Boosting Explanation

Interactive tutorial on boosting explanation with practical implementations and visualizations

Author

Nipun Batra

Published

July 24, 2025

Open In Colab

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline

from math import sqrt
SPINE_COLOR = 'gray'

x = np.linspace(0.04, 0.51, 1000)

def latexify(fig_width=None, fig_height=None, columns=1):
    """Set up matplotlib's RC params for LaTeX plotting.
    Call this before plotting a figure.

    Parameters
    ----------
    fig_width : float, optional, inches
    fig_height : float,  optional, inches
    columns : {1, 2}
    """

    # code adapted from http://www.scipy.org/Cookbook/Matplotlib/LaTeX_Examples

    # Width and max height in inches for IEEE journals taken from
    # computer.org/cms/Computer.org/Journal%20templates/transactions_art_guide.pdf

    assert(columns in [1,2])

    if fig_width is None:
        fig_width = 3.39 if columns==1 else 6.9 # width in inches

    if fig_height is None:
        golden_mean = (sqrt(5)-1.0)/2.0    # Aesthetic ratio
        fig_height = fig_width*golden_mean # height in inches

    MAX_HEIGHT_INCHES = 8.0
    if fig_height > MAX_HEIGHT_INCHES:
        print("WARNING: fig_height too large:" + fig_height + 
              "so will reduce to" + MAX_HEIGHT_INCHES + "inches.")
        fig_height = MAX_HEIGHT_INCHES

    params = {'backend': 'ps',
              'axes.labelsize': 8, # fontsize for x and y labels (was 10)
              'axes.titlesize': 8,
              'legend.fontsize': 8, # was 10
              'xtick.labelsize': 8,
              'ytick.labelsize': 8,
              'text.usetex': True,
              'figure.figsize': [fig_width,fig_height],
              'font.family': 'serif'
    }

    matplotlib.rcParams.update(params)


def format_axes(ax):

    for spine in ['top', 'right']:
        ax.spines[spine].set_visible(False)

    for spine in ['left', 'bottom']:
        ax.spines[spine].set_color(SPINE_COLOR)
        ax.spines[spine].set_linewidth(0.5)

    ax.xaxis.set_ticks_position('bottom')
    ax.yaxis.set_ticks_position('left')

    for axis in [ax.xaxis, ax.yaxis]:
        axis.set_tick_params(direction='out', color=SPINE_COLOR)

    return ax

plt.plot(x, 0.5*np.log((1-x)/x), color='k', linewidth=3)
plt.axvline(0.5, color='r', linewidth=0.9)
plt.axhline(0.0, color='r', linewidth=0.9)
plt.xlabel(r"$err_m$")
plt.ylabel(r"$\alpha_m$")

Text(0, 0.5, '$\\alpha_m$')

latexify()
plt.rcParams.update({'font.size': 40})
plt.plot(x, 0.5*np.log((1-x)/x), color='k', linewidth=2)
plt.axvline(0.5, color='r', linewidth=0.9)
plt.axhline(0.0, color='r', linewidth=0.9)
plt.xlabel(r"$err_m$")
plt.ylabel(r"$\alpha_m$")
format_axes(plt.gca())
plt.savefig("../supervised/assets/ensemble/figures/alpha-boosting.pdf", bbox_inches="tight", transparent=True)

latexify()
plt.rcParams.update({'font.size': 40})
plt.plot(x, np.exp(0.5*np.log((1-x)/x)), color='r', linewidth=2, label=r'$e^{\alpha_m}$ ')
plt.plot(x, np.exp(-0.5*np.log((1-x)/x)), color='g', linewidth=2, label=r'$e^{-\alpha_m}$')

plt.xlabel(r"$err_m$")
plt.ylabel("Weight Multiplier")
format_axes(plt.gca())
plt.legend()
plt.savefig("../supervised/assets/ensemble/figures/alpha-boosting-weight.pdf", bbox_inches="tight", transparent=True)

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