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Cross Examination On Data

On KL Divergence (Kullback-Leibler Divergence) and Cross-Entropy

10 min readJun 10, 2025
12 Angry Men (1957)

KL Divergence (Kullback-Leibler Divergence) and Cross-Entropy are closely related concepts in information theory and machine learning, particularly in classification and density estimation tasks. Here’s a breakdown of their advantages and disadvantages relative to each other.

For self-information: 1 bit: yes/no. For full certainty, there is no need to indicate the outcome. It is known.
Advantages of KL Divergence over Cross-Entropy
1. Explicit Comparison of Distributions
- KL Divergence directly measures how one probability distribution (usually the true distribution) diverges from another (the predicted distribution).
➜➤ useful when comparing or evaluating models that output probability distributions, such as in variational inference.2. Interpretability in Terms of Information Loss
- KL Divergence quantifies the expected…

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