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Formalizing statistical learning theory in Lean 4 [R]

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In my Lean 4 project, I am formalizing key components of statistical learning theory, aiming to create a structured "theorem ladder" that enhances readability and pedagogical value. Current results include finite-class ERM bounds, Rademacher symmetrization, and PAC-Bayes bounds, among others. Unlike existing Lean SLT efforts that emphasize abstract probability, my focus is on explicit finite-sample approaches and coherent theorem chains. I welcome feedback on theorem organization, proof structure, naming decisions, and suggestions for future formalization targets. Your insights would be invaluable. Thank you, R. S
Formalizing statistical learning theory in Lean 4 [R]
Formalizing statistical learning theory in Lean 4 [R]

I’ve been working on a Lean 4 project focused on formalizing parts of statistical learning theory:

FormalSLT repository

Current results include:

  • finite-class ERM bounds
  • Rademacher symmetrization
  • high-probability Rademacher bounds
  • Sauer–Shelah / VC-dimension bridge
  • finite scalar contraction
  • linear predictor bounds
  • finite PAC-Bayes bounds
  • algorithmic stability

The main idea is to build a readable and pedagogically structured “theorem ladder” for ML theory rather than just isolated declarations.

I’m trying to keep:

  • explicit assumptions
  • scoped theorem statements
  • zero sorry
  • close alignment with standard SLT presentations

Compared to some existing Lean SLT efforts that focus more heavily on empirical-process infrastructure and abstract probability machinery, this project is currently more focused on explicit finite-sample PAC/Rademacher/stability routes and readable end-to-end theorem chains.

I’d especially appreciate feedback on:

  • theorem organization
  • proof structure
  • naming/API decisions
  • useful next formalization targets

Thank you,
R. S

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