feat: state results and conjectures on VCₘ dim of convex sets in ℝⁿ #1408
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
VC dimension of a set family is an old notion in learning theory. VC dimension of a *set* in a group (defined as the VC dimension of its family of translates) is a more recent notion motivated by additive combinatorics. VCₙ dimension of a set family is a very recent notion that appeared in the context of model theory. Therefore very few questions have been asked and answered at the intersection of both, i.e. about the VCₙ dimension of a family of translates This PR offers some conjectures in this direction. The conjectures are all mine and do not appear in the literature. They are very easily stated due to the elementary nature of VCₙ dimension.
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
VC dimension of a set family is an old notion in learning theory. VC dimension of a set in a group (defined as the VC dimension of its family of translates) is a more recent notion motivated by additive combinatorics. VCₙ dimension of a set family is a very recent notion that appeared in the context of model theorym to extend the VC dimension of a set of translates.
This PR offers some conjectures in this direction. The conjectures are all mine and do not appear in the literature. They are very easily stated due to the elementary nature of VCₙ dimension.