Project 23: Information Theory Loss Engineering Lab

Build a metrics workbench for entropy, cross-entropy, KL divergence, and mutual information in model diagnostics.

Quick Reference

Attribute Value
Difficulty Level 3: Advanced (The Engineer)
Time Estimate 1-2 weeks
Main Programming Language Python
Alternative Programming Languages Julia, R, Rust
Coolness Level Level 4: Hardcore Tech Flex
Business Potential 2. The “Micro-SaaS / Pro Tool” (Solo-Preneur Potential)
Knowledge Area Information Theory / Probabilistic Modeling
Main Book “Elements of Information Theory” by Cover and Thomas

1. Learning Objectives

  1. Compute entropy-family metrics robustly on real predictions.
  2. Explain why cross-entropy is optimization-friendly and calibration-sensitive.
  3. Use KL and mutual information to isolate model failure modes.
  4. Produce decision-grade calibration recommendations.

2. All Theory Needed (Per-Concept Breakdown)

Concept A: Entropy and Surprise

Fundamentals Entropy measures uncertainty of a distribution, not correctness of predictions.

Deep Dive into the concept In ML, target entropy is partly irreducible noise. Overconfident but wrong models may have low predictive entropy yet high risk. Distinguishing aleatoric uncertainty from model mismatch requires more than one scalar metric.

Concept B: Cross-Entropy and KL

Fundamentals Cross-entropy decomposes into target entropy plus KL divergence.

Deep Dive into the concept This decomposition clarifies what training can improve: KL mismatch. It also explains why minimizing cross-entropy aligns model probabilities with empirical distributions.

Concept C: Mutual Information

Fundamentals Mutual information quantifies dependence and potential predictive value.

Deep Dive into the concept MI supports feature diagnostics and representation analysis but depends on estimator choices and sample regime.

3. Build Blueprint

  1. Implement stable probability checks and clipping.
  2. Compute entropy/cross-entropy/KL with class-wise decomposition.
  3. Add mutual-information estimation for selected features.
  4. Generate calibration report and recommendations.

4. Real-World Outcome (Target)

$ python info_lab.py --dataset sentiment_probs.csv --target labels.csv

Entropy H(Y): 0.6912
Cross-Entropy H(Y,Q): 0.8245
KL(Y||Q): 0.1333
Mutual Information I(X;Y): 0.2179
Recommendation: apply temperature scaling

5. Core Design Notes from Main Guide

Core Question

“What are our losses really measuring beyond accuracy?”

Common Pitfalls

  • Non-normalized probabilities
  • log(0) failures from zero bins
  • Overinterpreting noisy MI estimates

Definition of Done

  • Metrics validated on hand-computable toy distributions
  • Calibration slices identify high-risk confidence buckets
  • KL asymmetry is explicitly documented
  • Report ties metrics to concrete model actions

6. Extensions

  1. Add Jensen-Shannon divergence.
  2. Add class-conditional MI drift tracking over time.
  3. Compare NLL and Brier score decisions.