Apply Statistical Learning Theory to Your Own Dataset

Proof required

Submit: a typed solution set for at least fifteen exercises on PAC learning, VC dimension, or sample complexity (with all derivation steps — not just final answers); a typed proof of the VC dimension for a specific hypothesis class (e.g. half-spaces in R^n, axis-aligned rectangles in R^2) with all proof steps; and a 200-word explanation of why VC dimension predicts generalisation error. An ML researcher or mathematician must confirm the solutions and proof are correct.

What gets checked

• At least fifteen exercise solutions with all derivation steps — not just final answers
• VC dimension proof is complete — not a sketch or reference to the standard result
• An ML researcher or mathematician has confirmed the solutions and proof are correct

Common mistakes

• Exercise solutions with only final answers — the proof requires showing all derivation steps
• VC dimension proof that cites the standard result without actually proving it for the specific hypothesis class

Resources

What a verifier looks for

• Are at least fifteen exercise solutions shown with all derivation steps?
• Is the VC dimension proof complete for the specific hypothesis class — not a reference to the standard result?
• Ask: 'what does infinite VC dimension tell you about learnability?' — tests understanding of the learnability boundary

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Proof required

Submit: a typed derivation of the Rademacher complexity bound for a linear classifier with all steps; a public GitHub repository (or Colab) containing the trained classifier on a real dataset, code computing the empirical Rademacher complexity, and a comparison showing the theoretical bound alongside the train and test accuracy; and a 200-word analysis explaining what the gap between the theoretical bound and the empirical gap tells you. An ML researcher must confirm the derivation is correct and the empirical computation is valid.

What gets checked

• Rademacher complexity derivation includes all proof steps — not a citation of the result
• Empirical Rademacher complexity is computed from the actual dataset — not a theoretical estimate
• An ML researcher has confirmed the derivation is correct and the empirical computation is valid

Common mistakes

• Derivation that cites the Rademacher bound without proving it for the linear classifier
• Empirical computation that estimates complexity theoretically rather than computing it from the actual dataset

Resources

What a verifier looks for

• Does the derivation include all proof steps for the Rademacher bound?
• Is the empirical Rademacher complexity computed from the actual dataset — not estimated theoretically?
• Ask: 'why is the theoretical generalisation bound typically much looser than the empirical train/test gap?' — tests understanding of bound tightness

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Proof required

Submit: a technical analysis (at least 500 words) connecting classical statistical learning theory to the overparameterisation puzzle, citing at least two primary research papers; and a recording or transcript of a live review with an ML researcher who challenged your reasoning in at least two specific places.

What gets checked

• Analysis cites at least two primary research papers — not blog summaries of research
• Analysis engages specifically with why classical VC theory predicts poor generalisation for overparameterised models
• An ML researcher challenged the reasoning in at least two specific places in the documented live review

Common mistakes

• Analysis that describes neural network success without engaging with the specific prediction of classical VC theory
• Analysis drawn from blog summaries rather than primary papers

Resources

What a verifier looks for

• Does the analysis cite primary papers — not blog summaries?
• Does the analysis engage specifically with why classical VC theory predicts poor generalisation?
• Were at least two specific reasoning steps challenged in the documented live review?

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