{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"id": "ec2c8732",
"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>X1</th>\n",
   "    <th>X2</th>\n",
   "    <th>X3</th>\n",
   "    <th>Y</th>\n",
   " </tr>\n",
   " </thead>\n",
   " <tbody>\n",
   " <tr>\n",
   "    <th>0</th>\n",
   "    <td>0.433278</td>\n",
   "    <td>-0.180904</td>\n",
   "    <td>-0.426411</td>\n",
   "    <td>0.614182</td>\n",
   " </tr>\n",
   " <tr>\n",
   "    <th>1</th>\n",
   "    <td>-0.461811</td>\n",
   "    <td>-0.204108</td>\n",
   "    <td>0.036119</td>\n",
   "    <td>-0.036119</td>\n",
   " </tr>\n",
   " <tr>\n",
   "    <th>2</th>\n",
   "    <td>-0.011897</td>\n",
   "    <td>-0.182808</td>\n",
   "    <td>0.256612</td>\n",
   "    <td>0.100000</td>\n",
   " </tr>\n",
   " <tr>\n",
   "    <th>3</th>\n",
   "    <td>-0.451108</td>\n",
   "    <td>-0.151159</td>\n",
   "    <td>-0.007978</td>\n",
   "    <td>0.007978</td>\n",
   " </tr>\n",
   " <tr>\n",
   "    <th>4</th>\n",
   "    <td>0.192973</td>\n",
   "    <td>-0.412564</td>\n",
   "    <td>0.107185</td>\n",
   "    <td>-0.112406</td>\n",
   " </tr>\n",
   " </tbody>\n",
   "</table>\n",
   "</div>"
   ],
   "text/plain": [
   "       X1    X2    X3       Y\n",
   "0 0.433278 -0.180904 -0.426411 0.614182\n",
   "1 -0.461811 -0.204108 0.036119 -0.036119\n",
   "2 -0.011897 -0.182808 0.256612 0.100000\n",
   "3 -0.451108 -0.151159 -0.007978 0.007978\n",
   "4 0.192973 -0.412564 0.107185 -0.112406"
   ]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd \n",
"import numpy as np\n",
"\n",
"task1 = pd.read_csv('ML_test1.csv', index_col=None)\n",
"task1.head()"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "a94a4a14",
"metadata": {},
"outputs": [
{
"data": {
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\n",
   "text/plain": [
   "<Figure size 432x288 with 1 Axes>"
   ]
},
"metadata": {
   "needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"plt.scatter(df.loc[0:1000, 'X2'], df.loc[0:1000, 'Y'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "36d040a5",
"metadata": {},
"source": [
"### Train-Test Split"
]
},
{
"cell_type": "code",
"execution_count": 57,
"id": "06a43f8d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
   "Train Size is : 15995\n",
   "Test Size is : 3999\n"
]
}
],
"source": [
"from sklearn.model_selection import train_test_split\n",
"\n",
"df = task1.dropna()\n",
"X, y = df[['X1','X2', 'X3']], df.Y\n",
"\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state=42)\n",
"\n",
"print('Train Size is :', len(X_train))\n",
"print('Test Size is :', len(X_test))"
]
},
{
"cell_type": "markdown",
"id": "dc3e4f4c",
"metadata": {},
"source": [
"### Linear Regression Model Fit"
]
},
{
"cell_type": "code",
"execution_count": 58,
"id": "a352038c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
   "0.41614449840837364 0.4160349638886579\n",
   "RMSE for training data is 0.22068494482638712\n",
   "RMSE for testing data is 0.22322124820633987\n"
]
}
],
"source": [
"from sklearn.linear_model import LinearRegression\n",
"from sklearn.model_selection import cross_val_score\n",
"\n",
"def rmse(predictions, targets):\n",
" return np.sqrt(((predictions - targets) ** 2).mean())\n",
"\n",
"model = LinearRegression()\n",
"\n",
"model.fit(X_train, y_train)\n",
"\n",
"print(model.score(X_train, y_train), 1 - (1-model.score(X_train, y_train))*(len(y_train)-1)/(len(y_train)-X.shape[1]-1))\n",
"\n",
"print('RMSE for training data is ', rmse(model.predict(X_train), y_train))\n",
"\n",
"print('RMSE for testing data is ', rmse(model.predict(X_test), y_test))"
]
},
{
"cell_type": "markdown",
"id": "849802b0",
"metadata": {},
"source": [
"#### Cross-validation for Linear Model"
]
},
{
"cell_type": "code",
"execution_count": 67,
"id": "bc5ce4da",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
   "RMSE for cross-validation is : 0.22074631974174436\n"
]
}
],
"source": [
"scores = cross_val_score(model, X_train, y_train, cv=5, scoring='neg_mean_squared_error')\n",
"print('RMSE for cross-validation is : ', (np.sqrt(-1*scores)).mean())"
]
},
{
"cell_type": "markdown",
"id": "c8411e7f",
"metadata": {},
"source": [
"Based on the model fit above we note that:\n",
"\n",
" - Linear regression produces a poorer fit on the raw dataset. The resulting R-squared value for the model fit is 41% which simply means that 41% of the variability in Y is being explained by X1, X2 and X3 together. \n",
" - The RMSE value for the above model fit is 0.22 approximately. This simply means that on an average our dependent variable Y is 0.22 units away from the fitted values. Remember that for a dependent variable lies in the range (-0.5, 0.5) hence RMSE is significantly large in this case. \n",
" - The scatter plots earlier showed non-linear relationship between Y and the regressors. Hence a non-linear model can be considered to approximate the relationship between Y and the sets of regressors. \n",
" \n",
"### Decision Tree Model Fit"
]
},
{
"cell_type": "code",
"execution_count": 70,
"id": "083b31a3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
   "RMSE for Decision Tree training data is 5.941633618126038e-17\n",
   "RMSE for Decision Tree testing data is 0.06882460845937437\n"
]
}
],
"source": [
"# import the regressor\n",
"from sklearn.tree import DecisionTreeRegressor \n",
" \n",
"# create a regressor object\n",
"regressor = DecisionTreeRegressor(random_state = 0) \n",
" \n",
"# fit the regressor with X and Y data\n",
"regressor.fit(X_train, y_train)\n",
"\n",
"print('RMSE for Decision Tree training data is ', rmse(regressor.predict(X_train), y_train))\n",
"print('RMSE for Decision Tree testing data is ', rmse(regressor.predict(X_test), y_test))"
]
},
{
"cell_type": "markdown",
"id": "0b52793d",
"metadata": {},
"source": [
"#### Cross-validation for Decision Tree"
]
},
{
"cell_type": "code",
"execution_count": 71,
"id": "c64acd0d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
   "RMSE for cross-validation is : 0.07467924170608693\n"
]
}
],
"source": [
"scores = cross_val_score(regressor, X_train, y_train, cv=5, scoring='neg_mean_squared_error')\n",
"print('RMSE for cross-validation is : ', (np.sqrt(-1*scores)).mean())"
]
},
{
"cell_type": "markdown",
"id": "c1654d64",
"metadata": {},
"source": [
"We observe that the RMSE for the decision tree model is very-very small. This simply means that the decision tree model is a good fit. However, we should note that a decision tree model can easily overfit on a smaller dataset. Hence tuning parameters is an important step in this setting. Hence we perform cross-validation to check for the overfit of decision tree. We note that there is a significant difference between the cross-validation score and training score which imply that there is an overfit in this case."
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "26d81253",
"metadata": {},
"outputs": [],
"source": [
"# import export_graphviz\n",
"from sklearn.tree import export_graphviz \n",
" \n",
"# export the decision tree to a tree.dot file for visualizing the plot easily anywhere\n",
"export_graphviz(regressor, out_file ='tree.dot', feature_names = ['X1', 'X2', 'X3'])\n"
]
},
{
"cell_type": "markdown",
"id": "e0d2ebe3",
"metadata": {},
"source": [
"### Relationship Between Y and X1, X2, X3"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "a43aa16d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
   "|--- feature_0 <= -0.10\n",
   "| |--- feature_1 <= 0.00\n",
   "| | |--- feature_2 <= 0.01\n",
   "| | | |--- feature_2 <= -0.25\n",
   "| | | | |--- feature_2 <= -0.35\n",
   "| | | | | |--- feature_2 <= -0.43\n",
   "| | | | | | |--- feature_0 <= -0.48\n",
   "| | | | | | | |--- feature_0 <= -0.49\n",
   "| | | | | | | | |--- feature_2 <= -0.46\n",
   "| | | | | | | | | |--- feature_0 <= -0.49\n",
   "| | | | | | | | | | |--- feature_2 <= -0.47\n",
   "| | | | | | | | | | | |--- value: [0.47]\n",
   "| | | | | | | | | | |--- feature_2 > -0.47\n",
   "| | | | | | | | | | | |--- truncated branch of depth 2\n",
   "| | | | | | | | | |--- feature_0 > -0.49\n",
   "| | | | | | | | | | |--- value: [0.49]\n",
   "| | | | | | | | |--- feature_2 > -0.46\n",
   "| | | | | | | | | |--- feature_2 <= -0.45\n",
   "| | | | | | | | | | |--- value: [0.46]\n",
   "| | | | | | | | | |--- feature_2 > -0.45\n",
   "| | | | | | | | | | |--- feature_1 <= -0.12\n",
   "| | | | | | | | | | | |--- truncated branch of depth 2\n",
   "| | | | | | | | | | |--- feature_1 > -0.12\n",
   "| | | | | | | | | | | |--- value: [0.44]\n",
   "| | | | | | | |--- feature_0 > -0.49\n",
   "| | | | | | | | |--- value: [-0.36]\n",
   "| | | | | | |--- feature_0 > -0.48\n",
   "| | | | | | | |--- feature_2 <= -0.46\n",
   "| | | | | | | | |--- feature_0 <= -0.11\n",
   "| | | | | | | | | |--- feature_2 <= -0.49\n",
   "| | | | | | | | | | |--- feature_2 <= -0.50\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.50\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | |--- feature_2 > -0.49\n",
   "| | | | | | | | | | |--- feature_2 <= -0.49\n",
   "| | | | | | | | | | | |--- value: [-0.01]\n",
   "| | | | | | | | | | |--- feature_2 > -0.49\n",
   "| | | | | | | | | | | |--- truncated branch of depth 11\n",
   "| | | | | | | | |--- feature_0 > -0.11\n",
   "| | | | | | | | | |--- feature_1 <= -0.29\n",
   "| | | | | | | | | | |--- feature_1 <= -0.39\n",
   "| | | | | | | | | | | |--- value: [0.49]\n",
   "| | | | | | | | | | |--- feature_1 > -0.39\n",
   "| | | | | | | | | | | |--- truncated branch of depth 2\n",
   "| | | | | | | | | |--- feature_1 > -0.29\n",
   "| | | | | | | | | | |--- value: [0.11]\n",
   "| | | | | | | |--- feature_2 > -0.46\n",
   "| | | | | | | | |--- feature_2 <= -0.44\n",
   "| | | | | | | | | |--- feature_2 <= -0.45\n",
   "| | | | | | | | | | |--- feature_2 <= -0.45\n",
   "| | | | | | | | | | | |--- truncated branch of depth 4\n",
   "| | | | | | | | | | |--- feature_2 > -0.45\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | | |--- feature_2 > -0.45\n",
   "| | | | | | | | | | |--- feature_2 <= -0.45\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.45\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | |--- feature_2 > -0.44\n",
   "| | | | | | | | | |--- feature_2 <= -0.44\n",
   "| | | | | | | | | | |--- feature_2 <= -0.44\n",
   "| | | | | | | | | | | |--- truncated branch of depth 4\n",
   "| | | | | | | | | | |--- feature_2 > -0.44\n",
   "| | | | | | | | | | | |--- truncated branch of depth 3\n",
   "| | | | | | | | | |--- feature_2 > -0.44\n",
   "| | | | | | | | | | |--- feature_2 <= -0.43\n",
   "| | | | | | | | | | | |--- truncated branch of depth 4\n",
   "| | | | | | | | | | |--- feature_2 > -0.43\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | |--- feature_2 > -0.43\n",
   "| | | | | | |--- feature_2 <= -0.43\n",
   "| | | | | | | |--- value: [-0.10]\n",
   "| | | | | | |--- feature_2 > -0.43\n",
   "| | | | | | | |--- feature_2 <= -0.39\n",
   "| | | | | | | | |--- feature_2 <= -0.43\n",
   "| | | | | | | | | |--- feature_2 <= -0.43\n",
   "| | | | | | | | | | |--- feature_1 <= -0.10\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | | | |--- feature_1 > -0.10\n",
   "| | | | | | | | | | | |--- truncated branch of depth 3\n",
   "| | | | | | | | | |--- feature_2 > -0.43\n",
   "| | | | | | | | | | |--- value: [-0.01]\n",
   "| | | | | | | | |--- feature_2 > -0.43\n",
   "| | | | | | | | | |--- feature_2 <= -0.42\n",
   "| | | | | | | | | | |--- feature_2 <= -0.42\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.42\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | | |--- feature_2 > -0.42\n",
   "| | | | | | | | | | |--- feature_2 <= -0.42\n",
   "| | | | | | | | | | | |--- value: [-0.14]\n",
   "| | | | | | | | | | |--- feature_2 > -0.42\n",
   "| | | | | | | | | | | |--- truncated branch of depth 12\n",
   "| | | | | | | |--- feature_2 > -0.39\n",
   "| | | | | | | | |--- feature_2 <= -0.39\n",
   "| | | | | | | | | |--- value: [-0.43]\n",
   "| | | | | | | | |--- feature_2 > -0.39\n",
   "| | | | | | | | | |--- feature_2 <= -0.37\n",
   "| | | | | | | | | | |--- feature_2 <= -0.38\n",
   "| | | | | | | | | | | |--- truncated branch of depth 8\n",
   "| | | | | | | | | | |--- feature_2 > -0.38\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | | |--- feature_2 > -0.37\n",
   "| | | | | | | | | | |--- feature_2 <= -0.36\n",
   "| | | | | | | | | | | |--- truncated branch of depth 8\n",
   "| | | | | | | | | | |--- feature_2 > -0.36\n",
   "| | | | | | | | | | | |--- truncated branch of depth 8\n",
   "| | | | |--- feature_2 > -0.35\n",
   "| | | | | |--- feature_2 <= -0.35\n",
   "| | | | | | |--- value: [-0.18]\n",
   "| | | | | |--- feature_2 > -0.35\n",
   "| | | | | | |--- feature_2 <= -0.30\n",
   "| | | | | | | |--- feature_0 <= -0.49\n",
   "| | | | | | | | |--- feature_2 <= -0.34\n",
   "| | | | | | | | | |--- value: [-0.06]\n",
   "| | | | | | | | |--- feature_2 > -0.34\n",
   "| | | | | | | | | |--- feature_2 <= -0.32\n",
   "| | | | | | | | | | |--- value: [0.32]\n",
   "| | | | | | | | | |--- feature_2 > -0.32\n",
   "| | | | | | | | | | |--- value: [0.32]\n",
   "| | | | | | | |--- feature_0 > -0.49\n",
   "| | | | | | | | |--- feature_2 <= -0.32\n",
   "| | | | | | | | | |--- feature_2 <= -0.34\n",
   "| | | | | | | | | | |--- feature_2 <= -0.34\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.34\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | | |--- feature_2 > -0.34\n",
   "| | | | | | | | | | |--- feature_2 <= -0.33\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | | | |--- feature_2 > -0.33\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | |--- feature_2 > -0.32\n",
   "| | | | | | | | | |--- feature_2 <= -0.31\n",
   "| | | | | | | | | | |--- feature_2 <= -0.32\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.32\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | | |--- feature_2 > -0.31\n",
   "| | | | | | | | | | |--- feature_2 <= -0.31\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | | | |--- feature_2 > -0.31\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | |--- feature_2 > -0.30\n",
   "| | | | | | | |--- feature_2 <= -0.30\n",
   "| | | | | | | | |--- value: [-0.26]\n",
   "| | | | | | | |--- feature_2 > -0.30\n",
   "| | | | | | | | |--- feature_2 <= -0.30\n",
   "| | | | | | | | | |--- feature_1 <= -0.35\n",
   "| | | | | | | | | | |--- value: [0.00]\n",
   "| | | | | | | | | |--- feature_1 > -0.35\n",
   "| | | | | | | | | | |--- value: [0.30]\n",
   "| | | | | | | | |--- feature_2 > -0.30\n",
   "| | | | | | | | | |--- feature_2 <= -0.27\n",
   "| | | | | | | | | | |--- feature_1 <= -0.41\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_1 > -0.41\n",
   "| | | | | | | | | | | |--- truncated branch of depth 10\n",
   "| | | | | | | | | |--- feature_2 > -0.27\n",
   "| | | | | | | | | | |--- feature_2 <= -0.27\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | | | |--- feature_2 > -0.27\n",
   "| | | | | | | | | | | |--- truncated branch of depth 9\n",
   "| | | |--- feature_2 > -0.25\n",
   "| | | | |--- feature_2 <= -0.13\n",
   "| | | | | |--- feature_0 <= -0.50\n",
   "| | | | | | |--- value: [-0.44]\n",
   "| | | | | |--- feature_0 > -0.50\n",
   "| | | | | | |--- feature_2 <= -0.17\n",
   "| | | | | | | |--- feature_2 <= -0.25\n",
   "| | | | | | | | |--- value: [-0.34]\n",
   "| | | | | | | |--- feature_2 > -0.25\n",
   "| | | | | | | | |--- feature_2 <= -0.23\n",
   "| | | | | | | | | |--- feature_2 <= -0.24\n",
   "| | | | | | | | | | |--- feature_2 <= -0.25\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.25\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | |--- feature_2 > -0.24\n",
   "| | | | | | | | | | |--- feature_2 <= -0.24\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | | | |--- feature_2 > -0.24\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | |--- feature_2 > -0.23\n",
   "| | | | | | | | | |--- feature_2 <= -0.23\n",
   "| | | | | | | | | | |--- value: [-0.35]\n",
   "| | | | | | | | | |--- feature_2 > -0.23\n",
   "| | | | | | | | | | |--- feature_1 <= -0.01\n",
   "| | | | | | | | | | | |--- truncated branch of depth 15\n",
   "| | | | | | | | | | |--- feature_1 > -0.01\n",
   "| | | | | | | | | | | |--- truncated branch of depth 4\n",
   "| | | | | | |--- feature_2 > -0.17\n",
   "| | | | | | | |--- feature_2 <= -0.17\n",
   "| | | | | | | | |--- value: [-0.03]\n",
   "| | | | | | | |--- feature_2 > -0.17\n",
   "| | | | | | | | |--- feature_2 <= -0.16\n",
   "| | | | | | | | | |--- feature_2 <= -0.17\n",
   "| | | | | | | | | | |--- feature_2 <= -0.17\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.17\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | | |--- feature_2 > -0.17\n",
   "| | | | | | | | | | |--- feature_2 <= -0.16\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.16\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | |--- feature_2 > -0.16\n",
   "| | | | | | | | | |--- feature_2 <= -0.16\n",
   "| | | | | | | | | | |--- value: [-0.22]\n",
   "| | | | | | | | | |--- feature_2 > -0.16\n",
   "| | | | | | | | | | |--- feature_2 <= -0.14\n",
   "| | | | | | | | | | | |--- truncated branch of depth 8\n",
   "| | | | | | | | | | |--- feature_2 > -0.14\n",
   "| | | | | | | | | | | |--- truncated branch of depth 9\n",
   "| | | | |--- feature_2 > -0.13\n",
   "| | | | | |--- feature_2 <= -0.06\n",
   "| | | | | | |--- feature_2 <= -0.13\n",
   "| | | | | | | |--- value: [-0.32]\n",
   "| | | | | | |--- feature_2 > -0.13\n",
   "| | | | | | | |--- feature_2 <= -0.09\n",
   "| | | | | | | | |--- feature_2 <= -0.11\n",
   "| | | | | | | | | |--- feature_2 <= -0.12\n",
   "| | | | | | | | | | |--- feature_2 <= -0.12\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | | | |--- feature_2 > -0.12\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | |--- feature_2 > -0.12\n",
   "| | | | | | | | | | |--- feature_2 <= -0.11\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.11\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | |--- feature_2 > -0.11\n",
   "| | | | | | | | | |--- feature_2 <= -0.10\n",
   "| | | | | | | | | | |--- feature_2 <= -0.11\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | | | |--- feature_2 > -0.11\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | |--- feature_2 > -0.10\n",
   "| | | | | | | | | | |--- feature_2 <= -0.10\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.10\n",
   "| | | | | | | | | | | |--- truncated branch of depth 4\n",
   "| | | | | | | |--- feature_2 > -0.09\n",
   "| | | | | | | | |--- feature_2 <= -0.07\n",
   "| | | | | | | | | |--- feature_2 <= -0.08\n",
   "| | | | | | | | | | |--- feature_2 <= -0.09\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | | | |--- feature_2 > -0.09\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | |--- feature_2 > -0.08\n",
   "| | | | | | | | | | |--- feature_2 <= -0.08\n",
   "| | | | | | | | | | | |--- truncated branch of depth 4\n",
   "| | | | | | | | | | |--- feature_2 > -0.08\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | |--- feature_2 > -0.07\n",
   "| | | | | | | | | |--- feature_2 <= -0.07\n",
   "| | | | | | | | | | |--- feature_2 <= -0.07\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.07\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | |--- feature_2 > -0.07\n",
   "| | | | | | | | | | |--- feature_2 <= -0.06\n",
   "| | | | | | | | | | | |--- truncated branch of depth 7\n",
   "| | | | | | | | | | |--- feature_2 > -0.06\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | |--- feature_2 > -0.06\n",
   "| | | | | | |--- feature_2 <= -0.02\n",
   "| | | | | | | |--- feature_1 <= -0.49\n",
   "| | | | | | | | |--- feature_0 <= -0.32\n",
   "| | | | | | | | | |--- value: [0.05]\n",
   "| | | | | | | | |--- feature_0 > -0.32\n",
   "| | | | | | | | | |--- value: [0.34]\n",
   "| | | | | | | |--- feature_1 > -0.49\n",
   "| | | | | | | | |--- feature_2 <= -0.04\n",
   "| | | | | | | | | |--- feature_2 <= -0.05\n",
   "| | | | | | | | | | |--- feature_2 <= -0.05\n",
   "| | | | | | | | | | | |--- truncated branch of depth 5\n",
   "| | | | | | | | | | |--- feature_2 > -0.05\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | |--- feature_2 > -0.05\n",
   "| | | | | | | | | | |--- feature_2 <= -0.04\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | | | |--- feature_2 > -0.04\n",
   "| | | | | | | | | | | |--- truncated branch of depth 6\n",
   "| | | | | | | | |--- feature_2 > -0.04\n",
   "| | | | | | | | | |--- feature_2 <= -0.04\n",
   "| | | | | | | | | | |--- feature_2 <= -0.04\n",
   "| | | | | | | | | | | |--- value: [0.04]\n",
   "

5. Recall (2.28) En(X](w1 Wn) = E X(W1 WnWW+1 wN) and the S3 defi...