Decision Trees Real Input and Discrete Output

ML
Author

Nipun Batra

Published

January 1, 2024

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from io import StringIO
# Retina mode
%matplotlib inline
%config InlineBackend.figure_format = 'retina'

from latexify import latexify, format_axes
dataset = """Day,Temperature,PlayTennis
D1,40,No
D2,48,No
D3,60,Yes
D4,72,Yes
D5,80,Yes
D6,90,No"""

f = StringIO(dataset)
df = pd.read_csv(f, sep=",")
df
Day Temperature PlayTennis
0 D1 40 No
1 D2 48 No
2 D3 60 Yes
3 D4 72 Yes
4 D5 80 Yes
5 D6 90 No 
latexify(columns=2)
from sklearn.tree import DecisionTreeClassifier
from sklearn.tree import export_graphviz
import graphviz

dt = DecisionTreeClassifier(criterion='entropy', max_depth=1)

X = df[['Temperature']]
y = df['PlayTennis']

dt.fit(X, y)
DecisionTreeClassifier(criterion='entropy', max_depth=1)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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# Function to strore the decision tree's graphviz representation as pdf
def save_decision_tree_as_pdf(dt, feature_names, class_names, filename):
    dot_data = export_graphviz(dt, out_file=None, feature_names=feature_names, class_names=class_names, filled=True, rounded=True, special_characters=True)
    graph = graphviz.Source(dot_data)
    graph.render(filename, format='pdf')
    
save_decision_tree_as_pdf(dt, ['Temperature'], ['No', 'Yes'], '../figures/decision-trees/real-ip-1')
dt2 = DecisionTreeClassifier(criterion='entropy', max_depth=2)

dt2.fit(X, y)
save_decision_tree_as_pdf(dt2, ['Temperature'], ['No', 'Yes'], '../figures/decision-trees/real-ip-2')

Heavily borrowed and inspired from https://jakevdp.github.io/PythonDataScienceHandbook/05.08-random-forests.html

from sklearn.datasets import make_blobs

X, y = make_blobs(n_samples=300, centers=4,
                  random_state=0, cluster_std=1.2)
plt.scatter(X[:, 0], X[:, 1], c=y, s=10, cmap='rainbow')
format_axes(plt.gca())
plt.xlabel(r"$x_1$")
plt.ylabel(r"$x_2$")
Text(0, 0.5, '$x_2$')

from sklearn.tree import DecisionTreeClassifier
def visualize_tree(depth, X, y, ax=None, cmap='rainbow'):
    model = DecisionTreeClassifier(max_depth=depth)
    ax = ax or plt.gca()
    print(model, depth)
    
    # Plot the training points
    ax.scatter(X[:, 0], X[:, 1], c=y, s=10, cmap=cmap,
               clim=(y.min(), y.max()), zorder=3)
    ax.axis('tight')
    format_axes(plt.gca())
    plt.xlabel(r"$x_1$")
    plt.ylabel(r"$x_2$")
    xlim = ax.get_xlim()
    ylim = ax.get_ylim()
    
    # fit the estimator
    model.fit(X, y)
    xx, yy = np.meshgrid(np.linspace(*xlim, num=200),
                         np.linspace(*ylim, num=200))
    Z = model.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)

    # Create a color plot with the results
    n_classes = len(np.unique(y))
    contours = ax.contourf(xx, yy, Z, alpha=0.2,
                           levels=np.arange(n_classes + 1) - 0.5,
                           cmap=cmap, clim=(y.min(), y.max()),
                           zorder=1)

    ax.set(xlim=xlim, ylim=ylim)
    plt.tight_layout()
    plt.savefig(f"../figures/decision-trees/dt-{depth}.pdf", bbox_inches="tight")
    plt.clf()
for depth in range(1, 11):
    visualize_tree(depth, X, y)
DecisionTreeClassifier(max_depth=1) 1
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=2) 2
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=3) 3
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=4) 4
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=5) 5
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=6) 6
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=7) 7
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=8) 8
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=9) 9
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
DecisionTreeClassifier(max_depth=10) 10
/var/folders/1x/wmgn24mn1bbd2vgbqlk98tbc0000gn/T/ipykernel_73517/232881262.py:24: UserWarning: The following kwargs were not used by contour: 'clim'
  contours = ax.contourf(xx, yy, Z, alpha=0.2,
<Figure size 400x246.914 with 0 Axes>