{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lesson 4 - Introduction to gradient boosting \n",
"\n",
"> A first look at how gradient boosting combines several weak models into a strong model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[](https://mybinder.org/v2/gh/lewtun/hepml/master?urlpath=lab/tree/notebooks%2Flesson04_intro-to-gradient-boosting.ipynb) [](https://colab.research.google.com/github/lewtun/hepml/blob/master/notebooks/lesson04_intro-to-gradient-boosting.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Learning objectives\n",
"* Understand the conceptual difference between bagging and boosting ensembles\n",
"* Understand how gradient boosting works for regression tasks\n",
"* Learn how to tune the key hyperparameters of gradient boosting ensembles"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"This lesson is based on the gradient boosting example from\n",
"\n",
"* Chapter 7 of _Hands-On Machine Learning with Scikit-Learn and TensorFlow_ by Aurèlien Geron\n",
"\n",
"with parts of the theory coming from\n",
"\n",
"* _[How to explain gradient boosting](https://explained.ai/gradient-boosting/index.html)_ by Terence Parr and Jeremy Howard\n",
"* _[Gradient boosting explained](https://www.gormanalysis.com/blog/gradient-boosting-explained/)_ by Ben Gorman"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## What is gradient boosting?\n",
"Boosting refers to an ensemble technique that combines multiple simple or \"weak\" models into a single composite model. Unlike the bagging method we saw in previous lessons, boosting methods train the models _sequentially_, where each model is chosen to improve the overall performance. \n",
"\n",
"
\n",
"\n",
"In gradient boosting, the trick is to fit each new model to the _residual errors_ made by the previous one, e.g. the algorithm runs as follows:\n",
"\n",
"1. Fit a crappy model to the data $F_1(X) = y$\n",
"2. Fit a crappy model to the residuals $h_1(X) = y - F_1(X)$\n",
"3. Create a composite model $F_2(X) = F_1(X) + h_1(X)$\n",
"4. Repeat steps 2 and 3 recursively $F_{m+1}(X) = F_m(X) + h_m(X)$ for $M$ steps until $F_M(X)$ is good enough. Note that our task at each step is to train the model $h_m(X) = y - F_m(X)$ on the residual errors.\n",
"\n",
"For sufficiently large $M$, the result is a strong composite model $F_M(X) = \\hat{y}$ that estimates the target values $y$.\n",
"\n",
"> Note: although $h_m$ can be any model you want, in practice most boosting algorithms are based on tree regressors.\n",
"\n",
"The \"gradient\" part of gradient boosting is related to the fact that the loss function we wish to optimise is generically given by\n",
"\n",
"$$ L(y, F_M(X)) = \\frac{1}{N}\\sum_{i=1}^N L(y_i, F_M(x_i)) $$\n",
"\n",
"and for regression tasks it turns out that training models on the residual errors is equivalent to optimising the Mean Squared Error (MSE):\n",
"\n",
"$$ L(y, F_M(X)) = \\frac{1}{N}\\sum_{i=1}^N \\left(y_i - F_M(x_i) \\right)^2 $$\n",
"\n",
"In particular, for each $m\\in 1, \\ldots, M$ we calculate the gradient\n",
"\n",
"$$ r_{im} = - \\left[ \\frac{\\partial L(y_i, F(x_i)}{\\partial F(x_i)} \\right]_{F(x)=F_{m-1}(x)} \\,, \\qquad i = 1, \\ldots , N$$\n",
"\n",
"and fit a weak learner to these gradient components. The update step with gradient descent then looks like\n",
"\n",
"$$ F_{m+1}(X) = F_m(X) + \\gamma_m h_m(X)$$\n",
"\n",
"where $\\gamma_m$ is the learning rate or \"shrinkage\" parameter that controls the contribution of each tree (or how \"far\" a step we take in the direction of the average gradient).\n",
"\n",
"In this lesson we look at the basic mechanics behind gradient boosting for _regression_ tasks. The classification case is conceptually the same, but involves a different loss function and some technical details on how to combine predictions to build the ensemble."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Import libraries"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# reload modules before executing user code\n",
"%load_ext autoreload\n",
"# reload all modules every time before executing Python code\n",
"%autoreload 2\n",
"# render plots in notebook\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# uncomment this if running locally or on Google Colab\n",
"# !pip install --upgrade hepml"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# data wrangling\n",
"import pandas as pd\n",
"import numpy as np\n",
"\n",
"# data viz\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"from hepml.core import plot_regression_tree\n",
"\n",
"sns.set(color_codes=True)\n",
"sns.set_palette(sns.color_palette(\"muted\"))\n",
"\n",
"# ml magic\n",
"from sklearn.ensemble import GradientBoostingRegressor\n",
"from sklearn.tree import DecisionTreeRegressor\n",
"from sklearn.model_selection import train_test_split\n",
"from sklearn.metrics import mean_squared_error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generate the data\n",
"To keep things simple in this lesson, we will generate a noisy quadratic training set that has just a single feature per example, along with a continuous target:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.scatterplot(x=\"X\", y=\"y\", data=data)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step 1 - build a model on the data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To create a boosted regression model, we start by creating a crappy model that predicts the initial approximation of $y$. As discussed above it is common to use shallow Decision Trees, so let's fix the `max_depth` to a small number:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=2,\n",
" max_features=None, max_leaf_nodes=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, presort='deprecated',\n",
" random_state=None, splitter='best')"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tree_1 = DecisionTreeRegressor(max_depth=2)\n",
"tree_1.fit(X, y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The resulting tree can be visualised with a helper function from our `hepml` library:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_regression_tree(tree_1, data.columns, fontsize=24)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that this tree looks similar to the classification trees we have analysed in previous lessons. The main difference is that instead of predicting a discrete class like \"signal\" or \"background\" in each leaf node, a regression tree predicts a continuous _value_. This value is simply the average target value of the training examples associated with a given node. \n",
"\n",
"The CART algorithm is also similar to classification, except we now split the training set to minimise the Mean Squared Error (MSE) instead og Gini impurity:\n",
"\n",
"$$J(k, t_k) = \\frac{m_\\mathrm{left}}{m}\\mathrm{MSE}_\\mathrm{left} + \\frac{m_\\mathrm{right}}{m}\\mathrm{MSE}_\\mathrm{right} $$\n",
"\n",
"where \n",
"\n",
"$$ \\mathrm{MSE}_\\mathrm{node} = \\sum_{i\\in \\mathrm{node}} \\left(\\hat{y}_\\mathrm{node} - y^{(i)}\\right)^2 \n",
"\\qquad \\mathrm{and} \\qquad\n",
"\\hat{y}_\\mathrm{node} = \\frac{1}{m_\\mathrm{node}} \\sum_{i\\in \\mathrm{node}} y^{(i)}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, let's add a new column of predictions to our `pandas.DataFrame`"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_predictions(\n",
" [tree_1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(X)=h_1(X)$\", style=\"g-\", data_label=\"Training set\"\n",
")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step 2 - build a model on the residuals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Unsurprisingly, the weak model above is barely able to capture the structure of the data (i.e. it has high bias). However, we can improve the predictions by training a second regression tree on the _residual errors_ made by the first tree:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
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"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data[\"Tree 1 residual\"] = data[\"y\"] - data[\"Tree 1 prediction\"]\n",
"data.head()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=2,\n",
" max_features=None, max_leaf_nodes=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, presort='deprecated',\n",
" random_state=None, splitter='best')"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tree_2 = DecisionTreeRegressor(max_depth=2)\n",
"tree_2.fit(X, data[\"Tree 1 residual\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step 3 - create a composite model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we have an ensemble consisting of two trees. We can get the predictions from the ensemble by simply summing the predictions across all trees:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
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" X y Tree 1 prediction Tree 1 residual Tree 2 prediction \\\n",
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},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data[\"Tree 2 prediction\"] = tree_2.predict(X)\n",
"data[\"Tree 1 + tree 2 prediction\"] = sum(tree.predict(X) for tree in (tree_1, tree_2))\n",
"data.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As before, we can plot the predictions of both our second tree on the residuals, along with the predictions from the ensemble on the training set:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
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ggg==\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(20, 5))\n",
"\n",
"plt.subplot(ax0)\n",
"plot_predictions(\n",
" [tree_2],\n",
" X,\n",
" data[\"Tree 1 residual\"],\n",
" axes=[-0.5, 0.5, -0.5, 0.5],\n",
" label=\"$h_2(X)$\",\n",
" style=\"g-\",\n",
" data_style=\"k+\",\n",
" data_label=\"Residuals\",\n",
")\n",
"plt.ylabel(\"$y - h_1(X)$\", fontsize=18)\n",
"plt.title(\"Residuals and tree predictions\", fontsize=16)\n",
"\n",
"plt.subplot(ax1)\n",
"plot_predictions([tree_1, tree_2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(X) = h_1(X) + h_2(X)$\")\n",
"plt.title(\"Ensemble predictions\", fontsize=16)\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the figure, we see that the ensemble's predictions have improved compared to our first crappy model!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step 4 - rinse and repeat"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is not hard to see how we can continue this procedure by successively adding new models:\n",
"\n",
"$$ F_{m+1}(x) = F_m(x) + h_m(x)\\,, \\qquad \\mathrm{for} \\, m \\geq 0 $$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"