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varentropy vs entropy, two outcomes
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import numpy as np | |
import matplotlib.pyplot as plt | |
# Define a range of p0 values from 0 to 1 | |
p0 = np.linspace(0, 1, 500) | |
p1 = 1 - p0 | |
# To avoid log(0), replace zeros with a very small number | |
epsilon = 1e-12 | |
p0_safe = np.clip(p0, epsilon, 1 - epsilon) | |
p1_safe = np.clip(p1, epsilon, 1 - epsilon) | |
# Calculate the entropy H(p) = -Σ p_i log2(p_i) | |
entropy = - (p0_safe * np.log2(p0_safe) + p1_safe * np.log2(p1_safe)) | |
# Calculate varentropy V(p) = Σ p_i [ -log2(p_i) - H(p) ]^2 | |
log_p0 = -np.log2(p0_safe) | |
log_p1 = -np.log2(p1_safe) | |
varentropy = p0_safe * (log_p0 - entropy)**2 + p1_safe * (log_p1 - entropy)**2 | |
# Plotting the entropy and varentropy | |
plt.figure(figsize=(10, 6)) | |
plt.plot(p0, entropy, label='Entropy', color='blue') | |
plt.plot(p0, varentropy, label='Varentropy', color='red') | |
plt.xlabel('Probability $p_0$') | |
plt.ylabel('Value') | |
plt.title('Entropy and Varentropy vs. Probability $p_0$ for a Bernoulli Distribution') | |
plt.legend() | |
plt.grid(True) | |
plt.show() |
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