Information Theory
Entropy and Information Gain
Entropy
- Definition of entropy
- Shannon entropy formula
- Interpretation of entropy
- Maximum entropy principle
- Entropy for discrete distributions
- Entropy for continuous distributions (differential entropy)
Information Gain
- Definition of information gain
- Mutual information
- Conditional entropy
- Information gain in decision trees
- Kullback-Leibler divergence
Cross-Entropy
Cross-Entropy Loss
- Definition of cross-entropy
- Cross-entropy for binary classification
- Cross-entropy for multi-class classification
- Relationship to log-likelihood
- Why cross-entropy for classification
Applications
- Loss function in neural networks
- Evaluation metric
- Comparison with other loss functions
KL Divergence
Kullback-Leibler Divergence
- Definition of KL divergence
- Properties of KL divergence
- Asymmetry of KL divergence
- Relationship to entropy and cross-entropy
Applications
- Measuring difference between distributions
- Variational inference
- Generative models
- Model comparison
Related Concepts
- Jensen-Shannon divergence
- Wasserstein distance
- Total variation distance
Interview Questions
- What is entropy and how is it interpreted?
- Explain information gain and its use in decision trees.
- Why is cross-entropy used as a loss function for classification?
- What is KL divergence and what does it measure?
- How does information theory relate to machine learning?
Coding Practice
- Implement entropy calculation for a probability distribution.
- Write a function to calculate information gain for decision trees.
- Implement cross-entropy loss from scratch.
- Calculate KL divergence between two distributions.
- Visualize entropy for different probability distributions.
Resources
- "Elements of Information Theory" by Cover and Thomas
- Information Theory Course: https://www.inference.org.uk/mackay/itila/
- Cross-Entropy Explained: https://en.wikipedia.org/wiki/Cross_entropy
- KL Divergence: https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence