feat(MachineLearning/PACLearning): VC dimension#563
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Adds the Vapnik-Chervonenkis dimension for binary concept classes
`C : ConceptClass α Bool`, with:
- `SetShatters C W`: `C` shatters a set `W` if every `W' ⊆ W` arises as the
intersection of some `c ⁻¹' {true}` with `W` for `c ∈ C`.
- `SetShatters.subset` / `SetShatters.superset`: anti/monotonicity in the
shattered set and the concept class.
- `Finset.Shatters.toSetShatters`: bridge from Mathlib's `Finset.Shatters`
to `SetShatters` via characteristic functions.
- `vcDim C`: VC dimension as `sSup` of shattered finite-set cardinalities.
- `HasFiniteVCDim C` and `hasFiniteVCDim_iff`: the predicate making `vcDim`
mathematically meaningful (uniform bound on shattered cardinalities),
required as a hypothesis by downstream `vcDim`-stated lower bounds.
First layer of a stacked PR sequence formalizing the EHKV lower bound
on PAC sample complexity.
fmontesi
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May 14, 2026
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fmontesi
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Looks good enough to me for merging, but would be nice to get an extra confirmation from somebody more familiar with the domain.
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Adds the Vapnik-Chervonenkis dimension for binary concept classes
C : ConceptClass α Bool, with:SetShatters C W:Cshatters a setWif everyW' ⊆ Warises as the intersection of somec ⁻¹' {true}withWforc ∈ C.SetShatters.subset/SetShatters.superset: anti/monotonicity in the shattered set and the concept class.Finset.Shatters.toSetShatters: bridge from Mathlib'sFinset.ShatterstoSetShattersvia characteristic functions.vcDim C: VC dimension assSupof shattered finite-set cardinalities.HasFiniteVCDim CandhasFiniteVCDim_iff: the predicate makingvcDimmathematically meaningful (uniform bound on shattered cardinalities), required as a hypothesis by downstreamvcDim-stated lower bounds.First layer of a stacked PR sequence formalizing the EHKV lower bound on PAC sample complexity.