Contents

Generate Fake Data for WFH Data

Contents

55. Generate Fake Data for WFH Data#

import json

import pandas as pd
import numpy as np

import matplotlib.pyplot as plt
import seaborn as sns;sns.set();

from sklearn import tree

55.1. Create a model for the data#

feature_names = ['health', 'weather', 'holiday']

class WFH:
    def __init__(self, d, n, probabilities=None):
        if probabilities is None:
            probabilities = (0.8, 0.2)
        self.probabilities = probabilities
        self.d = d
        self.n = n
        self.x = self._generate_binary_features()
        self.y = self._generate_target_values()
        
    def _generate_binary_features(self):
    
        feat = np.random.choice([0,1], (self.n, self.d)).tolist()
    
        return feat

    def _desired_y(self):

        y = []
        for i in self.x:
            if i == [1,1,0]:
                y.append(1)
            else:
                y.append(0)
        
        return y
    
    @staticmethod
    def _randomize_y(y, probabilities):
        
        first_val = y
        second_val = 1 if y == 0 else 0
        
        return np.random.choice([first_val, second_val], 1, p=probabilities)[0]
    
    def _generate_target_values(self):
        
        y = self._desired_y()
        y = [self._randomize_y(i, self.probabilities) for i in y]
        
        return y

55.2. Generate Data#

wfh = WFH(d=3, n=100, probabilities=(1,0))

df = pd.merge(
    pd.DataFrame(wfh.x, columns=feature_names), 
    pd.DataFrame(wfh.y, columns=['go_to_office']),
    how='left',
    left_index=True,
    right_index=True
)

print(
    df.sample(10).to_markdown()
)

|    |   health |   weather |   holiday |   go_to_office |
|---:|---------:|----------:|----------:|---------------:|
|  7 |        1 |         1 |         0 |              1 |
| 78 |        0 |         1 |         0 |              0 |
| 89 |        1 |         1 |         1 |              0 |
|  0 |        0 |         0 |         1 |              0 |
| 77 |        1 |         1 |         0 |              1 |
| 61 |        0 |         1 |         0 |              0 |
| 64 |        0 |         1 |         0 |              0 |
| 92 |        0 |         1 |         1 |              0 |
|  9 |        0 |         0 |         1 |              0 |
| 49 |        1 |         0 |         1 |              0 |

55.3. Decision Tree#

clf = tree.DecisionTreeClassifier()
clf = clf.fit(wfh.x, wfh.y)

fig, ax=plt.subplots(figsize=(15,15))
tree.plot_tree(clf, feature_names=feature_names);

../../_images/decision_tree_example_11_0.png

55.4. Impure Data#

wfh_impure = WFH(d=3, n=100, probabilities=(0.9,0.1))

clf_impure = tree.DecisionTreeClassifier(max_depth=20, min_samples_leaf=1, min_samples_split=0.0001)
clf_impure = clf_impure.fit(wfh_impure.x, wfh_impure.y)

fig, ax = plt.subplots(figsize=(15,15))
tree.plot_tree(clf_impure, feature_names=feature_names);

../../_images/decision_tree_example_15_0.png

55.5. Gini Impurity#

55.5.1. Gini Impurity for 2 possible classes#

def gini_2(p1, p2):
    if p1+p2<=1:
        return p1 * (1 - p1) + p2 * (1 - p2)
    else:
        return None
    

gini_2_test_p1 = np.linspace(0,1,1001)
gini_2_test_p2 = np.linspace(0,1,1001)

gini_2_test_impurity = [
    [gini_2(p1, p2) for p1 in gini_2_test_p1]
    for p2 in gini_2_test_p2
]

df_gini_2_test = pd.DataFrame(
    gini_2_test_impurity,
    index=[f"{i:0.2f}" for i in gini_2_test_p2],
    columns=[f"{i:0.2f}" for i in gini_2_test_p1]
)

fig, ax = plt.subplots(figsize=(12,10))
sns.heatmap(
    df_gini_2_test.loc[::-1,], ax=ax
)
ax.set_xlabel('$p_1$')
ax.set_ylabel('$p_2$')
ax.set_title('Gini Impurity for Data with 2 Possible Values');

../../_images/decision_tree_example_21_0.png

55.5.2. Gini Impurity for 3 possible classes#

def gini_3(p1,p2):
    # return -2 * (p1**2 + p2**2 + p1*p2 - p1 - p2)
    if p1+p2<=1:
        return p1 * (1 - p1) + p2 * (1 - p2) + (1 - p1 - p2) * (p1 + p2)
    else:
        return None

gini_3_test_p1 = np.linspace(0,1,1001)
gini_3_test_p2 = np.linspace(0,1,1001)
gini_3_test_impurity = [
    [gini_3(p1, p2) for p1 in gini_3_test_p1]
    for p2 in gini_3_test_p2
]

df_gini_3_test = pd.DataFrame(
    gini_3_test_impurity,
    index=[f"{i:0.2f}" for i in gini_3_test_p2],
    columns=[f"{i:0.2f}" for i in gini_3_test_p1]
)

fig, ax = plt.subplots(figsize=(12,10))
sns.heatmap(
    df_gini_3_test.loc[::-1,], ax=ax
)
ax.set_xlabel('$p_1$')
ax.set_ylabel('$p_2$')
ax.set_title('Gini Impurity for Data with 3 Possible Values');

../../_images/decision_tree_example_26_0.png

55.6. Plotlyjs#

charts:
  - target: 3-possible-classes
    data: "[
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    layout: "{
      title: 'Gini Impurity for Data with 3 Possible Values',
      annotations: [],
      xaxis: {
        title: 'p1'
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      yaxis: {
        title: 'p2'
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