1. Random Forest Cross Validation And Hyperparameter Tuning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notebook 1: Building an Expected  Goals Model Using Random Forest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> Welcome to my first notebook on expected goals models. In these notebooks, we will build on the excellent work already done by David Sumpter on the Friends of Tracking Series and @clekraus on his soccer_analytics Github repo, and take a deeper dive into the concepts, compare the pros and cons of simpler and more complex models, examine how we would calibrate our models, and generate plots that could be helpful for a coaching staff <font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> In our first notebook on building expected goals models, we will look at building an Expected Goals Model using a Random Forest model. Random Forest models are generally the most widely known and simples model class in Machine Learning, and the concepts learned from building a Random Forest model translate when building other machine learning and deep learning models, such as a  LightGBM (which @clekraus uses in his notebook) or an xGBoost (which @DevinPleuler intends to release soon on his analytics-handbook Github repo). Random Forests are also notorious for not being well calibrated, which will come in handy during the notebook where we focus on calibrating our machine learning models. </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### <font color='black'> In this notebook, we will place an emphasis on the following points:  <br>\n",
    "\n",
    " 1.) The dangers of using the default sklearn parameters when training a Random Forest, particularly with regards to overfitting.<br> <br>\n",
    "2.) Hyperparameter tuning and cross validation, comparing Grid Search and Random Search <br> <br>\n",
    "3.) Feature importance for Random Forest Models. </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> First, let's import all of the packages that we will use in this notebook </font> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.inspection import permutation_importance\n",
    "\n",
    "from sklearn.model_selection import train_test_split, KFold, cross_val_score, GridSearchCV, RandomizedSearchCV\n",
    "\n",
    "from sklearn.metrics import log_loss, roc_auc_score, roc_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> Now, let's load in the data  from the CSV. To generate this code and to get an understanding of  how this dataset was generated, please download all the Wyscout data, and run all the code in notebook 0.</font> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction To Our Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we start, let's drop all rows with distance greater than 60 meters (as many of those datapoints are inaccurate, see: https://twitter.com/andrew_puopolo/status/1261412288856285192)  as well as the columns that are informational (those will come in handy later in the  series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "shots_model = pd.read_csv('shots_design_matrix.csv')\n",
    "shots_model=shots_model[shots_model['Distance'] < 75]\n",
    "shots_model=shots_model.drop(columns=['Unnamed: 0',  'firstName',  'lastName',  'label', 'venue', 'date', 'eventSec', 'matchPeriod'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> Let's separate our data into our target variables (goals),  and our design matrix used to predict  goals (everything else).</font> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "y=shots_model['Goal']\n",
    "x=shots_model.drop(['Goal'], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> Let's take a look at the data we have to predict the number of goals</font> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>side_of_field</th>\n",
       "      <th>left_foot</th>\n",
       "      <th>right_foot</th>\n",
       "      <th>header</th>\n",
       "      <th>counter_attack</th>\n",
       "      <th>strong_foot</th>\n",
       "      <th>C</th>\n",
       "      <th>Distance</th>\n",
       "      <th>Angle</th>\n",
       "      <th>out_swinging</th>\n",
       "      <th>in_swinging</th>\n",
       "      <th>rebound</th>\n",
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       "      <th>prev_smart_pass</th>\n",
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      "text/plain": [
       "    X   Y  side_of_field  left_foot  right_foot  header  counter_attack  \\\n",
       "0   9  29              1          0           1       0               0   \n",
       "1  29  29              1          0           1       0               0   \n",
       "2   4  57              0          0           1       0               0   \n",
       "3   4  61              0          0           0       1               0   \n",
       "4  25  33              1          1           0       0               0   \n",
       "\n",
       "   strong_foot     C   Distance     Angle  out_swinging  in_swinging  rebound  \\\n",
       "0            0  21.0  16.601958  0.257917             0            1        0   \n",
       "1            1  21.0  33.369522  0.199901             0            1        0   \n",
       "2            1   7.0   6.192132  0.889119             1            0        0   \n",
       "3            0  11.0   8.292316  0.506886             0            0        0   \n",
       "4            1  17.0  28.480959  0.236357             1            0        0   \n",
       "\n",
       "   prev_cross  prev_touch  prev_pass  prev_smart_pass  free_kick  prev_duel  \n",
       "0           0           0          1                0          0          0  \n",
       "1           0           0          1                0          0          0  \n",
       "2           0           0          0                0          0          1  \n",
       "3           0           0          0                0          0          1  \n",
       "4           0           0          1                0          0          0  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> For those that are unclear of what each of these 20 variables represent, here's a brief description of each: <br> <br>\n",
    "<b> X </b> (per wyscout): The percentage of X position in percentage from the left corner of the attacking team<br>\n",
    "<b>Y </b>: (per wyscout, and after a transformation) Y position in percentage from the rightcorner of the attacking team <br> \n",
    "<b>side_of_field </b>: 0 if the shot came from the right side of the field, from the perspective of the attacking team, 1 otherwise<br> \n",
    "<b> left_foot </b>: 1 if the shot was taken with the left foot, 0 otherwise. <br>\n",
    "<b> right_foot </b>: 1 if the shot was taken with the right foot, 0 otherwise. <br>\n",
    "<b> right_foot </b>: 1 if the shot was taken with the head or body, 0 otherwise. <br>\n",
    "<b> counter_attack </b>: 1 if the shot was taken with the head or body, 0 otherwise. <br>\n",
    "<b> strong_foot </b>: 1 if the shot was taken with the player's stronger foot, 0 otherwise. This feature was an inspiration from @clekraus. <br>\n",
    "<b> C </b> The number of meters from the center of the pitch, as calculated in David Sumpter's first Friends of Tracking Video on expected goals. <br>\n",
    "<b> Distance </b> The number of meters from the goal, also courtesy of David Sumpter. <br>\n",
    "<b> in-swinging </b> 1 if the shot was taken as an \"in-swinger\", 0 otherwise. An \"in-swinger\" is right footed shot from the left side of the field (relative to the attacking team), and vice versa for a left footed shot. <br>\n",
    "<b> out-swinging </b> The opposite of in-swinging. <br>\n",
    "<b> prev_rebound </b> 1 if the previous event was a shot, 0 otherwise. <br>\n",
    "<b> prev_cross </b> 1 if the previous event was a cross, 0 otherwise. <br>\n",
    "<b> prev_touch </b> 1 if the previous event was a touch, 0 otherwise. <br>\n",
    "<b> prev_pass </b> 1 if the previous event was a pass, 0 otherwise. <br>\n",
    "<b> prev_smart_pass </b> 1 if the previous event was a smart pass, 0 otherwise. <br>\n",
    "<b> free_kick </b> 1 if the event shot was a free kick, 0 otherwise. <br>\n",
    "<b> prev_duel </b> 1 if the previous event was a duel, 0 otherwise. <br> <br> </font>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting an Initial Random Forest Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> One of the most important concepts of machine learning is to ensure that your model is able to predict well on data that it has never seen before. Thus, in order to build and then test our model, we split our data into a training set which will be used to build the model, and a testing set that is not used  to build the model, but  which we use to evaluate the model's predictions  </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> Now, we will build a Random Forest model using the sklearn implementation of the model. However, first we ought to take a look at what a Random Forest is, and how it works. There are tons of resources available on the internet to help explain this better, but I'll just give a brief overview. </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> Random Forest is an example of a \"bagging\" algorithm, which means it fits a number of independent decision trees, and then averages the predictions across the decision trees. Each individual decision tree uses a random subset of the data, and at each node of the tree splits based on certain features that improve the accuracy of the model. </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font> The first model we will build will be the default sklearn implementation of Random Forest. We will build it on the training set and then evaluate on the testing set. As a brief note, ``sklearn`` is a Python package that contains many tools for working with predictive machine learning models. Sklearn functions will aid with the vast majority of the work we do throughout this series.  </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another note is that every model we fit will include a `random_state` that we set equal to 42. This has no impact on the performanace of the model, but ensures that the results will be identical every time the specific model is run, both on my computer and yours."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "naive_rf_model=RandomForestClassifier(random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, ccp_alpha=0.0, class_weight=None,\n",
       "                       criterion='gini', max_depth=None, max_features='auto',\n",
       "                       max_leaf_nodes=None, max_samples=None,\n",
       "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                       min_samples_leaf=1, min_samples_split=2,\n",
       "                       min_weight_fraction_leaf=0.0, n_estimators=100,\n",
       "                       n_jobs=None, oob_score=False, random_state=42, verbose=0,\n",
       "                       warm_start=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_rf_model.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to evaluate the performance of our model. To do that, we will examine the log-loss and ROC-AUC score on both the training set and the testing set. For more information on these two metrics, please refer to @clekraus and David Sumpter's work on this matter, as they explain this in detail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The log loss of our model on the training set is : 0.1373\n",
      "The ROC AUC of our model on the training set is : 0.969\n"
     ]
    }
   ],
   "source": [
    "train_y_hat=naive_rf_model.predict_proba(x_train)\n",
    "naive_train_log_loss=log_loss(y_train, train_y_hat[:,1])\n",
    "naive_train_roc_auc=roc_auc_score(y_train, train_y_hat[:,1])\n",
    "print('The log loss of our model on the training set is : ' +str(round(naive_train_log_loss, 4)))\n",
    "print('The ROC AUC of our model on the training set is : ' +str(round(naive_train_roc_auc, 3)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that for now, these metrics are pretty meaningless as there is nothing to compare them to. It is unclear what a log-loss of 0.1422 means, but will be useful when comparing two models  to one another."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at these  metrics on the test set, to see how our model performs on new data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The log loss of our model on the test set is : 0.876\n",
      "The ROC AUC of our model on the test set is : 0.695\n"
     ]
    }
   ],
   "source": [
    "test_y_hat=naive_rf_model.predict_proba(x_test)\n",
    "naive_test_log_loss=log_loss(y_test, test_y_hat[:,1])\n",
    "naive_test_roc_auc=roc_auc_score(y_test, test_y_hat[:,1])\n",
    "print('The log loss of our model on the test set is : ' +str(round(naive_test_log_loss, 4)))\n",
    "print('The ROC AUC of our model on the test set is : ' +str(round(naive_test_roc_auc, 3)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, this is a problem! Our model performs really well on the training set, but terribly on our test set, which means that the model does not predict well on new data. Overfitting is a classic problem in machine learning, and we'll spend the rest of this notebook learning how to avoid this issue."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another tool we have is a  plot of the ROC/AUC curve. Fortunately, sklearn already has an implementation of that, so we'll just use that and  compare the ROC/AUC between our models on the training  set and the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_fpr, train_tpr, train_thresholds = roc_curve(y_true=y_train, y_score=train_y_hat[:,1])\n",
    "test_fpr, test_tpr, test_thresholds = roc_curve(y_true=y_test, y_score=test_y_hat[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
    "plt.plot(train_fpr, train_tpr, label='Train ROC AUC')\n",
    "plt.plot(test_fpr, test_tpr, label='Test ROC AUC')\n",
    "plt.plot([0, 1], [0, 1], color = 'black', linewidth = 2, linestyle = '--')\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.legend()\n",
    "plt.title('ROC AUC Curve For Naive Random Forest Model On Train vs Test Set')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This hammers the point home further that this model performs very poorly on data it has not seen before. Thus, we need to dive deeper into what is going on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Random Forest  Hyperparameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ``naive_rf_model`` uses the default sklearn Random Forest implementation to build the model, so let's take a lot at that"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, ccp_alpha=0.0, class_weight=None,\n",
       "                       criterion='gini', max_depth=None, max_features='auto',\n",
       "                       max_leaf_nodes=None, max_samples=None,\n",
       "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                       min_samples_leaf=1, min_samples_split=2,\n",
       "                       min_weight_fraction_leaf=0.0, n_estimators=100,\n",
       "                       n_jobs=None, oob_score=False, random_state=42, verbose=0,\n",
       "                       warm_start=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_rf_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we see a series of values that are associated with this particular usage of the Random Forest. These values are known as ``hyperparameters`` that help the Random Forest model learn from the data. In this notebook, we will take a closer look at `n_estimators`, `max_depth`, `min_samples_leaf`, `min_samples_split`, `criterion`, and `max_features`. These parameters help with preventing overfitting, but still ensuring that the model learns from the training data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a ton of resources online that will explain the function of these hyperparameters way better than I can, but I will give a brief explanation of them. <br> <br>\n",
    "`n_estimators`: The number of decision tress used to train the model. Increasing the number of trees will reduce the variance of your predictions as each tree is independent, but increase the amount of time it takes to train the model.  The sklearn default is 100. <br>\n",
    "`max_depth`: The maximum allowed depth of any individual decision tree. A greater value leads to the model having more splits and learning from the data, but also makes it prone to overfitting. The sklearn default is `None`, which means that the model will keep splitting if it sees the opportunity to improve the `gain`.\n",
    "`min_samples_leaf`: The minimum number of samples allowed to be in a leaf. The greater the valaue, the less the tree will split, which reduces overfitting but gives the model less opportunity to learn from the data. The sklearn default is 1. <br>\n",
    "`min_samples_split`: The minimum number of samples allowed to split a leaf into a new leaf. The greater the value, the less likely the tree will split further, which reduces overfitting but gives the model less opportunity to learn from the data. The sklearn default is 2. <br>\n",
    "`criterion`: The mathematical representation of the \"gain\" that is used to split nodes. Either `gini` or `entropy`. sklearn defaults to `gini`. <br>\n",
    "`max_features`: The maximum number of features allowed to use when determining how to split a node. The sklearn default is `auto`, which represents the square  root of the total number of features. The greater the value, the more precise but more prone t overfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, every default `sklearn` parameter (except `n_estimators`) takes on a value that leads to the most extreme overfitting of the data. Thus, you must be really careful when fitting an sklearn (or any machine/deep learning model) to ensure that the hyperparameters are what you want them to be, otherwise your model will perform poorly and you might not understand why."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross Validation  and  Hyper Parameter Tuning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will go through the process of determining the optimal values of these 6 parameters. There are 3 very common approaches, `RandomSearch`, `GridSearch` and Bayesian methods. @clekraus mentions this in his notebook, but skips over some of the details on the tuning in order to showcasae the results. Thus, I figured this was a good opportunity to explain how to come to the optimal set of hyperparameters.  The optimal parameters will be found using a common machine learning methodology known as `cross_validation`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cross validation is a method to ensure that we find the optimal set of parameters to ensure that our model fits the data as well as possible, and is capable of generalizing to new data. The most common form of cross validation is `KFold`. In `KFold`, we split our data into `K` different folds (naturally). We then fit the model `K` times with the relevant hyperparameters. In each run of the model, we use `K-1` folds for training, and then test on the fold that isn't used for training. Thus, we are able to see how our model performs on data it hasn't seen before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reason why we fit this `K` times is to ensure that all datapoints are treated equally in training and testing. If we always train on the same data and test on the same data, then we are `overfitting to the test set`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's take a look into the methods for determining hyperparameters, as well as their pros and cons. For each method, we determine a \"grid\" of values for each parameter that  we use to test. Then, each algorithm attempts to pick the best value for each hyparameter:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Random Search: </b> <br> <br>\n",
    "Description: The user sets a number of iterations to test the model, and then on each iteration the algorithm picks a random set of parameters from the grid (without replacement) and computes the loss metrics. The more iterations, the more likely you are to find the best parameters, but the longer the algorithm takes to run. <br>\n",
    "Pros: Fastest method out of them all, does a reasonably good job of finding close to the best parameters. Allows for parallelization (which allows you to try multiple sets of parameters at the same time). <br> \n",
    "Cons: Setting too few values can lead to suboptimal solutions. Unlikely to find the absolute best set of parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Grid Search: </b> <br> <br>\n",
    "Description: The algorithm tries every permutation of values from the grid and computes the loss metrics. <br>\n",
    "Pros: Grid search guarantees that you will find the \"optimal\" set of hyperparameters, as it tries every single possibility. Like Random Search, it also plays nicely with parallelization. <br>\n",
    "Cons: By far the slowest out of all the options as it tries every single combination. Thus, you must limit the number of parameters to tune/the number of values for each parameter or else the grid will become massive and you will never finish running your grid search."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Bayesian Search: </b> <br> <br>\n",
    "Description: In Bayesian Search, the algorithm learns from results of the previous iterations to pick values that are more likely to produce optimal solutions  <br>\n",
    "Pros: Learns from previous iterations, so converges on the correct solution faster. <br>\n",
    "Cons: (Generally) doesn't play well with parallelization, so it takes much longer to find the solution. As with all Bayesian methods, there is a risk of converging on a local (rather than global) maximum.  <br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will implement both Grid and Random Searches. We won't look at Bayesian because the code is more complicated and due to the lack of parallelization, it is quite slow. In addition, GridSearch is guaranteed to find a \"more optimal\" solution than Bayesian (as it tries every set of value), albeit in a lot more time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will evaluate the performance of these 2 methods on `speed` and `performance`, where `performance` is determined on how the model with the chosen hyperparameters performs on the held out test set (which is not used at all in the cross validation procedure). We use `%timeit` to time the algorithms to illustrate how long they take"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "random_search_model = RandomForestClassifier(random_state=42)\n",
    "grid_search_model = RandomForestClassifier(random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up the cross validation folds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "cv_split = KFold(n_splits=5, random_state=42, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up the grid to pick hyperparameters from:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf_hyperparam_grid={\n",
    "    \"n_estimators\": [100, 500],\n",
    "    \"max_features\": ['auto', 7, 10, 15],\n",
    "    \"min_samples_leaf\": [1, 5, 20, 100],\n",
    "    \"min_samples_split\": [2, 10, 50, 250],\n",
    "    \"criterion\": [\"gini\", \"entropy\"],\n",
    "    \"max_depth\": [4, 6, 8, 10, None]\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the Random Search:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf_random_search=RandomizedSearchCV(\n",
    "    estimator=random_search_model,\n",
    "    param_distributions=rf_hyperparam_grid,\n",
    "    n_iter=200,\n",
    "    scoring=\"neg_log_loss\",\n",
    "    refit=True,\n",
    "    return_train_score=True,\n",
    "    cv=cv_split,    \n",
    "    verbose=10,\n",
    "    n_jobs=-1,\n",
    "    random_state=42\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the cross validation on the training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 200 candidates, totalling 1000 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 12 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done   1 tasks      | elapsed:    8.4s\n",
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      "[Parallel(n_jobs=-1)]: Done 1000 out of 1000 | elapsed: 22.3min finished\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 16.2 s, sys: 3.01 s, total: 19.3 s\n",
      "Wall time: 22min 27s\n"
     ]
    }
   ],
   "source": [
    "%time tuned_random_model = rf_random_search.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print out the \"optimal\" hyperparameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'n_estimators': 500,\n",
       " 'min_samples_split': 250,\n",
       " 'min_samples_leaf': 5,\n",
       " 'max_features': 7,\n",
       " 'max_depth': 8,\n",
       " 'criterion': 'gini'}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_random_model.best_params_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See how the model performs on the test  set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The log loss of the model with Random Search is: 0.28049189107821393\n",
      "The ROC AUC score of the model with Random Search is: 0.7814659668626089\n"
     ]
    }
   ],
   "source": [
    "random_y_hat = tuned_random_model.predict_proba(x_test)\n",
    "print(\"The log loss of the model with Random Search is: \" + str(log_loss(y_test, random_y_hat)))\n",
    "print(\"The ROC AUC score of the model with Random Search is: \" +str(roc_auc_score(y_test, random_y_hat[:,1])))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do the same for Grid Search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## This code takes forever to run, so please avoid running the next 4 cells unless you really want to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf_grid_search=GridSearchCV(\n",
    "    estimator=grid_search_model,\n",
    "    param_grid=rf_hyperparam_grid,\n",
    "    scoring=\"neg_log_loss\",\n",
    "    refit=True,\n",
    "    return_train_score=True,\n",
    "    cv=cv_split,\n",
    "    verbose=10,\n",
    "    n_jobs=-1,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 1280 candidates, totalling 6400 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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      "[Parallel(n_jobs=-1)]: Done 4026 tasks      | elapsed: 80.6min\n",
      "[Parallel(n_jobs=-1)]: Done 4117 tasks      | elapsed: 82.3min\n",
      "[Parallel(n_jobs=-1)]: Done 4208 tasks      | elapsed: 84.0min\n",
      "[Parallel(n_jobs=-1)]: Done 4301 tasks      | elapsed: 86.1min\n",
      "[Parallel(n_jobs=-1)]: Done 4394 tasks      | elapsed: 88.9min\n",
      "[Parallel(n_jobs=-1)]: Done 4489 tasks      | elapsed: 91.5min\n",
      "[Parallel(n_jobs=-1)]: Done 4584 tasks      | elapsed: 93.1min\n",
      "[Parallel(n_jobs=-1)]: Done 4681 tasks      | elapsed: 94.6min\n",
      "[Parallel(n_jobs=-1)]: Done 4778 tasks      | elapsed: 96.5min\n",
      "[Parallel(n_jobs=-1)]: Done 4877 tasks      | elapsed: 99.3min\n",
      "[Parallel(n_jobs=-1)]: Done 4976 tasks      | elapsed: 102.6min\n",
      "[Parallel(n_jobs=-1)]: Done 5077 tasks      | elapsed: 106.6min\n",
      "[Parallel(n_jobs=-1)]: Done 5178 tasks      | elapsed: 109.3min\n",
      "[Parallel(n_jobs=-1)]: Done 5281 tasks      | elapsed: 111.0min\n",
      "[Parallel(n_jobs=-1)]: Done 5384 tasks      | elapsed: 113.8min\n",
      "[Parallel(n_jobs=-1)]: Done 5489 tasks      | elapsed: 116.5min\n",
      "[Parallel(n_jobs=-1)]: Done 5594 tasks      | elapsed: 120.1min\n",
      "[Parallel(n_jobs=-1)]: Done 5701 tasks      | elapsed: 124.7min\n",
      "[Parallel(n_jobs=-1)]: Done 5808 tasks      | elapsed: 128.1min\n",
      "[Parallel(n_jobs=-1)]: Done 5917 tasks      | elapsed: 130.1min\n",
      "[Parallel(n_jobs=-1)]: Done 6026 tasks      | elapsed: 133.1min\n",
      "[Parallel(n_jobs=-1)]: Done 6137 tasks      | elapsed: 137.1min\n",
      "[Parallel(n_jobs=-1)]: Done 6248 tasks      | elapsed: 141.2min\n",
      "[Parallel(n_jobs=-1)]: Done 6361 tasks      | elapsed: 146.8min\n",
      "[Parallel(n_jobs=-1)]: Done 6400 out of 6400 | elapsed: 148.2min finished\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 55.8 s, sys: 7.61 s, total: 1min 3s\n",
      "Wall time: 2h 28min 22s\n"
     ]
    }
   ],
   "source": [
    "%time tuned_grid_model = rf_grid_search.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'criterion': 'gini',\n",
       " 'max_depth': 8,\n",
       " 'max_features': 7,\n",
       " 'min_samples_leaf': 1,\n",
       " 'min_samples_split': 250,\n",
       " 'n_estimators': 500}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_grid_model.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The log loss of the model with Grid Search is: 0.2804863243791734\n",
      "The ROC AUC score of the model with Grid Search is: 0.7814397059192428\n"
     ]
    }
   ],
   "source": [
    "grid_y_hat = tuned_grid_model.predict_proba(x_test)\n",
    "print(\"The log loss of the model with Grid Search is: \" + str(log_loss(y_test, grid_y_hat)))\n",
    "print(\"The ROC AUC score of the model with Grid Search is: \" +str(roc_auc_score(y_test, grid_y_hat[:,1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We end up with almost identical parameters (only difference is min_samples_leaf), and we get ever so slightly better performance from the grid search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the ROC-AUC curves as well to compare this model to the naive model above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "random_fpr, random_tpr, random_thresholds = roc_curve(y_true=y_test, y_score=random_y_hat[:,1])\n",
    "grid_fpr, grid_tpr, grid_thresholds = roc_curve(y_true=y_test, y_score=grid_y_hat[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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": [
    "plt.plot(random_fpr, random_tpr, label='Random Search ROC AUC')\n",
    "plt.plot(grid_fpr, grid_tpr, label='Grid Search ROC AUC')\n",
    "plt.plot(test_fpr, test_tpr, label='Original ROC AUC')\n",
    "plt.plot([0, 1], [0, 1], color = 'black', linewidth = 2, linestyle = '--')\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.legend()\n",
    "plt.title('ROC AUC Curve For Random Forest Model with Grid vs Random Search')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we look at our original grid and our fitted hyper-parameters, we found that we reached the edge of the grid for min_samples_split. Thus, we can potentially improve our accuracy by shrinking the parameter grid and fine tuning the model with another Random Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "better_rf_hyperparam_grid={\n",
    "    \"n_estimators\": [500],\n",
    "    \"max_features\": [5, 6, 7, 8, 9],\n",
    "    \"min_samples_leaf\": [1, 2, 5, 10, 15, 20],\n",
    "    \"min_samples_split\": [100, 200, 250, 300, 400],\n",
    "    \"criterion\": [\"gini\"],\n",
    "    \"max_depth\": [5, 6, 7, 8, 9]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "better_random_search_model = RandomForestClassifier(random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "better_rf_random_search=RandomizedSearchCV(\n",
    "    estimator=better_random_search_model,\n",
    "    param_distributions=better_rf_hyperparam_grid,\n",
    "    n_iter=250,\n",
    "    scoring=\"neg_log_loss\",\n",
    "    refit=True,\n",
    "    return_train_score=True,\n",
    "    cv=cv_split,    \n",
    "    verbose=10,\n",
    "    n_jobs=-1,\n",
    "    random_state=42\n",
    "\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 250 candidates, totalling 1250 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 12 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done   1 tasks      | elapsed:   19.8s\n",
      "[Parallel(n_jobs=-1)]: Done   8 tasks      | elapsed:   21.6s\n",
      "[Parallel(n_jobs=-1)]: Done  17 tasks      | elapsed:   40.8s\n",
      "[Parallel(n_jobs=-1)]: Done  26 tasks      | elapsed:   59.3s\n",
      "[Parallel(n_jobs=-1)]: Done  37 tasks      | elapsed:  1.2min\n",
      "[Parallel(n_jobs=-1)]: Done  48 tasks      | elapsed:  1.5min\n",
      "[Parallel(n_jobs=-1)]: Done  61 tasks      | elapsed:  1.9min\n",
      "[Parallel(n_jobs=-1)]: Done  74 tasks      | elapsed:  2.3min\n",
      "[Parallel(n_jobs=-1)]: Done  89 tasks      | elapsed:  2.7min\n",
      "[Parallel(n_jobs=-1)]: Done 104 tasks      | elapsed:  3.0min\n",
      "[Parallel(n_jobs=-1)]: Done 121 tasks      | elapsed:  3.4min\n",
      "[Parallel(n_jobs=-1)]: Done 138 tasks      | elapsed:  4.0min\n",
      "[Parallel(n_jobs=-1)]: Done 157 tasks      | elapsed:  4.4min\n",
      "[Parallel(n_jobs=-1)]: Done 176 tasks      | elapsed:  4.9min\n",
      "[Parallel(n_jobs=-1)]: Done 197 tasks      | elapsed:  5.4min\n",
      "[Parallel(n_jobs=-1)]: Done 218 tasks      | elapsed:  6.0min\n",
      "[Parallel(n_jobs=-1)]: Done 241 tasks      | elapsed:  6.7min\n",
      "[Parallel(n_jobs=-1)]: Done 264 tasks      | elapsed:  7.3min\n",
      "[Parallel(n_jobs=-1)]: Done 289 tasks      | elapsed:  7.9min\n",
      "[Parallel(n_jobs=-1)]: Done 314 tasks      | elapsed:  8.7min\n",
      "[Parallel(n_jobs=-1)]: Done 341 tasks      | elapsed:  9.4min\n",
      "[Parallel(n_jobs=-1)]: Done 368 tasks      | elapsed: 10.2min\n",
      "[Parallel(n_jobs=-1)]: Done 397 tasks      | elapsed: 11.1min\n",
      "[Parallel(n_jobs=-1)]: Done 426 tasks      | elapsed: 11.8min\n",
      "[Parallel(n_jobs=-1)]: Done 457 tasks      | elapsed: 12.7min\n",
      "[Parallel(n_jobs=-1)]: Done 488 tasks      | elapsed: 13.6min\n",
      "[Parallel(n_jobs=-1)]: Done 521 tasks      | elapsed: 14.4min\n",
      "[Parallel(n_jobs=-1)]: Done 554 tasks      | elapsed: 15.4min\n",
      "[Parallel(n_jobs=-1)]: Done 589 tasks      | elapsed: 16.3min\n",
      "[Parallel(n_jobs=-1)]: Done 624 tasks      | elapsed: 17.3min\n",
      "[Parallel(n_jobs=-1)]: Done 661 tasks      | elapsed: 18.3min\n",
      "[Parallel(n_jobs=-1)]: Done 698 tasks      | elapsed: 19.3min\n",
      "[Parallel(n_jobs=-1)]: Done 737 tasks      | elapsed: 20.4min\n",
      "[Parallel(n_jobs=-1)]: Done 776 tasks      | elapsed: 21.4min\n",
      "[Parallel(n_jobs=-1)]: Done 817 tasks      | elapsed: 22.4min\n",
      "[Parallel(n_jobs=-1)]: Done 858 tasks      | elapsed: 23.4min\n",
      "[Parallel(n_jobs=-1)]: Done 901 tasks      | elapsed: 24.6min\n",
      "[Parallel(n_jobs=-1)]: Done 944 tasks      | elapsed: 25.8min\n",
      "[Parallel(n_jobs=-1)]: Done 989 tasks      | elapsed: 27.0min\n",
      "[Parallel(n_jobs=-1)]: Done 1034 tasks      | elapsed: 28.4min\n",
      "[Parallel(n_jobs=-1)]: Done 1081 tasks      | elapsed: 29.6min\n",
      "[Parallel(n_jobs=-1)]: Done 1128 tasks      | elapsed: 31.0min\n",
      "[Parallel(n_jobs=-1)]: Done 1177 tasks      | elapsed: 32.2min\n",
      "[Parallel(n_jobs=-1)]: Done 1226 tasks      | elapsed: 33.6min\n",
      "[Parallel(n_jobs=-1)]: Done 1250 out of 1250 | elapsed: 34.1min finished\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 18.1 s, sys: 1.1 s, total: 19.2 s\n",
      "Wall time: 34min 16s\n"
     ]
    }
   ],
   "source": [
    "%time better_tuned_random_model = better_rf_random_search.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'n_estimators': 500,\n",
       " 'min_samples_split': 250,\n",
       " 'min_samples_leaf': 1,\n",
       " 'max_features': 8,\n",
       " 'max_depth': 8,\n",
       " 'criterion': 'gini'}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "better_tuned_random_model.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The log loss of the model with Random Search is: 0.2805453345052492\n",
      "The ROC AUC score of the model with Random Search is: 0.7811849355731523\n"
     ]
    }
   ],
   "source": [
    "better_random_y_hat = better_tuned_random_model.predict_proba(x_test)\n",
    "print(\"The log loss of the model with Random Search is: \" + str(log_loss(y_test, better_random_y_hat)))\n",
    "print(\"The ROC AUC score of the model with Random Search is: \" +str(roc_auc_score(y_test, better_random_y_hat[:,1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We  improve  our log loss  ever  so slightly. However, it appears as though we are getting diminishing marginal returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Partial Dependence Plots For Hyperparameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's take a look at how our accuracy changes as we change each of these parameters on both the training and testing set, to understand more fully how these parameters impact overfitting. In addition, this will help us show how close the Random Search came to determining the \"optimal parameters\" on a held out dataset (not the test set). To do this, we will create a \"validation set\" that is a subset of the original training set, so that we are not \"overfitting\" to our held out test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train_2, x_val, y_train_2, y_val = train_test_split(x_train, y_train, test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_random_forest_model = RandomForestClassifier(n_estimators=500,\n",
    "                                                     min_samples_split=250,\n",
    "                                                     min_samples_leaf=5,\n",
    "                                                     max_features=7,\n",
    "                                                     max_depth=8,\n",
    "                                                     criterion='gini',\n",
    "                                                     n_jobs=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#n_estimators: 0-1000, increasing by 20 each time\n",
    "n_estimators_x_axis=np.linspace(20, 800, 40).astype(int)\n",
    "n_estimators_train_loss=[]\n",
    "n_estimators_test_loss=[]\n",
    "for estimators in n_estimators_x_axis:\n",
    "    model_to_test = initial_random_forest_model.set_params(**{\"n_estimators\": estimators})\n",
    "    model_to_test.fit(x_train_2, y_train_2)\n",
    "    train_predict = model_to_test.predict_proba(x_train_2)\n",
    "    test_predict = model_to_test.predict_proba(x_val)\n",
    "    n_estimators_train_loss.append(log_loss(y_train_2, train_predict[:,-1]))\n",
    "    n_estimators_test_loss.append(log_loss(y_val, test_predict[:,-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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": [
    "plt.plot(n_estimators_x_axis, n_estimators_test_loss,label='validation set')\n",
    "plt.plot(n_estimators_x_axis, n_estimators_train_loss,label='train set')\n",
    "plt.legend()\n",
    "plt.axvline(x=500, color='green', linestyle='--')\n",
    "plt.title('Train and Test Log Loss By Number of Estimators')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, ccp_alpha=0.0, class_weight=None,\n",
       "                       criterion='gini', max_depth=8, max_features=7,\n",
       "                       max_leaf_nodes=None, max_samples=None,\n",
       "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                       min_samples_leaf=1, min_samples_split=250,\n",
       "                       min_weight_fraction_leaf=0.0, n_estimators=500,\n",
       "                       n_jobs=-1, oob_score=False, random_state=None, verbose=0,\n",
       "                       warm_start=False)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_random_forest_model.set_params(**{\"n_estimators\": 500})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Depth: #1-20\n",
    "max_depth_x_axis=np.linspace(1, 20, 20).astype(int)\n",
    "max_depth_train_loss=[]\n",
    "max_depth_test_loss=[]\n",
    "\n",
    "for depth in max_depth_x_axis:\n",
    "    model_to_test = initial_random_forest_model.set_params(**{\"max_depth\": depth})\n",
    "    model_to_test.fit(x_train_2, y_train_2)\n",
    "    train_predict = model_to_test.predict_proba(x_train_2)\n",
    "    test_predict = model_to_test.predict_proba(x_val)\n",
    "    max_depth_train_loss.append(log_loss(y_train_2, train_predict[:,-1]))\n",
    "    max_depth_test_loss.append(log_loss(y_val, test_predict[:,-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pWf379+eDDz4gKyuLw4cP8/7779O/f/+A38/69evp3bs3Dz74IKmpqWzdupVzzz2Xp556ipwcl6vWrFnD4cOHS4yhvKLuiB5cPf2Ts9bz5dpMRnVpHO5wjDHl0KFDBw4ePEiTJk1o1KgRANdccw2jRo2iU6dO9OzZk3bt2pW6jJtuuolf/OIXtG/fnvbt29OjRw8AunTpQrdu3WjXrh3NmjWjX79+hWXGjx/PyJEjady4MbNmzSp8vXv37owbN45evXoBcP3119OtW7diq2mKc+edd7J27VpUlaFDh9KlSxc6d+7Mpk2b6N69O6pKamoqH3zwAZ07dyYmJoYuXbowbtw4fvvb3wbz0Z0k4u4Z27NnTz3VG4/k5Ss9H/6UwW3TeGyMdZBVVdiNRyLLypUrad++fbjDMMUo7rsRkcWq2rO4+aPyiD7GJwxMT2X2mkzy8pUYn13GXRU8PvLxcIdgTFSKyjp6gMHt0th7+BjfZVTuFW2m/Lo27GpdFBtTAaI20Q9MT8UnMMuaWVYZMzfMZOaGmeEOw5ioE7WJvm5SPD1Or2ft6auQh798mIe/fDjcYRgTdaI20YOrvlm+/QA7D9gdcowx1VdUJ/oh7dIAq74xxlRvUZ3o256WTOM6iXxmid6YKmXfvn1MmjSpXGUrslvhUPcqWVmiOtGLCIPbpfG/dbs5mms3IzGmqigt0efm5pZatiK7FbZEH6GGtEsj61geCzbsDXcopgzPXPgMz1z4TLjDMBFgwoQJrF+/nq5du3LnnXcye/Zs+vfvz+jRoznzzDMBuPjii+nRowcdOnTg2WefLSxb0K1wVeg+uLJE5QVT/vq2SiEh1sfnq3YxID013OGYUrRNaRvuEExJZkyAHd+HdpkNO8F5jxY76dFHH2XZsmUsWbIEcJ18ffPNNyxbtoyWLVsC8OKLL1K/fn2OHDnCWWedxWWXXUaDBg1OWE6kdx9cWaL+iL5GfAxnt2rArNV2M5JIN231NKatnhbuMEyE6tWrV2GSB3eTkC5dutCnTx+2bt1abPe+kd59cGWJ+iN6cNU39/1nORt2H6ZVaq1wh2NK8Lf5fwNgVNtRYY7EnKSEI+/KVLNmzcLx2bNnM3PmTObPn09SUhKDBg0qtpvhSO8+uLJE/RE9wOC21szSmKqkrG569+/fT7169UhKSmLVqlV89dVX5V5XOLsPrizVItE3q59Em7RadpWsMVVEgwYN6NevHx07duTOO+88afrIkSPJzc2lffv2TJgwgT59+pR7XXfeeSedOnWiY8eO9O3bly5dunD99ddz5pln0r17dzp27MiNN95Ibm7uCd0HV6WTsVHZTXFx/u/DlbwwdyPf3jec5MS4kC/fnDrrpjiyWDfFkSvYboqrxRE9uO4QcvOVuWt3hzsUY4ypVAElehEZKSKrRWSdiEwoZvovReR7EVkiInNF5Ey/aXd55VaLyLlFy1aWHqfXIzkx1qpvItirl7zKq5e8Gu4wjIk6Zba6EZEY4ElgOJABLBSRqarqf8v0N1T1aW/+0cBjwEgv4V8FdAAaAzNFJF1VK/0y1bgYHwPSU5m1OpP8fMVnNyOJOM3qNAt3CKYIVUXEfiuRpDzV7YEc0fcC1qnqBlU9BrwFXFRkxQf8ntYECiK5CHhLVY+q6kZgnbe8sBjaLo3dh46ybPv+cIVgSvH2srd5e9nb4Q7DeBITE9mzZ49dfxJBVJU9e/aQmJgYVLlA2tE3Abb6Pc8AehedSURuBm4H4oEhfmX92z1leK+FxcD0VETg81W76Ny0YvrCMOX31KKnABjTcUyYIzEATZs2JSMjg8zMzHCHYvwkJibStGnToMqE7IIpVX0SeFJEfgLcC/w80LIiMh4YD9C8efNQhXSSBrUS6NqsLrNW7eK2YekVth5jokFcXNwJV6KaqiuQqpttgH/laVPvtZK8BVwcTFlVfVZVe6pqz9TUU+iP5sg+WPYe5Jd8CmBI2zS+y9hP5sGj5V+PMcZUIYEk+oVAGxFpKSLxuJOrU/1nEJE2fk8vAAo6hZgKXCUiCSLSEmgDfH3qYZdg3UyY8gvYtrjEWQZ7NyOZvdpa3xhjqocyE72q5gK3AB8DK4HJqrpcRB70WtgA3CIiy0VkCa6e/ude2eXAZGAF8BFwc4W2uGk9FCQG1nxc4iwdGtfmtNoJzLJEb4ypJqLvyth/nw/ZB+CmuSXOMuHdpfx36Q98c99w4mKqzTVjEW93lruYLSUpJcyRGFP1VK8rY9uMgJ3fw/6STyMMbpfGwaO5LNxkNyOJJClJKZbkjakA0Zfo00e6x7WflDjLOa1TiI/xWW+WEealJS/x0pKXwh2GMVEn+hJ9aluo27zUevqaCbH0PqO+dYcQYSzRG1Mxoi/Ri0Cbc2HjF5Bz8k0GCgxum8b6zMNs2ZNVicEZY0zli75ED676JicLNpV8QnaI18zy81U7KysqY4wJi+hM9C3OgbikUqtvWqTU5IyUmny+2i7vNsZEt+hM9HGJ0HIgrP0YSmk+OrhdGl9t2EPWsdxKDM4YYypXdCZ6gPRzYd8WyFxV4ixD2qVxLDef/63bU4mBmZJ8eM2HfHjNh+EOw5ioE72Jvs0I91hK9c1ZLepTK8FuRhIpkuKSSIpLCncYxkSd6E30dZrAaZ1KbU8fH+vjnNYpzF69y/rcjgCTFk5i0sJJ4Q7DmKgTvYkeXPXNlq/gyI8lzjKkXRo/7M9m5Q8HKzEwU5zJyyczefnkcIdhTNSJ/kSvebDusxJnGdTOdYtsnZwZY6JVdCf6Jj0gqUGp1TdpyYl0alLH6umNMVEruhO9LwZaD4e1n5Z6M5LB7dL4dsuP/Hj4WCUGZ4wxlSO6Ez1A+gg4shcySu76eEi7NPIVvlhjF08ZY6JP9Cf6Vt7NSNaW3Myyc5M6pNSKt+qbMJs9bjazx80OdxjGRJ3oT/Q16kLzs0ttT+/zCQPT05i9ehe5efmVGJwxxlS86E/04Kpvdi6D/RklzjKkXRoHsnP5Zsu+SgzM+Js4byIT500MdxjGRJ3qkejbnOseS2l90z89hVifWPVNGE1fM53pa6aHOwxjok71SPSpbaHu6aVW39ROjOOsFvXtrlPGmKhTPRK9iLt4akPpNyMZ0i6N1TsPsm6XXSVrjIke1SPRg6u+yT1S6s1ILunehFoJsfzpw5J7vDTGmKqm+iT6wpuRfFTiLCm1Erh1aGs+X7XLukQIgxpxNagRVyPcYRgTdapPoo9LhDMGwZpPSr0Zybi+LWmZUpOHpq8gx5paVqoZ18xgxjUzwh2GMVGn+iR6cH3U7y/9ZiTxsT7uvaA9GzIP88r8zZUYnDHGVIzqlejTvWaWpVTfgDspOyA9lcdnrmHPoaOVEJgBeOiLh3joi4fCHYYxUad6JfrajaFhJ1d9UwoR4b4L25N1LI+/fbqmkoIzn238jM82ltyltDGmfKpXogfX+mbrAsjaW+psrdOS+dnZp/Pm11tYvn1/JQVnjDGhV/0SffpIdzOS9Z+XOettQ9OpWyOOB6etsFsNGmOqrOqX6Jt0dzcjKeUq2QJ1kuK4Y0RbFmzcy4xlOyohOGOMCb3ql+gLbkayrvSbkRS4uldz2jVM5pH/riQ7p+z5Tfk1SGpAg6QG4Q7DmKhT/RI9uNY3R36EjIVlzhrjE+4f1YFt+47w3JcbKiG46uvdK9/l3SvfDXcYxkSd6pnoWw1xNyMJoPoG4OxWDTi/U0MmzV7PD/tL7ivHGGMiUUCJXkRGishqEVknIhOKmX67iKwQkaUi8pmInO437c8isswbxoQy+HIL4GYkRd11XnvyVPnzDOsHp6LcNfMu7pp5V7jDMCbqlJnoRSQGeBI4DzgTuFpEziwy27dAT1XtDEwB/uKVvQDoDnQFegO/E5HaoQv/FKSfC7uWw76tAc3erH4SNw44gw+WbGfx5tKbZprymZ8xn/kZ88MdhjFRJ5Aj+l7AOlXdoKrHgLeAi/xnUNVZqprlPf0KaOqNnwl8qaq5qnoYWAqMDE3opyi97JuRFHXToFY0rJ3IH6etID/fmlsaY6qGQBJ9E8D/sDfDe60k1wEFPVN9B4wUkSQRSQEGA82KFhCR8SKySEQWZWZmBhb5qUpJL/NmJEUlxccy4bx2LM3Yz7vflHxbQmOMiSQhPRkrImOBnsBfAVT1E+BDYB7wJjAfOKmNoqo+q6o9VbVnampqKEMqLVh38dTGL0u9GUlRF3VtTPfmdfnzR6s5mJ1TgQEaY0xoBJLot3HiUXhT77UTiMgw4B5gtKoW9gSmqo+oaldVHQ4IEDmdx6SPcDcj2Tgn4CIirrnl7kNHeXLW+goMrvppWrspTWs3LXtGY0xQAkn0C4E2ItJSROKBq4Cp/jOISDfgGVyS3+X3eoyINPDGOwOdgcArxSva6WXfjKQ4XZrV5fIeTXlx7kY27T5cQcFVP69d+hqvXfpauMMwJuqUmehVNRe4BfgYWAlMVtXlIvKgiIz2ZvsrUAt4R0SWiEjBjiAOmCMiK4BngbHe8iJDXCKcMdidkA2yL5vfn9uWuBjhkQ9XVlBwxhgTGrGBzKSqH+Lq2v1fu89vfFgJ5bJxLW8iV/oIWP1f2LUSTgs81LTaidwypA1//mgVc9Zm0r9NJZ1biGK3fXQbAI+PfDzMkRgTXarnlbH+2oxwj0FW3wBce04LTm+QxIPTVpBrtx08ZUt2LGHJjiXhDsOYqGOJvnZjaNg5qPb0BRJiY7jn/Pas3XWI1xdsqYDgjDHm1FmiB3fxVAA3IynO8DNP45zWKTz26Rp+PHysAoIzxphTY4ke3F2nNB/WBX8bOxHh/114JoeO5vL3mZHTctQYYwpYogfvZiQpsDbwq2T9tW2YzNjezXntq82s2nEgxMFVH+kN0klvkB7uMIyJOpbowd2MpM1wWDcT8srX+vO3w9OpbbcdPCXPjnqWZ0c9G+4wjIk6lugLtBkR8M1IilM3KZ47hqczb/0e7pj8HUdz7W5UxpjIYIm+QKsh4Istd/UNwNg+p3PH8HTe+3YbP3vha/Zl2cnZYIyfNp7x08aHOwxjoo4l+gKFNyMpfw8NIsKvh7bhH1d15dst+7h00jw277EuEgK1Zs8a1uyxE9rGhJolen9tRribkew6tbtIXdS1Ca9d35u9Wce4ZNI8u1GJMSasLNH763I1JNSBjyYE3fdNUb1a1uf9X/WjdmIsVz+3gOlLt4coSGOMCY4len+1UmHIPbBhFqycWvb8ZWiZUpP3ftWPzk3qcMsb3zJp9jprkWOMqXSW6IvqeR2c1hE+uhuOnXr9ev2a8bx2fW9Gd2nMXz5azYR3vyfH+sUpVteGXenasGu4wzAm6kikHWH27NlTFy1aFN4gNs+Hf4+Ec26HYfeHZJH5+crfZ67hn5+v45zWKUwa253aiXEhWbYxxojIYlXtWdw0O6Ivzulnu/r6ef+E3etCskifT7hjRFv+cnlnvtqwh8ufmkfGj1llFzTGmFNkib4kwx+EuBow4/enfGLW35U9m/HKtb34YX82Fz85j++27gvZsqu6se+NZex7Y8MdhjFRxxJ9SWqlweC7Yf1nsGp6SBfdt3UK793Ul8Q4H2Oenc/Hy3eEdPlVVcaBDDIOZIQ7DGOijiX60px1A6R1gI/ugmOhrWZpc1oy7/+qH20b1uaXry3m+TkbrEWOMaZCWKIvTUwsXDAR9m+FOX8L+eJTkxN464Y+jOzQkIf/u5L7py63O1UZY0LOEn1ZTu8LncfAvCdgz/qQL75GfAxP/qQ74wecwSvzN3Pdy4us2wRjTEhZog/E8AchJgFm/CGkJ2YL+HzC3ee355FLOjJ/wx6G/O0Lbp+8hA2Zh0K+rkh2dtOzObvp2eEOw5ioY+3oAzX/Sfj4brjqDWh3QYWtZteBbJ79cgOvLdjMsdx8RnVpzC2DW9PmtOQKW6cxpuorrR29JfpA5eXA0/0h5zDc/LVrelmBdh86ynNzNvDq/M0cycnj/E6N+PWQ1rRrWLtC12uMqZrsgqlQiIlzJ2b3bYG5f6/w1aXUSuCu89oz9w9D+NWgVnyxOpORj8/hl68uZvn2/RW+/nC4bPJlXDb5snCHYUzUsUQfjBbnQKcrYO7jsHdDpayyfs147jy3HXP/MM2FyDAAAB6HSURBVJhbh7bhf+t3c8ETc7n+5UUszYiui632ZO1hT9aecIdhTNSxRB+s4Q+5o/sZEyp1tXWT4rl9eDpz/zCE24ens3DTXkb/63/84t9f882WHys1FmNM1WKJPli1G8GgCe6Wg6tnVPrq69SI49ahbZj7h8HceW5blmx1d7L66QsLWLTJbnBijDmZJfry6P1LSG3nmlvmHAlLCMmJcdw8uDVz/zCEu85rx4rtB7j86flc+fR8nv1yPcu27ScvP7JOtBtjwiM23AFUSTFxcP5f4eVR8L9/uCP8MKmZEMuNA1vxs7Nb8PqCzby1cCt/+tDdCrFOjTj6nFGfvq1S6Ne6Aa1SayEiYYu1LENbDg13CMZEJWteeSqmXAsrp8PNC6B+y3BHU2jXgWzmb9jDvHV7mLdhN1v3un8dqckJ9G3VwBtSaFY/KcyRGmNCxdrRV5QD2+FfZ0GL/vCTt8IdTYm27s1i3vrdzFu/h3nr95B58CgATevVoG+rBvRrncLZZzQgrXZimCM1xpSXJfqK9L9/wKf3wU8mQ/q54Y6mTKrK+sxDLumv28P8DXvYfyQHgNZptTirRX3OSKlJs/pJNK+fRLP6NUiupDthnff6eQDMuKbyT3IbU9WVluitjv5U9b4Jvn3N3aCk5UCIi+yjYhGhdVoyrdOS+dnZLcjLV1b+cKDwiP/D738oTPwF6teMp1n9JJrVq0FzbwfgdgJJNKqTSGxMaM7pHwnTiW1jol1AiV5ERgL/AGKA51X10SLTbweuB3KBTOBaVd3sTfsLcAGuhc+nwG800v5GnIrYeHdi9pWLXA+XA38f7oiCEuMTOjapQ8cmdRg/oBUA+7Ny2PpjFlv2Hh+27s1i2bb9fLRsB7l+rXlifUITbwfQtF4STevVoHZiLLVrxJGcGEvtxDiSE+OoXSOW5MQ4asbHRPQJ4epIVcnJU47l5ZOvSo24GOJCtPMuWP6+rBwyDx1l14GjZB7KZteBo+w6eJTMg0fZdTDbezzKkWN5JMbFkBjn8x698djj4wlxMdQo5vXEuBjiY334RLzBdRhYMB7jE0SEGO+5iBDj8+YTwecTVJXcPCU3P5+cPCUvX8nJyyc3X8nNc68VTMvNU/Ly88nxm6aq+HxuHYXr80GMSOH6YorE5POLo37NBC7o3Chkn32BMhO9iMQATwLDgQxgoYhMVdUVfrN9C/RU1SwRuQn4CzBGRPoC/YDO3nxzgYHA7NC9hQhwxiDocInrs77zlVCvRZgDOjV1kuKok+SSf1G5efnsOJBdmPzdjuAIW/Zm8cnyHew5fKzUZcf4hFoJsS7xJxzfAdROjGPTnsPE+IRJs9dRw/sx14h3P+SC8Rrej79gvOAHH6k7j7x8JTsnj6O5+QE9Hst1yTbXSzK5+er3PJ88da/l5Sl56jeP95ibl8+xvHyO5eZzNNc9Fjw/aTw3n6Pe86JifUKNuBiXVON9hZ974Xfhfe4F30/B63n56pfQj5J5IJvMQ0fJyTv52C4xzkdaciJpyQmkn5bMOa1TSEqI5WhOPtm5eWTnFAzus8k6lsvew960Y3lke59Zdk4e4WxJHBcjxPp8xMa4pJ2f776bfFXy8yn8ngLRrmFyeBI90AtYp6obAETkLeAioDDRq+osv/m/Agpu/KlAIhAPCBAH7Dz1sCPQiEdgzSfw0d1w9RvhjqbCxMb4vCP3JGh18vTsnDwOZudyIDvHPR7J8Xuew4Ejue4xO7fw+da9WRzMziUz+yh5qvzlo9VBx1WwI4iP8SHiNraC5C/iDcgJ0wp3DUVeK/hJFvzxVI6/qEVfx/Vcrd6z/HxOSNy5Ic5Asb7jR4UxPjnheazPR4xPiI/1ER/jc4+xPmolxBKfdPy5/7T4WB8Jfs8FcckzN48jx/I5knM84R7JyePIsTz2ZR3jBy8BH8lxSfeI33utXzOetOQEUpMTaJXagLTkRFKTEwpfK3islRAbkh10wT+S7NzjO0pVt5MtOu4GyPeSr/qNF3xVBYk7LsZ9rnExLokXvBYb4yPWez3GF3j86q0nz9sB5GvB+PH1B7G4oASS6JsAW/2eZwC9S5n/OmAGgKrOF5FZwA+439K/VHVl0QIiMh4YD9C8efPAIo80dZq4apuZ98MXf4WBd4Y7orAoOLpLTU4IuuzEeT9DVfl1r5EnJJaCZFOQeLKO5XrP8ziSk+83PY+juXle4vVLwHo8QR9//eRErrgffsFOAcD/oXDHgZvHb3LhTkJEXPVCbEyRR1e1kOBVN/g/+s8bH+uSSKzPh89HYfIu+Gsfqf9cAHK8u6OFstonECJCfKzbwUUyEXE7jDCsO6TrFJGxQE9c9Qwi0hpoDzT1ZvlURPqr6hz/cqr6LPAsuFY3oYypUvX9NexaCbMedplgwO/CHVGV8ru+xz+vxLgY6oYxFhO8yk7wJnCBJPptQDO/5029104gIsOAe4CBqnrUe/kS4CtVPeTNMwM4G5hTtHxU8MXAxZNA8+Hzh0B80P/2cEdljKnmAtkFLwTaiEhLEYkHrgKm+s8gIt2AZ4DRqrrLb9IWYKCIxIpIHO5I/6Sqm6jii4FLnnbdGX/2R9elsQnIoJcGMeilQeEOw5ioU+YRvarmisgtwMe45pUvqupyEXkQWKSqU4G/ArWAd7w6xC2qOhqYAgwBvsdVhX6kqtMq5q1EEF8MXPy0O7Kfeb87su93a7ijMsZUUwHV0avqh8CHRV67z298WAnl8oAbTyXAKismFi551iX7T/+fS/Z9bwl3VMaYasiujK1IMbFw6fOumccn97gTtGffHO6ojDHVjCX6ihYTC5c9747sP77bHdn3uSncURljqhFL9JUhJg4ufxGm/AI+muCSfe/qWaNVmis7XBnuEIyJSpboK0tMHFz+b3hnnOsATXzQ64ZwRxVRfnXWr8IdgjFRya5wqEwFyb7tBfDh7+Dr58IdUUTJyskiKycr3GEYE3Us0Ve22Hi44iVIP88l+4XPhzuiiHH+6+dz/uvnhzsMY6KOJfpwiI2HK1+G9JHw3ztg0YvhjsgYE8Us0YdLbAJc+Qq0GQHTfwuLXwp3RMaYKGWJPpxiE+DKV6H1cJj2G/jmlXBHZIyJQpbowy0uEca8Bq2HwdRb4ZtXwx2RMSbKWPPKSBCXCGNeh7euhqm3uK6Oh93vjvirkXFdx4U7BGOikkTa7Vt79uypixYtCncY4ZGTDZ/cCwufg9M6weUvQGrbcEdljKkCRGSxqvYsbppV3USSuES4YCJc/RYc3A7PDHQtciJsZ1xRdmftZnfW7nCHYUzUsUQfidqeBzfNg+Z9XIuct66Bw3vCHVWFu3zy5Vw++fJwh2FM1LFEH6mSG8LY99xNx9d+Ak/3gw2zwx2VMaYKskQfyXxeH/Y3fAYJyfDKxfDJ/4PcY+GOzBhThViirwoadYHxX0CPcTDvCXhhOOxeF+6ojDFVhCX6qiI+CUY97pph7tsMz/R3F1hVkxO1xpjys3b0VU37C6FJd3j/Rpj6a1g3E0b9A2rUC3dkp+ymnnZDFmMqgrWjr6ry82H+P+GzB6HWaXDps9DinHBHZYwJE2tHH418Puj3G7h+JsQmwksXuqSflxPuyMpt6/6tbN2/NdxhGBN1LNFXdY27wY1fQrexMOdv8MII2PF9uKMql5++/1N++v5Pwx2GMVHHEn00SKgFF/0LrngZ9m2BZwbAjAmQfSDckRljIoAl+mjS4WL49SLo8QtY8DT8qyd8P8Va5hhTzVmijzY16sGFj7mLrGo3hnevg5dHQebqcEdmjAkTS/TRqkkPuP4zuOAx2LEUnuoHn94Pxw6HOzJjTCWzdvTRzBcDZ10H7UfDzPvhf4/Dsndh5P9BuwtBJNwRnuCOs+8IdwjGRCVrR1+dbJ7vbka+a7m7feH5f4H6Z4Q7KmNMCFg7euOcfrZrinnun2DLfHiyD8x+1N3wJAKs3r2a1bvtXIIxoWaJvrqJiYWzb4ZbFrnuFGb/H0zqA2s/DXdk3Dj9Rm6cfmO4wzAm6liir65qN4LLX4Sf/Qd8sfD65e4GJ/vsylRjoo0l+urujEFw0/9g6H2w7jP411nw2UN2sZUxUSSgRC8iI0VktYisE5EJxUy/XURWiMhSEflMRE73Xh8sIkv8hmwRuTjUb8KcotgE6H8H3LwA2p0PcybCE11hwTN2kxNjokCZiV5EYoAngfOAM4GrReTMIrN9C/RU1c7AFOAvAKo6S1W7qmpXYAiQBXwSwvhNKNU73VXn3DAL0s6EGb+HJ3vB8vft6lpjqrBA2tH3Atap6gYAEXkLuAhYUTCDqs7ym/8rYGwxy7kcmKGqWeUP11SKJt3h59PcCdqZ98M749wFWMMfrNCukO8dcG+FLduY6iyQqpsmgP8ZugzvtZJcB8wo5vWrgDeLKyAi40VkkYgsyszMDCAkU+FEIH0E/HIuXPQkHPgBXroA3hgDu1ZWyCqHnTGMYWcMq5BlG1OdhfRkrIiMBXoCfy3yeiOgE/BxceVU9VlV7amqPVNTU0MZkjlVvhjXBfKt38DQ+2HzPHiqL/znFjiwPaSrWrJjCUt2LAnpMo0xgSX6bUAzv+dNvddOICLDgHuA0ap6tMjkK4H3VbXq3hWjuourAf1vh998B71vgu/egie6u5udZO8PySpu++g2bvvotpAsyxhzXCCJfiHQRkRaikg8rgpmqv8MItINeAaX5HcVs4yrKaHaxlQxSfVh5J9cd8jtL3Q3O/lHV/jqaWuhY0yEKjPRq2oucAuu2mUlMFlVl4vIgyIy2pvtr0At4B2vGWXhjkBEWuD+EXwR4thNONVrAZc9D+NnQ8OO8NEf4MmzXKdp+flhDs4Y4y+g3itV9UPgwyKv3ec3XuIZNFXdROknb01V1rgb/Gyqu9hq5v0w5Vo47TEYfA+0PS/iesg0pjqyK2PNqROBNsNch2mXPg85WfDW1fDcELcDsDb4xoSV9UdvQscXA52vgA6XwHdvwhd/htcuheZ9Yci90KJfqcX/NPRPlRSoMdWL9UdvKk7uUfjmFfhyIhza4frVGXwvNDsr3JEZE3WsP3oTHrEJ0OsG+M0S1wf+jmXwwjB30dUP3500+7yt85i3dV4YAjUmutkRvak8Rw/B18/A/56A7H3uFoeD74a09gAMemkQALPHzQ5fjMZUUXZEbyJDQi3XS+ZtS2HgBFg/CyadDe/eAHvWhzs6Y6KWJXpT+RLrwOC7XMLv9xtYOc31g797ravXN8aElCV6Ez5J9WH4H123Cr3Gw+FdsG2RO8Ivpg7fGFM+luhN+CWfBuc9Ck16QnIjWP0hPDMAXroQ1nxsV9oac4qsHb2JGI9f+JQbqdMCvnnZ3eHqjSshJR36/Aq6XOU6VzPGBMVa3ZjIlZcDyz+A+f90VTlJKXDW9W6oZd1ZG+PPWt2YKmHmhpnM3DDz+Asxce5K2/FfwM+nQ9Oe8MWj8PcOMPVWyFwTvmCNqUKs6sZEjIe/fBjg5LtMiUDL/m7IXANfPen6w//mZWhzLvS9BVr0tw7UjCmBHdGbqiU1HUb9A367HAbdBdsWw8uj3Mnb79521T3GmBNYojdVU80UGDQBfrvMJf7cbHh/vKvW+eguyFhsvWYa47GqG1O1xdWAHuOg289g3aew+GVY+Dx8NQnqtYSOl7nhtDPDHakxYWOJ3kQHnw/Sz3XDkR9h5XRYNgXmPgZzJkLamceTfv2W4Y7WmEplzStNxFi9ezUAbVPahm6hB3fCiv+4pL91gXutSQ/oeLnrN792o9Cty5gwKq15pSV6U33s2+LuabvsXdjxPSDQ4hx3lH/mRa5LBmOqKEv0pkqYtnoaAKPajqr4lWWudgn/+ymwdz34YqHVUJf02450Ha8ZU4VYojdVQlj6o1d1V90umwLL3oMD28AX5+6G1X4UtLvAtfAxJsKVlujtZKyp3kSgcVc3DHsQMhbCyqlumPYpTL8NTu/nJf0LoU6TcEdsTNAs0RtTwOeD5r3dMOJh2LHU9ZW/chrM+L0bmvR0Sb/9KGjQKtwRGxMQS/TGFEcEGnVxw5B7XdcLBUf6M+93w2kdvaQ/2t0O0bpgMBHKEr0xgUhNh9TfwYDfwY+bYdV0WDEVZj8Ks/8P6rc6Xr3TuBvE2E/LRA47GWsixtb9WwFoVqdZmCMJwsEdsOq/7kh/4xzQPIhPhtP7uk7YWvSHhp3AFxPuSE2Us1Y3xlSGrL2w/nPYNMcl/b3eDc8T67r2+i28HjhT27vzAcaEkLW6MVXC28veBmBMxzFhjqSckupDp8vdALB/G2yaC5u+hI1fuuoegKQGLvG3HAAtBkBKG6vfNxXKEr2JGE8tcrcSrLKJvqg6TaDLGDeAq9svONrfNMd1zQBQq6GX+PtD875Q/wyr4zchZVuTMZWl3ulu6DbWXai1d4M70t80xz0um+Lm88W5ppsp6W5IbeuNt4H4muF9D6ZKskRvTDiIuGTeoBX0/IVL/LvXuBupZK5247tWuBO9mne8XJ1mfsm/DaS0deN29a4phSV6YyKBiEvYqUV67sw96o78d69xbfl3ezuBxfMhJ+v4fDXqe0f9raFuC/fPoa73D6LWaXYOoJqzRG9MJItNcBdjpbU/8fX8fDiQ4SV/bweQuQbWfgqHdhZZRqL7J+Cf/OueDnWbQ70WUKOe7QiiXECJXkRGAv8AYoDnVfXRItNvB64HcoFM4FpV3exNaw48DzQDFDhfVTeF6g2Y6DHlyinhDqHq8Plcoq7bHNoUuZl6zhHXJfOPm2GfNxSMZyyC7H0nzh+ffGLyr93YnUiu3dQ91mpoJ4eruDK/PRGJAZ4EhgMZwEIRmaqqK/xm+xboqapZInIT8BegoOnEK8AjqvqpiNQC8kP6DkzUSEmyeuaQiKtRfDVQgez9J+4ICh83wsYv4NihE+eXGEhuCLWbeDuAJn7j3s6gZppdGxDBAtlN9wLWqeoGABF5C7gIKEz0qjrLb/6vgLHevGcCsar6qTdfkS3ImONeWvISAOO6jgtrHFEvsY67Wrdhp5OnqbodwYFtcGA77M9w4/u3uaqiH5bC6hnuZuz+fHHubl3JjaFWmhtqphU/Hlejct6nKRRIom8CbPV7ngH0LmX+64AZ3ng6sE9E3gNaAjOBCar+zQhARMYD4wGaN28eWOQm6liijwAiUKOuG07rUPw8qu4q4APbvJ2A387g4A+u1dCmOe7evcWJT/bbAaS6k8UF44l1XHcR4itmkBOfIyfP44txO5LYRDfEJUJsDXeuoxqfhwhpxZuIjAV6AgP9lt8f6AZsAd4GxgEv+JdT1WeBZ8F1gRDKmIwxISYCNRu4oVHnkufLPQaHM+HwLjjkDSeMZ0LmKncNQdHzBhWhMPl7iT+2hrcjKPJ6TDzExHmPCcfHY/3GTxiKTk84vpzCx8QTX/PFVuqOJ5BEvw13IrVAU++1E4jIMOAeYKCqHvVezgCW+FX7fAD0oUiiN8ZEodh4V38fyM1aco+6xJ99AFDQ/CJDca8VnaaQd8xVKxUMOdmQe8QtP+eI95r3PPeINz3bnZc4vNuN5+e4nVTeMcjLgbyjbn5CeQwqXuJPcJ9Twc4hrT1c9XoI1+MEkugXAm1EpCUuwV8F/OSEkEW6Ac8AI1V1V5GydUUkVVUzgSGA9VhmjDlRbALUaQqRfKve/DxvR3LU2wEcO3nIPebtGI4d30HkHi3ymt+0guUVzJPcqEJCLzPRq2quiNwCfIxrXvmiqi4XkQeBRao6FfgrUAt4R9zfkS2qOlpV80Tkd8Bn4iYsBp6rkHdijDEVyRcDvhpV8mSydVNsIkaWd6VnUlxSmCMxpuqxbopNlWAJ3piKYVc4mIgxaeEkJi2cFO4wjIk6luhNxJi8fDKTl08OdxjGRB1L9MYYE+Us0RtjTJSzRG+MMVHOEr0xxkS5iGtHLyIHgdWnsIgUYLeVt/JW3spXs/Knq2pqsVNUNaIG3NW2Vt7KW3krb+VDNFjVjTHGRDlL9MYYE+UiMdE/a+WtvJW38lY+dCLuZKwxxpjQisQjemOMMSFkid4YY6JcRCV6ERkpIqtFZJ2ITAiy7IsisktElpVz3c1EZJaIrBCR5SLymyDLJ4rI1yLynVf+j+WMI0ZEvhWR6eUou0lEvheRJSISdKf+IlJXRKaIyCoRWSkiZwdRtq233oLhgIjcFuT6f+t9dstE5E0RSQyy/G+8sssDWXdx24yI1BeRT0VkrfdYL8jyV3jrzxeRYvsGL6P8X73Pf6mIvC8idYMs/5BXdomIfCIijYMp7zftDhFREUkJcv0PiMg2v+3g/GDXLyK/9j6D5SLylyDX/7bfujeJyJIgy3cVka8KfkMi0ivI8l1EZL73O5wmIrVLKV9szglmGwxYRbTZLGf70RhgPXAGEA98B5wZRPkBQHdgWTnX3wjo7o0nA2uCXL8AtbzxOGAB0KcccdwOvAFML0fZTUDKKXwHLwPXe+PxQN1T+C534C7gCLRME2AjUMN7PhkYF0T5jsAyIAl3n4WZQOtgtxngL8AEb3wC8Ocgy7cH2gKzgZ7lWP8IINYb/3M51l/bb/xW4OlgynuvN8PdUW5zadtTCet/APhdgN9ZceUHe99dgvc8Ldj4/ab/DbgvyPV/ApznjZ8PzA6y/ELcfbMBrgUeKqV8sTknmG0w0CGSjuh7AetUdYOqHgPeAi4KtLCqfgnsLe/KVfUHVf3GGz8IrMQln0DLq6oe8p7GeUNQZ7pFpClwAfB8MOVCQUTq4DbcFwBU9Ziq7ivn4oYC61V1c5DlYoEaIhKLS9jbgyjbHligqlmqmgt8AVxaWoEStpmLcDs8vMeLgymvqitVNaAru0so/4kXP8BXQNMgyx/we1qTUrbBUn4zfwd+X1rZMsoHpITyNwGPqupRb55dJxUMYP0iIsCVwJtBlleg4Ci8DqVsgyWUTwe+9MY/BS4rpXxJOSfgbTBQkZTomwBb/Z5nEESiDSURaQF0wx2VB1MuxvuruAv4VFWDKg88jvuB5QdZroACn4jIYhEZH2TZlkAm8G+v6uh5EalZzjiuopQfWHFUdRswEdgC/ADsV9VPgljEMqC/iDQQkSTc0VizYGLwnKaqP3jjO4DTyrGMULkWmBFsIRF5RES2AtcA9wVZ9iJgm6p+F+x6/dziVR+9WI5qh3Tc97hARL4QkbPKGUN/YKeqrg2y3G3AX73PbyJwV5Dll3P8APUKAtwGi+SckG+DkZToI4KI1ALeBW4rcnRUJlXNU9WuuKOwXiLSMYj1XgjsUtXFQQV8onNUtTtwHnCziAwIomws7m/oU6raDTiM+9sYFBGJB0YD7wRZrh7uB9ISaAzUFJGxgZZX1ZW4qo5PgI+AJUBeMDEUs0wlyH9loSIi9wC5wOvBllXVe1S1mVf2liDWmQTcTZA7hyKeAloBXXE77L8FWT4WqA/0Ae4EJntH58G6miAPNjw3Ab/1Pr/f4v3DDcK1wK9EZDGuOuZYWQVKyzmh2gYjKdFv48S9X1PvtUojInG4D/x1VX2vvMvxqjxmASODKNYPGC0im3DVVkNE5LUg17vNe9wFvI+rDgtUBpDh9y9kCi7xB+s84BtV3RlkuWHARlXNVNUc4D2gbzALUNUXVLWHqg4AfsTVeQZrp4g0AvAeS6w6qCgiMg64ELjG+6GX1+uUUnVQjFa4He133nbYFPhGRBoGugBV3ekd8OQDzxHcNghuO3zPqwr9GvfvtsQTwsXxqv4uBd4Oct0AP8dte+AOVoKKX1VXqeoIVe2B29GsLyPW4nJOyLfBSEr0C4E2ItLSOyq8CphaWSv3jhpeAFaq6mPlKJ9a0EJCRGoAw4FVgZZX1btUtamqtsC9989VNeAjWhGpKSLJBeO4k3oBt0BS1R3AVhFp6700FFgRaHk/5T2S2gL0EZEk77sYiquzDJiIpHmPzXE/9DfKEcdU3I8d7/E/5VhGuYnISFz13WhVzSpH+TZ+Ty8iuG3we1VNU9UW3naYgTtZuCOI9Tfye3oJQWyDng9wJ2QRkXRco4Bge3McBqxS1Ywgy4Grkx/ojQ8Bgqr68dsGfcC9wNOlzFtSzgn9NniqZ3NDOeDqVdfg9oL3BFn2TdxfxRzcBnpdkOXPwf1FWor7278EOD+I8p2Bb73yyyjlbH8AyxpEkK1ucK2VvvOG5cF+ft4yugKLvPfwAVAvyPI1gT1AnXK+7z/iEtMy4FW8lhdBlJ+D2zl9BwwtzzYDNAA+w/3AZwL1gyx/iTd+FNgJfBxk+XW4c1UF22BprWaKK/+u9/ktBaYBTcr7m6GMVlwlrP9V4Htv/VOBRkGWjwde897DN8CQYOMHXgJ+Wc7v/xxgsbcNLQB6BFn+N7gctgZ4FK/3gRLKF5tzgtkGAx2sCwRjjIlykVR1Y4wxpgJYojfGmChnid4YY6KcJXpjjIlyluiNMSbKWaI3xpgoZ4neGGOi3P8HZz0ZL22d7lkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(max_depth_x_axis, max_depth_test_loss,label='validation set')\n",
    "plt.plot(max_depth_x_axis, max_depth_train_loss,label='train set')\n",
    "plt.legend()\n",
    "plt.axvline(x=8, color='green', linestyle='--')\n",
    "plt.xticks(np.arange(21))\n",
    "plt.title('Train and Test Log Loss By Max Depth')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, ccp_alpha=0.0, class_weight=None,\n",
       "                       criterion='gini', max_depth=8, max_features=7,\n",
       "                       max_leaf_nodes=None, max_samples=None,\n",
       "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                       min_samples_leaf=1, min_samples_split=250,\n",
       "                       min_weight_fraction_leaf=0.0, n_estimators=500,\n",
       "                       n_jobs=-1, oob_score=False, random_state=None, verbose=0,\n",
       "                       warm_start=False)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_random_forest_model.set_params(**{\"max_depth\": 8})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "#max_features: 0-18\n",
    "max_features_x_axis=np.linspace(1, 17, 17).astype(int)\n",
    "max_features_train_loss=[]\n",
    "max_features_test_loss=[]\n",
    "\n",
    "for features in max_features_x_axis:\n",
    "    model_to_test = initial_random_forest_model.set_params(**{\"max_features\": features})\n",
    "    model_to_test.fit(x_train_2, y_train_2)\n",
    "    train_predict = model_to_test.predict_proba(x_train_2)\n",
    "    test_predict = model_to_test.predict_proba(x_val)\n",
    "    max_features_train_loss.append(log_loss(y_train_2, train_predict[:,-1]))\n",
    "    max_features_test_loss.append(log_loss(y_val, test_predict[:,-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": [
    "plt.plot(max_features_x_axis, max_features_test_loss,label='validation set')\n",
    "plt.plot(max_features_x_axis, max_features_train_loss,label='train set')\n",
    "plt.legend()\n",
    "plt.axvline(x=7, color='green', linestyle='--')\n",
    "plt.xticks(np.arange(19))\n",
    "plt.title('Train and Test Log Loss By Max Features')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, ccp_alpha=0.0, class_weight=None,\n",
       "                       criterion='gini', max_depth=8, max_features=7,\n",
       "                       max_leaf_nodes=None, max_samples=None,\n",
       "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                       min_samples_leaf=1, min_samples_split=250,\n",
       "                       min_weight_fraction_leaf=0.0, n_estimators=500,\n",
       "                       n_jobs=-1, oob_score=False, random_state=None, verbose=0,\n",
       "                       warm_start=False)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_random_forest_model.set_params(**{\"max_features\": 7})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "#min_samples_leaf: 1-100, increase by 3:\n",
    "min_samples_leaf_x_axis=np.linspace(1, 100, 34).astype(int)\n",
    "min_samples_leaf_train_loss=[]\n",
    "min_samples_leaf_test_loss=[]\n",
    "\n",
    "for samples in min_samples_leaf_x_axis:\n",
    "    model_to_test = initial_random_forest_model.set_params(**{\"min_samples_leaf\": samples})\n",
    "    model_to_test.fit(x_train_2, y_train_2)\n",
    "    train_predict = model_to_test.predict_proba(x_train_2)\n",
    "    test_predict = model_to_test.predict_proba(x_val)\n",
    "    min_samples_leaf_train_loss.append(log_loss(y_train_2, train_predict[:,-1]))\n",
    "    min_samples_leaf_test_loss.append(log_loss(y_val, test_predict[:,-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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": [
    "plt.plot(min_samples_leaf_x_axis, min_samples_leaf_test_loss,label='validation set')\n",
    "plt.plot(min_samples_leaf_x_axis, min_samples_leaf_train_loss,label='train set')\n",
    "plt.legend()\n",
    "plt.axvline(x=1, color='green', linestyle='--')\n",
    "plt.title('Train and Test Log Loss By Min Samples Leaf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears as though this parameter has little effect on the test set predictions of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, ccp_alpha=0.0, class_weight=None,\n",
       "                       criterion='gini', max_depth=8, max_features=7,\n",
       "                       max_leaf_nodes=None, max_samples=None,\n",
       "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                       min_samples_leaf=1, min_samples_split=250,\n",
       "                       min_weight_fraction_leaf=0.0, n_estimators=500,\n",
       "                       n_jobs=-1, oob_score=False, random_state=None, verbose=0,\n",
       "                       warm_start=False)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_random_forest_model.set_params(**{\"min_samples_leaf\": 1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "#min_samples_split: 0-500, increasing by 20 each time\n",
    "min_samples_split_x_axis=np.linspace(25, 600, 25).astype(int)\n",
    "min_samples_split_train_loss=[]\n",
    "min_samples_split_test_loss=[]\n",
    "\n",
    "for samples in min_samples_split_x_axis:\n",
    "    model_to_test = initial_random_forest_model.set_params(**{\"min_samples_split\": samples})\n",
    "    model_to_test.fit(x_train_2, y_train_2)\n",
    "    train_predict = model_to_test.predict_proba(x_train_2)\n",
    "    test_predict = model_to_test.predict_proba(x_val)\n",
    "    min_samples_split_train_loss.append(log_loss(y_train_2, train_predict[:,-1]))\n",
    "    min_samples_split_test_loss.append(log_loss(y_val, test_predict[:,-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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": [
    "plt.plot(min_samples_split_x_axis, min_samples_split_test_loss,label='validation set')\n",
    "plt.plot(min_samples_split_x_axis, min_samples_split_train_loss,label='train set')\n",
    "plt.legend()\n",
    "plt.axvline(x=250, color='green', linestyle='--')\n",
    "plt.title('Train and Test Log Loss By Min Samples Split')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, ccp_alpha=0.0, class_weight=None,\n",
       "                       criterion='gini', max_depth=8, max_features=7,\n",
       "                       max_leaf_nodes=None, max_samples=None,\n",
       "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                       min_samples_leaf=1, min_samples_split=250,\n",
       "                       min_weight_fraction_leaf=0.0, n_estimators=500,\n",
       "                       n_jobs=-1, oob_score=False, random_state=None, verbose=0,\n",
       "                       warm_start=False)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_random_forest_model.set_params(**{\"min_samples_split\": 250})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "final_rf_model=initial_random_forest_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, ccp_alpha=0.0, class_weight=None,\n",
       "                       criterion='gini', max_depth=8, max_features=7,\n",
       "                       max_leaf_nodes=None, max_samples=None,\n",
       "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                       min_samples_leaf=1, min_samples_split=250,\n",
       "                       min_weight_fraction_leaf=0.0, n_estimators=500,\n",
       "                       n_jobs=-1, oob_score=False, random_state=None, verbose=0,\n",
       "                       warm_start=False)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_rf_model.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Permutation Importance For Feature Selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the main criticisms of tree based models as that it is relatively uninterpretable and that it is unclear how to determine which features are contributing to your model. ``sklearn`` has a built in feature importance attribute, but I would recommend against using it because it counts the number of splits on each variable. Thus, continuous variables feature more heavily as they have more variables to split on, while categorical variables can only split on 0/1, so the built in  method counts categorical features less. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another method for feature importance is by using Shap values, which @clekraus goes into detail on his notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My favorite method for feature importance is permutation importance. The way permutation importance works is on each permutataion, it randomizes the values in columns, re-trains the model, and compares the acacuracy of the predictions between the model with some randomized columns and the original model. The more important a column is, the bigger the disparity between the results of the model with that column randomized and the actual model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will take a look at the feature importances on the training set. This is  helpful in seeing where the model saw places to split their decision tree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5.64 s, sys: 339 ms, total: 5.98 s\n",
      "Wall time: 5min 20s\n"
     ]
    },
    {
     "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": [
    "%time  result = permutation_importance(final_rf_model, x_train_2, y_train_2, n_repeats=100, random_state=42, n_jobs=-1)\n",
    "sorted_idx = result.importances_mean.argsort()\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.boxplot(result.importances[sorted_idx].T, vert=False, labels=x_train.columns[sorted_idx])\n",
    "ax.set_title(\"Random Forest Permutation Importances (Training Set)\")\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that the features that we expected to be criticial are important, notably Distance and angle. We also find that certain features that are perfectly correlated with other features (Y, left_foot  and  out_swinging) were not important in the model, so that is something to keep in mind."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we will also run this analysis on the validatoin set so that we know which features are overfit to the training set, as these features would feature prominently when permuted in sample, but hardly (or negatively) feature out of sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%time  result = permutation_importance(final_rf_model, x_val, y_val, n_repeats=250, random_state=42, n_jobs=-1)\n",
    "sorted_idx = result.importances_mean.argsort()\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.boxplot(result.importances[sorted_idx].T, vert=False, labels=x_train.columns[sorted_idx])\n",
    "ax.set_title(\"Random Forest Permutation Importances (Validation Set)\")\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We end up seeing here that many features have 0 (or event negative) effect on the validation set, including some variables that I would have expected to be very important (such as strong foot). This is a fascinating discovery, but also puts into question the quality of this methodology for feature importance.\n",
    "\n",
    "This is useful as we move to Logistic Regression, as we will compare this output to the \"traditional\" way of feature selecting as proposed by David Sumpter. We will improve this model during the Logistic regression notebook, taking into knowledge acquired from these plots and variables in the  logistic regression model."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}