0FLjr+eVK1rl90Q/P7fJYAAAAAACZiQL9EFVU1er+NypbtF98/GEBRAMAAAAAyFQU6IegoqpWl933dtJ5d195QhdHAwAAAADIZBToh+CqB+Ykbc+zLg4EAAAAAJDxGMW9k8be+pwaYsnnffY4urcDAAAAADqGAr0TRt3yXKvzTh83gO7tAAAAAIAOo0DvgGt+P1dvrNjS6vyfXnKMpk0Z2YURAQAAAACyBQV6O118z1taVL299fnHH0ZxDgAAAADoNAaJa4eKqto2i/Pjh/ehWzsAAAAA4JBQoLfDNb+f2+q844f30ayvndaF0QAAAAAAshFd3A/im4+/o9110aTzbjp9jG65YEIXRwQAAAAAyEYU6G2YMXetZi1a36K9KM/0wX9cEEBEAAAAAIBslVVd3Oes2qJfvfSBKqpqU7K+J+avTdo+48aTU7J+AAAAAAAaZc0Z9HmrazTtwblykh54s1LTr5+qstKSQ1pnXUOsRdvwvt0Oeb0AAAAAADSXNWfQ5685cNa8riGm8sqaQ17nh5t2Npk2SW/dcvYhrxcAAAAAgOaypkCfOqa/ivK9t+MkTRnd75DWd84vX1O02Qn0vIgd0joBAAAAAGhN1hToZaUlmn7DVF1w9BA5J62p2dPpdZ34k5e1YvPuFu19exQcSogAAAAAALQqa65Bl7wi/YQRk3TpfW/rx88u00dbd+v0IwZ16JrxCd9/QXuTXHsuSf92zvhUhQoAAAAAQBNZcwa9USRiuuqkEdq+t16/+ftKXfG7OZoxN/lo7Ikqqmo17tbnWi3Oxw3sqWlTRqY6XAAAAAAAJGVhgS5JW3bVxR83xJxuf2ZJm7deq6iq1WX3va365LW5+nbP18vfPjPFUQIAAAAAcEBWdXFvNHVMf+VHTA0xJ8kr0r86vUIlPQq1Y1+9uhfm69pTR2ve6ho9+956tXLSXJJ0/PA+mvW107oocgAAAABArgrkDLqZfd7MlppZzMwmp3r9ZaUluvOio5WfMOr6xzv2a/nHO7Vu2z6t3LRLt85crFmL2i7Obzp9DMU50EHpzm8AwSG/gexFfgPhEFQX9yWSLpX0RrpeYNqUkXriyydraJ9uHX6uSfrpJcfolgsmpD4wIPulPb8BBIb8BrIX+Q2EQCBd3J1zyyXJLL33FS8rLdG/fnKcbp25uN3PKcwzffgfF6QxKiC7dVV+A+h65DeQvchvIBxCfw26md0o6UZJGjmy46OoN468/sT8tdq2p15VW5PfH90kHcf15kCXOtT8BhBe5DeQvchvIH3SVqCb2SuShiSZdZtz7pn2rsc594CkByRp8uTJrjOxTJsyMl6oV1TV6v7XV2ne6hrVNTidO3Gw7r7yhM6sFshZYcpvAKlFfgPZi/wGwi9tBbpz7lPpWvehKCst0YPXMO4FcCjCmt8ADh35DWQv8hsIv6y8DzoAAAAAAJkmqNusXWJm1ZJOlvScmf0tiDgApB75DWQv8hvIXuQ3EA5BjeI+U9LMVKyrvr5e1dXV2rdvXypWhyzQrVs3DR8+XAUFBUGHkpNSmd8AwoX8BrIX+Q2EQ+hHcT+Y6upqFRcXa9SoUdwWAnLOqaamRtXV1Ro9enTQ4QAAAABAu2X8Nej79u1T//79Kc4hybt3Z//+/elRAQAAACDjZHyBLoniHE3wfQAAAACQibKiQAcAAAAAINNRoB+is846S3/7W9NBLu+++27dfPPNrT7nzDPP1IIFCw75tRcsWKCvf/3rnXruHXfc0WT6/fff18knn6yioiL94he/aDLvxRdf1Pjx4zV27Fjddddd8fbVq1drypQpGjt2rK644grV1dW1eB3nnL7+9a9r7NixOvbYY7Vw4cL4vD/84Q8aN26cxo0bpz/84Q/x9oqKCh1zzDEaO3asvv71r8s5J0n60pe+pNdee61T7xcAAAAAwo4C/RBdddVVevzxx5u0Pf7447rqqqvS/tqTJ0/Wb3/72w49Z+bMmZo0aZLuu+8+nXLKKVq8eLEkqV+/fvrtb3+r73znO02Wj0aj+upXv6oXXnhBy5Yt02OPPaZly5ZJkr773e/qW9/6llauXKmSkhL9/ve/b/F6L7zwglasWKEVK1bogQceiB+42Lp1q370ox9p7ty5mjdvnn70ox+ptrZWknTzzTfrwQcfjD/vxRdf7PBnAwAAAACZJicL9IqqWt07e6UqqmoPeV2XX365nnvuufjZ4zVr1mj9+vX6xCc+oZtvvlmTJ0/WxIkT9cMf/jDp83v16hV//Kc//Ulf+tKXJEmbN2/WZZddphNPPFEnnnii/vGPf7R47muvvabPfOYzkrwz4tdee63OPPNMjRkzptXC/Stf+Yqefvpp3XzzzZo5c6YGDRokSRo0aJBOPPHEFrcmmzdvnsaOHasxY8aosLBQV155pZ555hk55/Tqq6/q8ssvlyR98Ytf1KxZs1q83jPPPKNrrrlGZqapU6dq27Zt2rBhg/72t7/pnHPOUb9+/VRSUqJzzjlHL774ojZs2KAdO3Zo6tSpMjNdc8018fX26dNHhYWFkqRbbrlFRx11lI499tgWBxUAAAAAIBNl/G3WEv3or0u1bP2ONpfZua9e73+8UzEnRUw6ckixiru1fr/sow7rrR9+dmKr8/v166eTTjpJL7zwgi666CI9/vjj+sIXviAz03/8x3+oX79+ikajOvvss/Xee+/p2GOPbdd7+cY3vqFvfetbOu2007R27Vqde+65Wr58eZvPef/99zV79mzt3LlT48eP180339yi4C4oKNCmTZskSYMHDz5oHOvWrdOIESPi08OHD9fcuXNVU1Ojvn37Kj8/P96+bt26dj1/3bp1bbYPHz68Rbsk/eY3v5Ek1dTUaObMmXr//fdlZtq2bdtB3wcAAAAAhF3OnUHfsa9BMe+SZsWcN32oEru5J3Zvf/LJJzVp0iSdcMIJWrp0abxreHu88sor+trXvqbjjz9en/vc57Rjxw7t2rWrzedceOGFKioq0oABAzRo0CBt3LixxTKPPfaYvve97+nee+/VjTfeqC1btnTgnYZDnz591K1bN1133XX685//rB49egQdEgAAAAAcsqw6g97Wme5GFVW1uvqhctU3xFSQH9FvrjxBZaUlh/S6F110kb71rW9p4cKF2rNnj8rKyrR69Wr94he/0Pz581VSUqIvfelLSe/NnXhLsMT5sVhM5eXl6tatW7vjKCoqij/Oy8tTQ0PLgw+nnnqqXn31VX33u99VXl6evvvd7ya9drzRsGHD9NFHH8Wnq6urNWzYMPXv31/btm1TQ0OD8vPz4+3tff6wYcOaDPhWXV2tM888U8OGDVN1dXWL5RPl5+dr3rx5+vvf/64//elPuueee/Tqq6+2/eEAAAAAQMjl3Bn0stISTb9+qv7t0+M1/fqph1ycS9515GeddZauvfba+NnzHTt2qGfPnurTp482btyoF154IelzBw8erOXLlysWi2nmzJnx9k9/+tP67//+7/j0okWLDjlOSVqyZIkkqXv37jr22GO1c+fONpc/8cQTtWLFCq1evVp1dXV6/PHH9bnPfU5mprPOOkt/+tOfJHkjsl900UWSvIHovve970mSPve5z+nRRx+Vc07l5eXq06ePhg4dqnPPPVcvvfSSamtrVVtbq5deeknnnnuuhg4dqt69e6u8vFzOOT366KPx9TbatWuXtm/frgsuuEC//vWv9e6776bkswEAAACAIGXVGfT2KistSUlhnuiqq67SJZdcEu/qftxxx+mEE07QkUceqREjRujUU09N+ry77rpLn/nMZzRw4EBNnjw53o39t7/9rb761a/q2GOPVUNDg04//XTdf//9hxznD37wA23atElr1qzRsGHD9PDDD0uSPv74Y02ePFk7duxQJBLR3XffrWXLlql379665557dO655yoajeraa6/VxIleT4Wf/exnuvLKK/X9739fJ5xwgq677jpJ0qpVq9S7d29J0gUXXKDnn39eY8eOVY8ePfS///u/krxr93/wgx/oxBNPlCTdfvvt6tevnyTpf/7nf/SlL31Je/fu1fnnn6/zzz+/yXvYuXOnLrroIu3bt0/OOf3qV7865M8FAAAAAIJmjfeYzgSTJ092ze8fvnz5ck2YMCFlr7Fqs1cgHz6w10Hb29PWkfW11d7e+e19zh133NHiXuip8k//9E/69a9/rYEDB6Zl/e2R6u9FV7vid3MkSU98+eQ2lzOzCufc5K6IKd2S5XcmaO/fKlXr6erXC+J5XR1bWNeZq/l9xe/maMGarYom7J5MGd0vpX8DIF3I74Mbdctz8cdr7rowHSEBKdeVuZ2TZ9AhnXnmmWlb9//93/+lbd0AAAAAkK1y7hp0eNJZoAMAAAAAOi4rCvRM6qaP9OP7AAAAACATZXyB3q1bN9XU1FCUQZJXnNfU1HTo9nQAAAAAEAYZfw368OHDVV1drc2bN6dkfZt37pck1W0pOmh7e9o6sr622ts7P1XPyWTdunXT8OHDgw4DAAAAADok4wv0goICjR49OmXruyM+Qt/xB21vT1tH1tdWe3vnp+o5AAAAAICulfFd3AEAAAAAyAYU6AAAAAAAhAAFOgAAAAAAIWCZNPq5mW2WVOVPDpC0JcBwgpCL71nifbel1Dk3sCuCSbdm+d0oTH97YmldmOLJpliyPb8Thenv1tV477kpF/I7bH/fMMVDLK0LUzydieWQczujCvREZrbAOTc56Di6Ui6+Z4n3HXQcQQrTZ0AsrQtTPMSSmXL5s+K95+Z7zwVh+/uGKR5iaV2Y4gkqFrq4AwAAAAAQAhToAAAAAACEQCYX6A8EHUAAcvE9S7zvXBamz4BYWhemeIglM+XyZ8V7R7YK2983TPEQS+vCFE8gsWTsNegAAAAAAGSTTD6DDgAAAABA1qBABwAAAAAgBDKuQDez88zsAzNbaWa3BB1PVzGzNWa22MwWmdmCoONJFzN72Mw2mdmShLZ+Zvayma3w/y8JMsZ0aOV932Fm6/y/+SIzuyDIGLtakLkepu+hmY0ws9lmtszMlprZN4KKx8y6mdk8M3vXj+VHfvtoM5vr/62eMLPCdMeSEFOemb1jZs8GGUuybXQubLsOVa79pufa96Qj21Lz/Nb/LrxnZpOCixyHKky5HfQ+dMj2KUKzvxmy/ZvWYgnks8moAt3M8iTdK+l8SUdJusrMjgo2qi51lnPu+LDcGzBNHpF0XrO2WyT93Tk3TtLf/els84havm9J+rX/Nz/eOfd8F8cUmBDk+iMKz/ewQdK3nXNHSZoq6av+ZxFEPPslfdI5d5yk4yWdZ2ZTJf1M3nd1rKRaSdd1QSyNviFpecJ0kLE030bnwrar00KQ50HJpe/JI2r/tvR8SeP8fzdKuq+LYkSKhTS3g9yHfkTh2adIFosUzP5mmPZvWotFCuCzyagCXdJJklY65yqdc3WSHpd0UcAxIYWcc29I2tqs+SJJf/Af/0HSxV0ZU1do5X3nskBzPUzfQ+fcBufcQv/xTnnF6LAg4nGeXf5kgf/PSfqkpD91ZSySZGbDJV0o6SF/2oKKpRVZv+06RPyme7L2e9LBbelFkh71tzPlkvqa2dAuCRSpRm4nCNk+RWj2N0O2f9NaLIHItAJ9mKSPEqarFeCH18WcpJfMrMLMbgw6mC422Dm3wX/8saTBQQbTxb7md/V7OJu6PbZDGHM98O+hmY2SdIKkuUHF43cpXyRpk6SXJa2StM051+Av0pV/q7sl/bukmD/dP8BYkm2jA//OhFwY8zzd+J60/n5z8fuQrcL2twzjPnTY8j7Q/c0w7N+0EosUwGeTaQV6LjvNOTdJXnehr5rZ6UEHFATn3RcwV+4NeJ+kw+V1Jd4g6ZeBRoO4IL6HZtZL0tOSvumc2xFUPM65qHPueEnD5Z0lObIrXrc5M/uMpE3OuYogXj+JNrfRObbtQuv4niTItfeLwIR6HzoEeRDo/mZY9m9aiSWQzybTCvR1kkYkTA/327Kec26d//8mSTPl7Rjnio2N3dz8/zcFHE+XcM5t9IuhmKQHlVt/8zDmemDfQzMrkPeDMd059+eg45Ek59w2SbMlnSyvK2q+P6ur/lanSvqcma2R133yk5J+E1AsrW2jc3Lb1QFhzPO04nsiqfX3m3PfhywWqr9lSPehQ5P3Qe5vhmn/JlksQX02mVagz5c0zrxRegslXSnpLwHHlHZm1tPMihsfS/q0pCVtPyur/EXSF/3HX5T0TICxdJlm195dotz6m4cx1wP5HvrXVf9e0nLn3K+CjMfMBppZX/9xd0nnyLtOa7aky7syFufc95xzw51zo+R9P151zl0dRCxtbKNzctvVAWHM87ThexLX2vv9i6RrzDNV0vaEbq7ILKHJ7RDvQ4cm74Pa3wzZ/k3SWALbF3fOZdQ/SRdI+lDedY+3BR1PF73nMZLe9f8tzeb3LekxeV1I6uVds3SdvOtK/y5phaRXJPULOs4uet9/lLRY0nvyNlZDg46ziz+TwHI9TN9DSafJ6971nqRF/r8LgohH0rGS3vFjWSLpdr99jKR5klZKekpSURf/vc6U9GxQsbS2jc6FbVcKPruc+U3Pxe9JR7alkkzeyN+r/N++yUHHz79D+tuHIrdby7sujiFM+xSh2d8M2f5Na7EE8tmYHxQAAAAAAAhQpnVxBwAAAAAgK1GgAwAAAAAQAhToAAAAAACEAAU6AAAAAAAhQIEOAAAAAEAIUKDnGDNzZvZ/CdP5ZrbZzJ7t4HpeM7PJ/uM1ZjYg1bECaMnMdjWb/pKZ3dOFrz/AzOrN7Kauek0gV5jZxf7v9JGdfP5rZvaBmb1rZvPN7PgUhwigg1KY14vMbLmZ3djB55/Z0f18BIsCPffslnS0mXX3p8+RtC7AeABkls9LKpd0VdCBAFnoKklv6dDy62rn3HGS/kfSz1MSFYBDkaq8Pl7SqZJ+ZmaFhxqUmeUf6jqQHhTouel5SRf6j6+S9FjjDDPraWYPm9k8M3vHzC7y27ub2eP+kbuZkro3X6mZjfLnP2hmS83spcYDAWY21sxe8Y/qLzSzw9P/NoHc4ufgq2b2npn93cxG+u2PmNnlCcvt8v8famZv+Efll5jZJ/z2T5vZHD9XnzKzXgkvc5Wkb0saZmbDE9Z5nZl96G87Hmw8q29mA83saf9s3nwzO7ULPgog4/h5dpqk6yRdaWbnmdlTCfPjZ8EOkqON5kga5i/fz8xm+duGcjM79iDtd5jZH8zsTTOrMrNLzey/zGyxmb1oZgX+cneZ2TL/+b9I6wcEZKA05HUveSfbom09x3+d981soaRLE17vDjP7o5n9Q9IfyfVwokDPTY/L20h0k3SspLkJ826T9Kpz7iRJZ0n6uZn1lHSzpD3OuQmSfiiprJV1j5N0r3NuoqRtki7z26f77cdJOkXShtS+JSBndPcL6kVmtkjSnQnz/lvSH5xzx8rLud8eZF3TJP3NPyp/nKRF5l2u8n1Jn3LOTZK0QNK/SZKZjZA01Dk3T9KTkq7w2w+T9ANJU+Ud3U/sxvcbSb92zp0ob3vwUGffOJDlLpL0onPuQ0k1kmolTfF/gyUv3x5vK0ebOU/SLP/xjyS9428bbpX06EHaJelwSZ+U9DlJ/ydptnPuGEl7JV1oZv0lXSJpov/8nxzi+weyUaryerqZvSfpA0k/ds5FW3uOv3//oKTPyttfH9IspqP85zSe0SfXQ4auDTnIOfeemY2Sdybs+WazPy3pc2b2HX+6m6SRkk6Xv7PvP/+9Vla/2jm3yH9cIWmUmRVLGuacm+k/f1+q3guQg/b6BbUk7xp0SZP9yZN14Ej5HyX910HWNV/Sw/4R8lnOuUVmdoa8H+9/mJkkFco7Eyd5OxJP+o8fl/SwpF9KOknS6865rX5MT0k6wl/uU5KO8tclSb3NrJdzrsm19AB0lbwDWpKXX5+X9KKkz5rZn+T1fPt3SW3lqOTtyBfKO9N2vN92mvwD5s65V82sv5n1bqNdkl5wztWb2WJJeX4skrRY0ihJz0raJ+n3/hlArnEFWkpVXl/tnFtgZgMlvW1mL0o6ppXnHClvf3yFJJk39lTidet/cc7tTZgm10OGAj13/UXSLySdKal/QrtJusw590Hiwgk71wezP+FxVEm6wgPocg3ye0yZWUTej7icc2+Y2enydhAeMbNfyTu6/3LCkfVEV0kaYmZX+9OHmdm4g7x2RNJUDswBrTOzfvLOYB1jZk7eTrKT9C+Svippq6QFzrmd5v0gt5ajknS1vAPkP5fXq+bSVpY7mP2S5JyLmVm9c8757TFJ+c65BjM7SdLZki6X9DX/PQBQyvNakuSc2+x3W58i7wx3i+fYwQeH3N1smlwPGbq4566HJf3IObe4WfvfJP2rv6GQmZ3gt78hrzuszOxoeV3j28U5t1NStZld7D+/yMx6HFr4AJJ4W9KV/uOrJb3pP16jA5elfE5S4zVlpZI2OucelNf1fJK8AeBONbOx/jI9zewIMztCUi/n3DDn3Cjn3ChJ/ymvaJ8v6QwzKzFv0JnGS1sk6SVJ/9o40Y4dByAXXS7pj865Uj+/RkhaLe/g2iRJN8g7+ya1kqOJK/N3sH8gaap5I0e/KW+bIDM7U9IW59yONtoPyr/WtY9z7nlJ35J3mQyAA1Ka1357D0knSFrVxnPel9eDtXG8p0Ma1JVc73oU6DnKOVftnEt2feqP5e28v2dmS/1pSbpPUi8zWy7vmteKDr7kP0v6ut81/m21vB4GwKH7V0n/4ufZP0v6ht/+oLwC+l153eAbj56fKeldM3tHXvf13zjnNkv6kqTH/PU0dpe7StLMZq/3tKSrnHPrJP1U0jxJ/5B3QGC7v8zXJU32B5ZZJonbswEttZZfV8rrTnq+/7/ayNEm/C6sv5T0/yTdIanMX/4uSV/0F2utvT2KJT3rP/ctJb8OHshlqczr6f64MxWSHnHOVbT2HL/H2o2SnvPPtm86xPdBrncxO9CLAQCAzmm8rtw/gz5T0sON404AAACgfTiDDgBIhTv8o/tL5HXhmxVoNAAAABmIM+gAAAAAAIQAZ9ABAAAAAAgBCnQAAAAAAEKAAh0AAAAAgBCgQAcAAAAAIAQo0AEAAAAACAEKdAAAAAAAQoACHQAAAACAEKBABwAAAAAgBCjQAQAAAAAIgfygA+iIAQMGuFGjRgUdBhAaFRUVW5xzA4OOIxXIb6Ap8hvIXuQ3kJ1SkdsZVaCPGjVKCxYsCDoMIDTMrCroGFKF/AaaIr+B7EV+A9kpFblNF3cAAAAAAEKAAh0AAAAAgBCgQAcAAAAAIAQo0AEAAAAACAEKdAAAAAAAQoACHQAAAACAEKBABwAAAAAgBAIr0M2sm5nNM7N3zWypmf0oqFgApBb5DWQv8hvIXuQ3ELz8AF97v6RPOud2mVmBpLfM7AXnXHmAMQFIDfIbyF7kN5C9yG8gYIEV6M45J2mXP1ng/3NBxQMgdchvIHuR30D2Ir+B4AV6DbqZ5ZnZIkmbJL3snJubZJkbzWyBmS3YvHlzl8cIoHPIbyB7kd9A9iK/gWAFWqA756LOueMlDZd0kpkdnWSZB5xzk51zkwcOHNjlMQLoHPIbyF7kN5C9yG8gWKEYxd05t03SbEnnBRwKgBQjv4HsRX4D2Yv8BoIR5CjuA82sr/+4u6RzJL0fVDwAUof8BrIX+Q1kL/IbCF6Qo7gPlfQHM8uTd6DgSefcswHGAyB1yG8ge5HfQPYiv4GABTmK+3uSTgjq9QGkD/kNZC/yG8he5DcQvFBcgw4AAAAAQK6jQAcAAAAAIAQo0AEAAAAACAEKdAAAAAAAQoACHQAAAACAEKBABwAAAAAgBCjQAQAAAAAIAQp0AAAAAABCgAIdAAAAAIAQoEAHAAAAACAEKNABAAAAAAgBCnQAAAAAAEKAAh0AAAAAgBCgQAcAAAAAIAQo0AEAAAAACAEKdAAAAAAAQoACHQAAAACAEKBABwAAAAAgBCjQAQAAAAAIAQp0AAAAAABCgAIdAAAAAIAQoEAHAAAAACAEKNABAAAAAAgBCnQAAAAAAEKAAh0AAAAAgBCgQAcAAAAAIAQo0AEAAAAACAEKdAAAAAAAQoACHQAAAACAEKBABwAAAAAgBCjQAQAAAAAIAQp0AAAAAABCILAC3cxGmNlsM1tmZkvN7BtBxQIgtchvIHuR30D2Ir+B4OUH+NoNkr7tnFtoZsWSKszsZefcsgBjApAa5DeQvchvIHuR30DAAjuD7pzb4Jxb6D/eKWm5pGFBxQMgdchvIHuR30D2Ir+B4IXiGnQzGyXpBElzk8y70cwWmNmCzZs3d3lsAA4N+Q1kL/IbyF7kNxCMwAt0M+sl6WlJ33TO7Wg+3zn3gHNusnNu8sCBA7s+QACdRn4D2Yv8BrIX+Q0EJ9AC3cwK5CX/dOfcn4OMBUBqkd9A9iK/gexFfgPBCnIUd5P0e0nLnXO/CioOAKlHfgPZi/wGshf5DQQvyDPop0r6Z0mfNLNF/r8LAowHQOqQ30D2Ir+B7EV+AwEL7DZrzrm3JFlQrw8gfchvIHuR30D2Ir+B4AU+SBwAAAAAAKBABwAAAAAgFCjQAQAAAAAIAQp0AAAAAABCgAIdAAAAAIAQoEAHAAAAACAEKNABAAAAAAgBCnQAAAAAAEKAAh0AAAAAgBCgQAcAAAAAIAQo0AEAAAAACAEKdAAAAAAAQiA/6AAAoD1O+c9XtGH7fg3r201v3XJ20OEAAAAAKccZdAChd9pdf9f67fvlJFVv26fT7vp70CEBAAAAKUeBDiD0qrfta3MaAAAAyAYU6AAAAAAAhAAFOoDQ61YQaXMaAAAAyAbs5QIIveKi/DanAQAAgGxAgQ4g9IryI21OAwAAANmAvVwAoTfhsD5tTgMAAADZgAIdQOi9unxjm9MAAABANqBABxB6Udf2NAAAyA4VVbW6d/ZKVVTVBh0KEAhGWgIAAAAQmIZoTJVbduu59zbo3tkrFY055eeZbjn/SJ06doAGFXdTSY8CmZkqqmpVXlmjqWP6q6y0JOjQgZSjQAcAAACQFokFtZzTGyu2aHDvIkVjTss27NDS9Tv0wcc7tb8h1uR59VGnHz+7PD5dkGfq061ANXvq5JyUHzH96gvH6bPHHaaFa7dRtCNrUKADAAAASLnH5q3V9/68uNX5fXsUaOJhvXXNyaU66rDekjN9b+Z7qm+IKT8voh9ceJT69izQph37tWnnfr25YrO27K6TJDXEnL7++CL94Jkl2rmvQc5JRQURTb9+aosi/c0VmzV/9VadMX4QBTxCjwIdAAAAQMqt3rJbJqn50DERk248fYy+e96RMrMm80b279Hq2fBzjhqsqx8qjxfw1502Sq99sEXLNuyQJO2rj2l6eZWeXlgtkzRhSLH+VFGtRdXbJUn/PXul/uPiYzRtysg0vWPg0FGgAwAAAEi5cycO0aNz1qi+Iaa8iElmikZjKsiP6JyjhrQoziWprLSk1bPcZaUlmn791CYF/NkTanX1Q+XaXx+Tk/Tnd9a1Go9z0m0zF2v8kGLOpCO0KNABhF7zo+8tf84BAEDYNC+oJR3yteLNC/jE11i6brueX/Jxm893kp5eWE2BjtCiQAcQenkRKXHsmDxuEAkAQEZIVlCn6zUqqmr1t6UfH/R2rFt27k95DECqsJsLIPSG9O7W5jQAAEBZaYl+fPExTQocEwf2kVk4gw4g9L5y1jjdOnNxk2kAAIDmpk0ZqfFDiuMDxV06abj+vLBa0+eujS8zsLgouACBg6BABxB606aM1O9eX6Vte+v13fOOZPRVAADQqubd6j/4eGeT+RMP69PVIQHtFmiHDzN72Mw2mdmSIOMAkHqpzu+Pt+/V9r31+t+3KlOxOgCdxG83kL2yNb9r99TFH0es6TQQNkFfkfGIpPMCjgFAejyiFOX3Ob98Tfv9EV9WbN6tc375WipWC6BzHhG/3UC2ekRZmN9Tx/RXQZ53D5iCvEh8RHkgjAIt0J1zb0jaGmQMANIjlfm9YvPuNqcBdB1+u4Hsla35XVZaou98erwk6UcXTeQWawi1oM+gAwAAAEBanTS6nyRpcDF3gkG4hb5AN7MbzWyBmS3YvHlz0OEASKH25neR3y2ttWkA4cPvN5C9MjG/+/UslCTV7Ob6c4Rbpwp0M+uy0d+dcw845yY75yYPHDiwq14WyFlhzO9uRXltTgNonzDmN4DUIL/b1lig3zt7pWYk3HINCJtWC3Qzeyvh8R+bzZ6XtogApF2m5XeeRdqcBnBApuU3gPYjvzvvr4vWS5JWb9mtW2cupkhHaLW1l9sz4fHEZvNS0r/UzB6TNEfSeDOrNrPrUrFeAAeVUfl99GG925wG0ERa85vfbiBQ5HcnvbD04ybTT8ynQEc4tdUVxnVyXrs5565KxXoAdFhG5ff6bXvbnAbQRFrzm99uIFDkdyedf/RQvbliS3x62YYdqqiqZUR3hE5bBXpfM7tE3ln2vmZ2qd9ukvqkPTIA6ZRR+V3drCBvPg2giYzKb0mas2qLFq7dpqlj+rOzDLQt4/I7LKZNGam/vrtOcyq9u8hFo07llTVscxA6bRXor0v6XMLjzybMeyNtEQHoChmV33X1sTanATSRUfn98tKNuuGPCyRJ+RHT9aeN1o79DTJJl04azs4z0FRG5XfYnD1hcLxAj0kq6VEYbEBAEq0W6M65f2ltnpldlp5wAHSFTMvv3j0KtG1PfZNpAMllWn6/t25b/HFDzOn+Nyrj0zPmrtVFxx+m7oV5aog6nTCyRLV76jjTjpyVafkdNpVbdjWZnvlOtaZNGRlQNEBynb0dw68lPZ3KQACERujyuyBibU4DaLfQ5feZ4wfpvtdWqSHW8vJZJ2mWP/KyJD1VUS1JKsgzfWHyCM6wA02FLr/DZuXGpgX6/DW1mjF3LUU6QqWz9ypi7xjIXqHL78276tqcBtBuocvvstIS3XnR0erIcbf6qNP0uWt19UPlqqiqTV9wQGYJXX6Hzf6GlpfIMZo7wqazBXpKRnkGEErkN5C9Qpnf06aM1E8uPqbDOyX762N60t+5rqiq1b2zV1KwI5eFMr/D5IoTW54p37h9XwCRAK1rtYu7mS1W8kQ3SYPTFhGAtCO/geyVqfk9bcpIjR9SrPtfX6XVm3epIC+iwvyITh7TPz5o3MTD+mjJ+u16Yt5aRZ33Jp9YUK1Zi9arriEmJ7q/I7tlan6HxbQpI3XXC8u1Y19DvO3jnft18T1vadbXTgswMuCAtq5B/0ySNpM0QtL30hMOgC5CfgPZK2Pzu6y0RA9eM/mgy5mk6XPXxh/361moDf5ZsMbu70/M/0h3XnQ015Yi22RsfofFtJNGNhmMUpIWVW/XiT95WfO/f05AUQEHtNqbzDlX1fhPUj9JX5P0mqQ7JT3fNeEBSAfyG8heuZDfl04arm4FEeWZVFQQ0b9+cpy6FUSaXIDbEHP6wazFdHlHVsmF/E63Wy6YoEHFLW+vtnlXnc755WtdHxDQTFtd3I+QdJX/b4ukJySZc+6sLooNQJqQ30D2yoX8List0fTrp6q8siZ+y7XxQ4r19MJqPT53rRqHgYo66emF1XR1R9bIhfzuCt/81HjdOnNxi/YVm3frrueX65YLJgQQFeBpq4v7+5LelPQZ59xKSTKzb3VJVADSjfwGsldO5HdZaUmTwrtxesvO/Xpp2cZ4+8qNO4MID0iXnMjvdGu89OX2Zxar+cDuj85ZQ4GOQLU1YOqlkjZImm1mD5rZ2eL2DUC2IL+B7JXT+f3lMw5vcsu2ef59joEskdP5nUrTpozUyp9eqKK8ph/fnvoY2wwEqq1r0Gc5566UdKSk2ZK+KWmQmd1nZp/uovgApAH5DWSvXM/vstISHTOsT5M27nOMbJHr+Z0OZ4wf1KLtzr8uDSASwHPQW44653Y752Y45z4rabikdyR9N+2RAUi7TMnvwmZHt5tPA2gpU/I7HZrf63jJ+u1NBoubMXetLrrnLd346AIGkUNGyuX8TrUvn3F4i7Z9DTFdfM9bAUQDtKNAT+Scq3XOPeCcOztdAQEIRpjzuzAv0uY0gLaFOb/TYdqUkTpx1IHr06Mxb7A4ySvOb525WO9Wb9dLyzbqsvve1jcffyeoUIFDlmv5nWplpSW6+PjDWrQvqt5OV3cEoq1B4gAgFHbVRducBoDmSno0vY3SO/6Z8heWbGix7KxF6zWkdzcGhgJy1N1XnqCl67ZrxebdTdp/5Hd1bxxULpmKqlo9vbBaW3bu18DiIl06aTh3jsAhoUAHAABZb/nHOzVj7lqdf/RQvbliS4v5sxato0AHctjL3z5Tp931d1Vv2xdv298Q060zF2ve6hqNG1wcv61jo7ueX67736hssp7H5q3VpyYM1pfPOJxCHZ1CgQ4AALLOwOKiFm13/nWppt8wNenyzc+4A8g9owf2alKgN5q1aL1MUlFBRNOv97YhX/2/Cn28c3+LZWNOemnZRr2yfKN+cvExbZ59B5LhQk4AAJB1Lp00vEXbvoaYrn6wPOnykzjTBeS8848e2uo8J2lffUx3vbBcl933dtLiPFHMSbfNXMx17OgwCnQAAJB1ykpLdNKolkX3voZY0uWLi+hUCOS6aVNG6qeXHKNhfbupKD95mTR/TfI7P/Tpnt/ihvRO0vdnLtZtMxdzxwi0GwU6AADISt89v/3XlP/ujUpVVNWqoqpW985eyc40kKOmTRmpf9xytj74yfn66SXHKNLOO7s+/KWT9B9Jlo9Jmj53rb7wuzmcTUe7cLgYAABkpbLSEj198ym64ndvq5UT53FO0lUPzFFDzCnmpPyI6c6Ljub6USCHNeb/D2YtVtQlX2Zo7yLdc3WZykpLVFZaovFDinX/66v06vubFIs5NT4tGnO6/ZklGj+kmMHj0CbOoAMIveZHo9t7NBsAykpLdMWJ7Suy66JecS5JDf7ONGfSgdw2bcpIPXnTKZowpLjFvJtOH6M5t36qScFdVlqiB6+ZrCe/fLKumjJSeQk7LTHnVF5Z0yVxI3NRoAMIvfxmFXnzaQBoS7IB4yRpVP8ebT6PnWkAkld0v/DN03XT6WM0pHeRThrl9c5p69aMZaUl+uklx+jHFx3dpEjnjhE4GAp0AKFX16xfWfNpAGhLY1f3IcVFMknFRXn66SXH6JdfOL7N5+VHTFPH9O+SGAGE3y0XTFD5rZ/Skzed0u5u6tOmjNSdn5soyRvZ/c5nl9IzB23iGnQAAJD1ykpLVH7bp1q0P33zKbrrheVatWmXBvfupkmlJTpySLH+84X3Nbyke/wMOteMAuisbXvr44/318f09MJqtiloFQU6AADIWWWlJXrqplNatL+3brueWlCtX770gQrzI5p+/VR2qAF0ytQx/VWYZ6qLeoPGPTZ3reZV1mjMwF46c/wg1e6pU0mPQtXuqdPUMf3Z1uS4rCrQK6pqVV5ZwxcbAAAckgG9iiR5XVLrG2Iqr6xh3wJAp5SVlujzk0doxty1cvLuGrFy826t3LxbLy3b2GTZbvkRTb+BA4K5LGuuQa+oqtVVD8zRL1/6QFc/VM61HQAAoNM+NWFw/I4RBfkRrkUHcEgunTRcRQUHL732NcT065c/pJbJYVlToJdX1sRvj1JXH2PUVQAA0GllpSW69tTRkqT/uuxYzmYBOCRlpSWafv1UnXPU4Bbzmt+b5q2VW3TFA3N0258XU6jnoKzp4p54y4KYUnsLg7ueX64nF3ykvIhpQK8i1Udj6tezUH391xhYXKSJh/XRkvXbtWXn/vh04/UkS9Zvl8k7cpb4A5+sSz7d9CHxPQCAMLjuE6P10Fur9VHt3qBDAZAFGu+RPmPuWj0xf60G9+7W5Br0F5Zs0JsrtkiSGqJO0+et1dPvVDMGRo7JmgJ9yfrtbU4fzPE/+pu27W046HKbd9X5D3Z3aP2S9Pj8j3TpCYeppGeRPtq6Ry8t3aioc4qYdPKY/oo6p3mrtyrmpIhJk0aWqG+Pgg6/TmoEf59pCz6EQD6FbXvqtKCqVs5JRQUMTAQAQRnap7uOG95HLy39WF89a2zQ4QDIEtOmjNS0KSNbtI8fUqz5a7Zqf31MjTeU3Vcf0w1/mK9InrdXWlxUoJPH9FNJz0IN69NdtXvrVdKjULM/2KRNO/bpihOTrxuZI9AC3czOk/QbSXmSHnLO3dXZda3cuLPN6eZG3fJcZ1+q06Ixp6cq1qmbf/1J1HmpF3PSso93KCJTzM/GmJPWbt2jvfVFXR6nC8EtpkMQglxAH0TNrv3x70EmD0yUyvwGEC65lN+fnjhEP//bB7rrheU656ghGbk9Bjoil/I7bBq7wT+9sFp/WlCtumhMkrR1z4HbtG3ZWafVW1o/Ufhu9WL9cc4ajejXQ9v21Gnr7jr161mocYOLW/TwXblxp7burtOYgb305TMOZ/sWEoEV6GaWJ+leSedIqpY038z+4pxb1pn1JX5xJamypuUXt6uLclPTQrMwL6LHbpiislH9VFFVq6sfKld9Q0wF+RE9dM2JktSk7b5/KiNRclDz70YmDkyU6vwGEB65lt8jSrpLkn73eqUeeXsNvZqQ1XItv8OorLREZaUlumzScH37iUVas3VPh9ex/OOdWv5xwsnKzbs1b03r17I3jiZ/8fGH6e4rT+hM2EihIM+gnyRppXOuUpLM7HFJF0nqXIG+a3+T6S0769JakE8YUqwR/XpI6tw16I1HyJpfZ5ysDbmlte9GhklpfgMIlZzK78brz52kugzu1QS0U07ld5iVlZboxjMO160zF7e5XPMTgodi1qL1kkSRHrAgC/Rhkj5KmK6WNKWtJ9TU1OiRRx5JOm/73v5qOii9U/uuIE72lT7QZpL65Mc0sfd+7Y+ZJNNxffZpRPfN3mh0krRdqtsuHSHvX+N0T0l1jW2SFs+uUPMU6ylpcZWatCdrQ+7J8O9BSvNb6i8vGxt/hlwbywJIsxTnd7ht3ZuvfOurBuddfvbxsnI9UvVWfP5He/O1Zk+BRvWo14juBx/LBgi5nMrvTPCZIUUq39pd+6JeXdM9z+mIXnXqlufUPS+mvdGIuufFtHh7kar2dnaQ7MaayWnWonXqX7uU7VmAQj9InJndKOlGSRo2bFiry5XkR7WlPrFAb6s4b16UO/8ZTteW7uALCXSR9uY3gMyTLfk9onuDvjhymyq2ddOi7d30zrbuGtNjp8y84vwPa73iPd+kL47cxj4EckK25HcmmNx3vyb33d+u5T7am693txdpV0OeJGlv1LQ7GlHPvKgGFsU0pFt9vKD/eF++KncVamtDng6c2PROhPyjpruuHN72eF5IHwtqICwzO1nSHc65c/3p70mSc+4/W3vO5MmT3YIFC5LO++ffz43flqAjuNYCmczMKpxzk4OOo7lU53eyy1XW3HVhSmIFwipX8juT3Dt7pX7+tw907amj1K0gT39b+rFWJdzVZdwgb6Cl/r0KtWz9jky+TAlpRn4jLK75/Vy90ayGGjuwp1759pnBBJThUpHbQZ5Bny9pnJmNlrRO0pWSpnV2ZecfPbRDBTo790BapTS/AYRKzub3zWccrtnvb9LD/1gTb4v4HfbMTFt27dd3nno33l6Yz60ykXFyNr9z1aPXTdGZP5+tNTUHBqMbM7BXgBEhsALdOddgZl+T9Dd5t3F42Dm3tLPrmzZlpP73rUqtaOX+5BTkQNdJdX4DCI9czu9IxHTK4f21oMobDTli0pUnjdSwvt01dUx/TRrZVz98ZqkeLa9SzGX2rTKRm3I5v3PZL79wvC6/7205SXkmffmMw4MOKacFeg26c+55Sc+nan0vf/vMFt00uudHtPwn56fqJQC0U6rzG0B45HJ+nzF+kB54szJ+K8zLEu7QIkkXnTBM0+euVdS5jL1VJnJbLud3LjOTnPP+R7BCP0hcRz16XZsDTQIAAHTawW6FWVZaou9dcKR+8txy/ds5R3D2HEDoPb2wWjF/WLKGmHTXC8v11E2nBBtUDoscfBEAAAA0Kist0VfPGttq8X3NyaPUozBPj89bq9tmLlaF3yUeAMKo+Unz+WtqNWPu2kBiAQU6AABASi1et1376qKq3LJH0+eu1VUPlHdZkV5RVat7Z6/koACAdrt00vAWRfoLSzYEEguysIs7AABAkMora5R4E9u6aEz//qd3dfoRA+WcdMExQ3TS6PZfm15RVdukS33z6cTlpj1YrrqGmPIiputPG63i7gXc7g1Am8pKS/SJcQOajOPVv2dhgBHlNgp0AACAFJo6pr8K8kx1Ua9Mj5hUu7tO/+vfnu2Rt9doREl3HTu8r8YN7qVxg4o1bnAvjerfU4vXbfeK79H9dFhJdz30ZqX+9x9rFHNSfsQ0ZXQ/la/eKudck9u4VVTV6ofPLNH+hpgkqSHmdP8blTJJRQUR3f6ZiardU0exDiAp12y6ZnddIHGAAh0AACClykpL9NiNJ+vphdUyed1Hyytr9MuXPlDMedd7Fubnaen67Xp+yQY5f8844o+i3HxHuVFDzGlOZU18MKf99THd//oqbdtTpwVrapM+z0naVx/TrTMXx9uK8iM6/+ghuvvKE1L3pgFktIlDe+vNZmfQ7529koN6AaBABwAASLGy0pIWO7WF+ZH47dn+6/JjVVZaon31UVVu3q0Vm3bqsXlrVV65VZJXxI8Z1EuVm3bFC+/8iOnOi47WD55ZrGjMK75fXraxxWsnFvqmlgX//oaYZi1ar0UfbdMvv3A8O98AVNy9oMn0rEXr44+H9i7SPVeXsa3oIhToAAAAadba7dm6FeTpqMN666jDemt4SQ9d/VB5vIi/7tTRuvPZpaqrjyniF+fTpozU0vXbNb2VEZYjJv3k4mNUu6dOJT0KVbunTu9+tE0vJSnk19Ts0efvf1s/ufgYTZsyUpJ3HXvimX92yIHcMHVMf+XnmRqiLfvibNixX5fd97aevvkUtgldgAIdAACgCyQ7q958fvMifvyQ4hZF/aWThuvphdWqq48p1mwdN35iTLzYblRRVau/v79R0eYLS4o56bZZXvf38UOKdeUDc1Tv76A/VVGtx26Yyg45kAPKSkv0ibH9NfuDLa0uc8Mf5mvh7Z/uwqhyEwU6AABASDQv4pMV9YmFfEmPQs3+YJM27dinK04c2aI4b1z+yS+fovtfX6W3V27R7rpok/nOST+YtVhXnjQyXpxLUn1DTOWVNRToQI7YvS/a5vyte+p18T1vadbXTuuiiHITBToAAECGSSzckxXlyZZ/8JrJkqQZc9fq+7MWxwebk6SokxY2u3d6JOJ1ewWQG9Zt33vQZRZVb9c5v3xNL3/7zPQHlKMiQQcAAACArjNtykg9ddMpGjuoV5P29zfubLakdV1QAALXvbB9525XbN6ti+95K83R5C4KdAAAgBxTVlqin112rPIiB4pw12xsqGjM6emF1V0cGYCgXHvq6CbTeRHp4uMPS7rsourtmtHKYJU4NBToAAAAOaistEQ3nDa6zWWemL9WFc26vgPITtOmjNRPLzlGxw3vo08fNVhPfvkU3X3lCTp+eJ+kyz8xnwI9HSjQAQAAclTzex83F41J97++qouiARC0aVNG6pmvnaYHrpkcH+di1tdO002nj1Gk2VUvRfmUkunApwoAAJCjpo7p32Knu7lX39/EWXQgx91ywQQ9ddMpykvYXiz8aBvbhjSgQAcAAMhRZaUluvETY9pcJhZzKq+s6aKIAIRVWWmJzj5ycHy6IeroYZMGFOgAAAA57JYLJrQYCCrxmlMnqaRHYRdHBSCMBvYuajL99+UbOYueYhToAAAAOe7uK0/QTy85Rp8YN0A/veQYnTNxSHxexKTaPXUBRgcgLC6dNLxJARlz4m4PKda+m90BAAAgq02bMlLTpoyUJFVU1SrPpKjz7obOGXQAktfNffKoEs1bc+Cs+Zad+wOMKPtwBh0AAACtijrpjr8upRsrAElSXw7YpRUFOoCMxI4iAKRPeWWNYu7AdF1DjIHiAEiSBhY3vQ592frt7JelEF3cAWSky+97W2MG9lSvonzJTCbvOknzH5tJJpPMb5d5bU0eJy7bbLrZeuLPjbc3fW7EfxBf1p8XMW9aydr99ajZ6yS+DzVvT1jPgffddN2N62zRrsZYms9L9rjlOlt+Rv77bvF5mP8emr9vP97Igb9Nk3ZLfG+J77tpLEpsT/Lemj6nHe8j6d/3wPto+Xe1+N9C8e9Uy/fR8u/qzX9nba3KV2/V1DH94/eYBcJm6pj+yotIDbEDbXRzByB516E/Pm+tov5BvOpt+/T5+9/WTy4+Jn6ZDDqPAh1ARnKSnJNKehbKucZp5z/2//cfx/yF4+3+sjH/sTcvYfnYgWWkputx/rJqsZ4Dr6lk7Wqc13Q9rq3Hzd5Hk/epA6+FzGOSigoimn79VIp0hFJZaYmuOHGkps9dG29bsn57gBEBCIuy0hIdPayP3q0+sE2IOen2Z5Zo/JBiftcOEQU6gIxkkn7++eNy/kfgwEGJpoV7rNnBhcZlYv7yaqXd+UceEteTePBDydrV/OBDKwcXkhxoiPnPSzyIkXhwIzGW5AdJnB9Py1ji7c1eU4nvt8Vn1yyWeOzJD6Ic9HNuts7yyhrNWVUjJ6ne7zKc699hhNfEw/o0mX583lqZvLNnfG+B3HbFiSP1bvXiJm0x5/hdSwEKdAAZqX+vQn4AdKBLuj8VZChoh1PHDtDVD5WrviGmgvyIpo7pH3RIQKua31ot5qTpc9fqqQUf6YwjBsnMOwBlMg3sXUThDuSQxq7sD79ZqZVbdkuSCvldSwkKdAAZadJIdgKRecpKSzT9+qkqr6zhGnSE3tQx/eO3WktUF3V6efnGFss/VVGtx27gsg0gVzTemvGmP1bo5WUf66LjDgs6pKzAKO4AMtKXzzg86BCATikrLdFXzxpLEYPQKyst0Y8vPkZ5kfb1zqlriOnphdVpjgpA2EwZ3U9RJz25oFpXP1TOiO6HiDPoAEJvzV0XatQtz8Wnn775FIobAOgC06aM1PghxSqvrFFJj0ItWb9dTy74SA3NT6v7Hpu7Vq9/uFkTh/bWl884nG01kAN21TVI8sZa2V/vHagj9zuPAh1ARlhz14VBhwAAOamstKTJzvZlk4br6YXV2rJzvyRp1eZdWrXZuwbVSVpXu1fravfq5eUb9R/cdgnIeqccPkB324eK+gOiPrngI13GmBSdRoEOAACAdmtesFdU1erz97/t35XhAOek789aLOectu2tZ9wFIEuVlZbojPED9er7myVJDVGn+19fpQevmRxwZJmJAh0AAACdVlZaok9NGKyXlrUcOC7mpNtmLZFJKsgzfX7yCEZ7B7LQ0D7dm0z/fflGVVTVkuudEMggcWb2eTNbamYxM+PQCpBFyG8ge5HfaM2Xzzhchfktdysbx5dz8kZ/nz53ra54YI5u/fNizZi7VvfOXsmAUiFBfuNQXDppuBLHk4w56a4XlgcXUAYL6gz6EkmXSvpdQK8PIH3IbyB7kd9Iqqy0RI/dMLXJYHImaeJhfXTns0u1vz6mxh7wDVGnGfPWSpJMUlF+RLd/dqJq99TRDT5Y5Dc6LVlPmvlranXN7+fq0eumBBhZ5gmkQHfOLZcks/bdtgNA5iC/gexFfqMtza9NbzR+SLGeXlitP1VUq77hQKEueWfW9zXEdNusxTJJhfkRTb+ee6kHgfzGofryGYe3uNTljRVbdNfzy3XLBRMCiirzcB90AAAApE1ZaYl+eskxeuyGqbpqykgV5kfiO6Dm/3PO6xJb1xBTeWVNgNEC6Kyy0hKdNKrlwbVH56zp+mAyWNrOoJvZK5KGJJl1m3PumQ6s50ZJN0rSyJHcpgMIA/IbyF7kN9Kl8Qz7ZZOGx7vC1+6pU0mPQt3x16Wqa4gp5qTKLbt07+yVTbq7V1TVqryyhi7wh4j8Rrp99/wJuuy+t5u07amPacbctdxysZ3SVqA75z6VovU8IOkBSZo8ebI7yOIAugD5DWQv8hvplqwr/PghxXr1/Y16YfEGPV2xTpKUZ6ZPHjlQkYjpleWbFIs55UVM/3r2OE0Z3U+Dios0qHc39SpqujubrJhvb1u2I7+RbmWlJbrp9DG6/43KJu0Pv1VJgd5O3GYNAAAAgWos2rsV5OlXL30oJynqnOZU1igWk6L+TdYbYk6/fvnDJs/tWZinQb27aWBxkQoipvLVWxWNOUVMGjOwl3bsrdOmnXXx5Qf0KlRhXkQbtu+TkzfS/Emj+2l4SQ/1KspXz6I89SzK9x4X5h94XJTn/3+gLS/S9HrtXCz6geZuuWCC3lixWcs27Iy3VW7ZzW3X2imQAt3MLpH035IGSnrOzBY5584NIhYAqUV+A9mL/Ea6nXL4AN1bsFL1DTEV5Ef0h2u90Z+vfqhc9Q0x5edF9F+XHasBxUXatHOfNu3Yr4079nuPd+7Xsg074sV8zEkN0ZgG9CqKF+gmaXDvborGnNZv3xdf7sONu1RVs0e79jdo9/4Gxdp5TrhbQSRetJuktVv3SMrMwe7Ib6TSjy8+Rp+//+14LjknlVfWZFROBCWoUdxnSpoZxGsDSC/yG8he5DfSray0RNOvn9riLHSytmQqqmrjxXxBfkS//MLxktSk7c6Ljm7R9uA1k+Prdc5pX30sXqw3/r+7rkG79ke9xwntjW1L12+PFyP1/mB3mVSMkN9IpbLSEl1/2mg98OZqSd4dG0p6FAYbVIagizsAAABCI9k16q3dwi3Zc9tb4LdW9JuZuhfmqXthngYWF7U77uYHB6aO6d/u5wLZqE9CQR4xqXZPXRtLoxEFOgAAALJGewv89hb9HXnd9p7pB3JB4kGq/Ihx0KqdKNABAACAFEh10Q9ki7qo0xW/e1slPQo1ekBPjRtcrEsnDSdfkogEHQAAAAAAILvc//qqJtMNMWnzrjrNW1Or6XPX6soH5qiiqjag6MKLM+gAAAAAgJTatGNfm/Pro05fmV6hL50yWqX9emh1zW4uDxEFOgAAAAAgxa44caTerV7c6vy8iKm4W4F+9uL78bai/Ihm3JBZtyhMNQp0AAAAAEBKTZsyUmtrduv+NyrjbSU98jVuUHGTa9B/+vxyPfhGpZyk/Q0xzZhbldODLVKgAwAAAABS7pYLJuiciUPaLLjPnThEj85Zo7qGmGJO+vPCdTKTCvMjmn597p1Np0AHAAAAAKTFwe5ukHiLwnfW1uqV5ZvknFTXEFN5ZQ0FOgAAAAAAXaWxiK+oqtWbK7Zov382/d2PtmlPXYN6FOZO2cpt1gAAAAAAgSsrLdGMG6bqW58ap4uOP0wvL9+oC3/7lt5Zmzu3Y8udQxEAAAAAgFBL7BJ/5Ykj9Z2n3tXl98/RZZOGaUS/Hjrl8AFtdnuvqKpN+SBz6VhnayjQAQAAAAChc/Lh/fXCNz+hf52xUE8uqJYk/co+1DGH9dGIfj3Uu3uB+nQvUO/u+erTvUA1u+p0z6srVR+NKT/P9NWzxuqwPt21PxrT/vqo9jfEtL8hprqGmPY3RBMee/ProjHtr/fmNT7esbdeG3ful+QNXPdYmm8Dl5UF+hW/m6NlG3a0Ov+oob31xJdPji8rKT4NhAHfy5ZG3fKcJGnNXRcGHAlwaMjv9Ev2GTe2NffEl0/O6L/JocTe2nM7s85M/gxTic8h/A71e5/uv3FXf4cSX6+1x52JLZXvo3e3Ap00ur/e+HCLnCTnpM279mtXXYN27K3X9r31qo+6Fs+rjzrd/cqKpOsszIuoKD+iooKI97ggT0X5ERXme+09CvNV4k9X1eyOF+gN0fQPXJeVBToAAAAAIDtMHdNfRQUR1TfEVJAf0T3TJsWLZOec9tXHtH1vveasqtF3n35PDbGY8vMi+sXnj9WkkSV+4e0X4XkRRSLW7teuqKrV5fe/Lee8M+hTx/RP19uURIEOAAAAAAixxFuxNb8O3MzUvTBP3QvzdMmkYRrZv0dKrxcvKy3RUUN7a8feet195Qlcgw4AAAAAyG0Hu596R5friF5F+epVlN8l92TnNmsAAAAAAIQABToAAAAAACFAgQ4AAAAAQAhQoAMAAAAAEAIU6AAAAAAAhAAFOgAAAAAAIWDOuaBjaDcz2yyp6iCLDZC0pQvCSTfeR7iE9X2UOucGBh1EKmRofhNP24inbQeLJ9fyuyuF7bvQiLg6JqxxSeR3e4XpbximWCTiaUuYYpGaxnPIuZ1RBXp7mNkC59zkoOM4VLyPcMmW95HpwvZ3IJ62EU/bwhZPLgnrZ09cHRPWuKRwxxYmYfqcwhSLRDxtCVMsUurjoYs7AAAAAAAhQIEOAAAAAEAIZGOB/kDQAaQI7yNcsuV9ZLqw/R2Ip23E07awxZNLwvrZE1fHhDUuKdyxhUmYPqcwxSIRT1vCFIuU4niy7hp0AAAAAAAyUTaeQQcAAAAAIONQoAMAAAAAEAJZU6Cb2Xlm9oGZrTSzW4KOR5LM7GEz22RmSxLa+pnZy2a2wv+/xG83M/utH/97ZjYp4Tlf9JdfYWZfTGgvM7PF/nN+a2aWpvcxwsxmm9kyM1tqZt/IxPdiZt3MbJ6Zveu/jx/57aPNbK7/2k+YWaHfXuRPr/Tnj0pY1/f89g/M7NyE9tB9D7NBEJ9rG9/7O8xsnZkt8v9dkPCcpN+LFMa0xs+TRWa2wG/rcB6mKJbxCZ/BIjPbYWbf7MrPx9K8jU1RPD83s/f915xpZn399lFmtjfhc7o/4Tldsm3PFa1t+xPm/9bMdoUlLv+7+h9m9qGZLTezr4ckrrPNbKH/fX3LzMZ2ZVwJ8eWZ2Ttm9qw/PdqS/IaHIK7p/rZuib9tKAgirrAws8/736eYmU1OaD/HzCr8bV6FmX0yyXP/krhdDSIeM+thZs/52/OlZnZXULH489L2O9FGPP3N2y/aZWb3NHvOVX4875nZi2Y2IOB4Cs3sAX87+r6ZXRZULAnLtP977JzL+H+S8iStkjRGUqGkdyUdFYK4Tpc0SdKShLb/knSL//gWST/zH18g6QVJJmmqpLl+ez9Jlf7/Jf7jEn/ePH9Z8597fprex1BJk/zHxZI+lHRUpr0Xf929/McFkub6r/mkpCv99vsl3ew//oqk+/3HV0p6wn98lP8dK5I02v/u5YX1e5jp/4L6XNv43t8h6TtJlk/6vUhxTGskDWjW1qE8TOPf6GNJpV35+SjN29gUxfNpSfn+458lxDMqcblm6+mSbXuu/Gtt2+9PT5b0R0m7whKXpH+R9KikiD9vUEji+lDSBL/9K5IeCejv+W+SZkh61p9O+hsegrgu8D9Lk/RYUHGF5Z+kCZLGS3pN0uSE9hMkHeY/PlrSumbPu9T/XJNuL7sqHkk9JJ3lPy6U9Gaqts2d+WzS+TvRRjw9JZ0m6SZJ9yS050vaJH//RN7v8B1BxePP+5Gkn/iPI2q279SVsXTme5wtZ9BPkrTSOVfpnKuT9LikiwKOSc65NyRtbdZ8kaQ/+I//IOnihPZHnadcUl8zGyrpXEkvO+e2OudqJb0s6Tx/Xm/nXLnz/vKPJqwr1e9jg3Nuof94p6TlkoZl2nvx42k8S1Lg/3OSPinpT628j8b39ydJZ/tHKC+S9Lhzbr9zbrWklfK+g6H8HmaBQD7XNr73rWnte5FuHc3DdDhb0irnXNVB4kzp55PObWyq4nHOveSca/AnyyUNb2sdXbltzxWtbfvNLE/SzyX9e5jiknSzpDudczF/uU0hictJ6u2395G0vivjkiQzGy7pQkkP+dOm1n/DA4tLkpxzz/ufpZNXTLWZ+9nOObfcOfdBkvZ3nHON36WlkrqbWZEkmVkveQc+fhJ0PM65Pc652f4ydZIWKkV/047Gku7fiTbi2e2ce0vSvmazGg9E9fRzsrdSuH3oRDySdK2k//SXiznntgQVS2e+x9lSoA+T9FHCdLXa3pEO0mDn3Ab/8ceSBvuPW3sPbbVXJ2lPK/O6eZ8g74h6xr0XvwvaInlH+l6WdxZvW8IOdOJrx+P152+X1P8g7yNTvoeZJPDPtdn3XpK+5nfjetj8LtTqmjidpJf8rm43+m0dzcN0uFLeGaJGQX0+Uuq2S+lwrbwzHY1G+11iXzezTyTE2eXb9mzXfNvvnJsr6WuS/pLwfQlLXIdLusLMFpjZC2Y2LiRxXS/peTOrlvTPklLWxbcD7pZ3QCXmT/dX67/hQcYV53dt/2dJL3ZxTJnoMkkLnXP7/ekfS/qlpD0hiUeSZN6lSp+V9PeAYgnV74Rzrl7egcXF8grzoyT9Pqh4/L+PJP3YvMtynjKzwW09J806/D3OlgI9I/lHvTLmPnf+EaCnJX3TObcjcV6mvBfnXNQ5d7y8o54nSToy2IgQdkm+9/fJ24E+XtIGeRvdrnKac26SpPMlfdXMTk+cGUQemne95+ckPeU3Bfn5NBGm7ZKZ3SapQdJ0v2mDpJHOuRPkd401s96tPR+Hpvm238+dz0v675DFdbS8y0D2OecmS3pQ0sMhietbki5wzg2X9L+SftWVMZnZZyRtcs5VdOXrHkw74vofSW84597swrACYWavmHfNffN/B+31ZmYT5V0G9GV/+nhJhzvnZoYhnoT2fHkHpH/rnKsMMpZDcSjxJFlXgbwC/QRJh0l6T9L3gopHXpf74ZLe9veZ5kj6RRCxdPZ7nN/RFwqpdZJGJEwP99vCaKOZDXXObfC7qDR2XWvtPayTdGaz9tf89uFJlk8LP/meljTdOfdnvzkj34skOee2mdlsSSfL6+qa7x+BT3ztxvdR7W+Q+0iqUdvft0z5HmaSwPI72ffeObcxYf6Dkp7tqjidc+v8/zeZ2Ux5B5k6moepdr68o/ob/dgC+3x8qdoupYyZfUnSZySd7R80kH8WZL//uMLMVkk6QgFsD3NJwrb/LEljJa30emSqh5mtdM4FMvBZQlznyTsb1vg7O1NeMRyIhLjOl3ScfyZdkp5Q158RPlXS58wbeLKbvG60v1Hrv+GBxWVm/+ec+ycz+6GkgUphYRVmzrlPdeZ55l0iMFPSNc65VX7zyZImm9kaefXKIDN7zTl3ZkDxNHpA0grn3N0dWWeKYznk34nOxtOK4/11rpIkM3tS3hgwQcVTI+9sdeN29ClJ1wUUS6e+x9lyBn2+pHHmjeRZKK+75V8Cjqk1f5H0Rf/xFyU9k9B+jXmmStrud7v7m6RPm1mJ31X005L+5s/bYWZTzdu7uCZhXSnlr//3kpY75xKPmGfUezGzgXZgBOXuks6Rd13xbEmXt/I+Gt/f5ZJe9Xeu/yLpSvOuAxotaZy868sy6XuYSQL5XFv73lvT67gvkdQ4Imdr34tUxdPTzIobH8vLnyXqeB6m2lVK6N4e1OeTICXbpVQFY2bnyev6+jnn3J6E9oHmXQMtMxsj7/Oo7Mpte65oZdtf4Zwb4pwb5ZwbJWlPVxfnrcT1vqRZ8g4gSNIZ8gZnCzqu5ZL6mNkR/mKNbV3GOfc959xw/+91pbzf5KvV+m94kHH9k5ldL2+Mi6ucP54AWvK/a8/JG9zzH43tzrn7nHOH+Z/raZI+7Ehxnup4/Hk/kXey5pvpjqOtWEL4O7FO0lFmNtCf7vLtQyJ/X/2vOnDw/WxJywKKpXPfY5eiEfaC/idvtMwP5V1TfFvQ8fgxPSavG2O9vCPi18m7XurvklZIekVSP39Zk3SvH/9iNR0Z8Fp5AyqtlPQvCe2T5e38rpJ0jyRL0/s4TV430fckLfL/XZBp70XSsZLe8d/HEkm3++1j5BUKK+UdZSvy27v50yv9+WMS1nWbH+sHShg5M4zfw2z4F8Tn2sb3/o/+9/o9eUXf0IN9L1IUzxh5o6C/K2+wmNv89g7nYQpj6invSHWfhLYu+3yU5m1siuJZKe8a98bvUOOdIS7z/46L5A029NmE9XTJtj1X/qmVbX+zZYIYxb2136S+8nbKF8vrmnlcSOK6xI/pXXm9TMZ0ZVzNYjxTB0ZLT/obHoK4Gvwcbsz9Ft+7XPrnf3+q5fUc2ijvBI0kfV/S7oTPaZGa3blAbdz1oqvikXeW2skrPBvbrw/qs0nn70Rr8fjz1sgbDHWXv8xRfvtN/mfznrziuH/A8ZRKesOP5+/yLikLJJbOfI/NfwIAAAAAAAhQtnRxBwAAAAAgo1GgAwAAAAAQAhToAAAAAACEAAU6AAAAAAAhQIEOAAAAAEAIUKBnGTOLmtkiM1tiZk+ZWY8Ur/81M5t8kGW+mfi6ZvZ84z1VAaSGmV1sZs7Mjuzk8wvN7G4zW2lmK8zsGTMbnuo4ARwaM9vVgWXPNLNTEqZvMrNr/MdfMrPDOvH6a8xsQEefB6CpjuRyJ9f/vJn19f99pRPPP9PMnk1HbOgYCvTss9c5d7xz7mhJdfLuS9jVvikpXqA75y5wzm0LIA4gm10l6S3//874qaRiSeOdc+MkzZL0ZzOz1IQHIABnSooX6M65+51zj/qTX5LU4QIdQGZI2N/uK6nDBTrCgwI9u70paayZ9TOzWWb2npmVm9mxkmRmd5jZH81sjn8G7Qa/vckRNDO7x8y+1HzlZnafmS0ws6Vm9iO/7evydgBmm9lsvy1+9N3M/s0/u7/EzL7pt40ys+Vm9qC/rpfMrHtaPxkgg5lZL0mnSbpO0pVmdp6ZPZUwP57DZvZpP8cX+r1qevk9XP5F0recc1FJcs79r6T9kj7pP+8af5vxrpn90W8bbGYz/bZ3zewUP3+XJLz2d8zsDv/xa2b2m4RePSd1xecDZDsz+6yZzTWzd8zsFT83R8k7KP8tP+c+4f/Of8fMLpc0WdJ0f173Zr/Nk83sNf9xf/93eKmZPSTJEl73n8xsnr+O35lZXpe/eSCLmNnx/r75e/7va4nf/pqZ/czPtw/N7BN+ew8ze9LMlvnLzzW/Z2tCTt8l6XA/T3/e1n69v//wvpktlHRpwjI9zexh//XfMbOLuu5TAQV6ljKzfEnnS1os6UeS3nHOHSvpVkmPJix6rLwd8pMl3W4d6/52m3Nusr+OM8zsWOfcbyWtl3SWc+6sZjGVySsKpkiaKukGMzvBnz1O0r3OuYmStkm6rCPvF8gxF0l60Tn3oaQaSbWSpphZT3/+FZIe93+ovy/pU865SZIWSPo3SWMlrXXO7Wi23gWSJprZRP95n3TOHSfpG/7830p63W+bJGlpO2Lt4Zw7Xt7R/Ic79W4BNPeWpKnOuRMkPS7p351zayTdL+nXfk+6NxsXds79SV5+X+3P29vGun8o6S3/93impJGSZGYT5G1bTvVzOirp6pS/MyC3PCrpu/4++mJ5+dco3zl3kryeqY3tX5FU65w7StIPJJUlWectklb5uf7/WnthM+sm6UFJn/XXMyRh9m2SXvVf/yxJP0/Yx0CaUaBnn+5mtkjeD/FaSb+Xd6btj5LknHtVUn8z6+0v/4xzbq9zbouk2ZI6cobrC/4Rt3ckTZR01EGWP03STOfcbufcLkl/lvQJf95q59wi/3GFpFEdiAPINVfJ2ymX///nJb0o6bP+wbkLJT0j70DYUZL+4W8XviiptB3r/6Skp/ztgpxzWxPa7/Pbos657e1Y12P+8m9I6m2MRwGkwnBJfzOzxZL+n7zf4FQ5XdL/SZJz7jl5BwAl6Wx5O/Hz/e3J2ZLGpPB1gZxiZn0k9XXOve43/UFe/jX6s/9/4n7xafJ//51zSyS9dwghHClv/3uFc87Jz3vfpyXd4uf6a5K6yT9Yh/TLDzoApNxe/8h2nLV9SalLMt2gpgdvujV/kpmNlvQdSSc652rN7JFky3XA/oTHUUl0cQeSMLN+8grlY8zMScqTl7f/IumrkrZKWuCc22le8r/snLuq2Tp6ShppZsXOuZ0Js8okPauDH2xLdLDtRbJtDIBD89+SfuWc+4uZnSnpjk6sIzF32/P7bZL+4Jz7XideC0DHNe4bR3VoNdtB9+uTMEmXOec+OITXRSdxBj03vCm/G5r/Q74loWvrRWbWzcz6yxtcZr6kKklHmVmRf7br7CTr7C1pt6TtZjZYXnf6RjvlDT6VLI6L/etnekq6xG8D0H6XS/qjc67UOTfKOTdC0mp5P8CTJN2gA2fXyyWdamZjpfg1ZUc453bLO1L/q8ZrSM0b6bmHpFf9f5/3twuNBwUk6e+Sbvbb8vyj/xslDfKvWy2S9Jlm8V7hL3+apO3tPOsOoG19JK3zH38xob21399k89boQPfYxMvK3pA0TZLM7HxJJX773yVdbmaD/Hn9zKw9PXIAJOH/HtY2Xl8u6Z8lvd7GUyTpH5K+IElmdpSkY5Is0zzXW9uvf1/SKDM73J9OPJj/N0n/6h/oV8IlqegCFOi54Q5JZWb2nryBIxJ/zN+T17W9XNKPnXPrnXMfSXpS0hL//3ear9A5967f/r6kGfI2GI0ekPSi+YPEJTxnoaRHJM2TNFfSQ865FusG0Kar5F0XmuhpSVfKO/t9vv+/nHOb5Y3c/Jif/3PkdWmTpO9J2ifpQzNbIa+b/CXOs1TSf0h63czelfQr/znfkHSW3622QtJRzrl6SXfKy+uX5W0TEu0zs3fkXRt73aG/fSDn9DCz6oR//ybvd/0pM6uQtCVh2b9KusQfHOoTzdbziKT7/Xnd5Y1P8xszWyDvDF2jH0k63cyWyhs0aq0kOeeWyRub4iV/e/KypKGpfrNAFkuWy1+Ud333e5KOl/d72pb/kTTQzJZJ+om8sWCaHPh2ztXIu7RtiZn9vLX9eufcPkk3SnrOv2R1U8JqfiypQNJ7/rbgx4fyxtEx5l1ygFxk3kjLu5xzvwg6FgDZx7xRob/jnFsQdCwAAGQ6v9dbgXNun3/m+xV5t0utCzg0pBDXoAMAAABA+PWQdyvjAnnXiX+F4jz7cAYdAAAAAIAQ4Bp0AAAAAABCgAIdAAAAAIAQoEAHAAAAACAEKNABAAAAAAgBCnQAAAAAAELg/wPJNzd0Rgmt6AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1008x504 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = plot_ale(rf_exp, n_cols=4, fig_kw={'figwidth':14, 'figheight': 7});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the model is no longer linear, the ALE plots are non-linear also and in some cases also non-monotonic. The interpretation of the plots is still the same—the ALE value at a point is the relative feature effect with respect to the mean feature effect, however the non-linear model used shows that the feature effects differ both in shape and magnitude when compared to the linear model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From these plots, it seems that the feature `MedInc` (median income) has the biggest impact on the prediction. Checking the built-in feature importances of the random forest classifier confirms this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'MedInc'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_names[rf[1].feature_importances_.argmax()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's explore the feature `Latitude` and how its effects are different between the two models. To do this, we can pass in matplotlib `axes` objects for the `plot_ale` function to plot on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "plot_ale(lr_exp, features=['Latitude'], ax=ax, line_kw={'label': 'Linear regression'});\n",
    "plot_ale(rf_exp, features=['Latitude'], ax=ax, line_kw={'label': 'Random forest'});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this plot we can gain a couple of interesting insights:\n",
    "\n",
    " - Whilst for linear regression the feature effects are the same across the range of the values of `Latitude`, for a random forest model, because it's a more capable predictor, there are intervals of `Latitude` where different behaviour is observed\n",
    " - For both models the feature effects of `Latitude` are negatively correlated, i.e. for areas more South (lower latitude) the effects on house price predictions are positive. However, for the random forest, the ALE curve is sometimes piece-wise constant which tells us that there are regions where the effects are roughly the same for different latitudes (e.g. between latitudes 36 and 37)\n",
    " - In general, the ALE for a non-linear model doesn't have to be monotonic, although in this case there are only very small departures from monotonicity which may be due to artifacts from the grid-size used to calculate the ALE. It may be useful to experiment with different resolutions of the grid size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing the ALE plots of multiple models on the same axis should be done with care. In general, we can only make qualitative comparisons of the plots between different intervals of the feature values as we have done here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare multiple models and multiple features we can plot the ALE's on a common axis that is big enough to accommodate all features of interest:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2, 4, sharey='all');\n",
    "\n",
    "plot_ale(lr_exp, ax=ax, fig_kw={'figwidth':14, 'figheight': 7},\n",
    "         line_kw={'label': 'Linear regression'});\n",
    "plot_ale(rf_exp, ax=ax, line_kw={'label': 'Random forest'});"
   ]
  }
 ],
 "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": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}