English

PAC Learning, VC Dimension, and the Arithmetic Hierarchy

Logic 2014-06-05 v1 Machine Learning Logic in Computer Science

Abstract

We compute that the index set of PAC-learnable concept classes is mm-complete Σ30\Sigma^0_3 within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable Π10\Pi^0_1 classes, in a sense made precise here. This family of concept classes is sufficient to cover all standard examples, and also has the property that PAC learnability is equivalent to finite VC dimension.

Cite

@article{arxiv.1406.1111,
  title  = {PAC Learning, VC Dimension, and the Arithmetic Hierarchy},
  author = {Wesley Calvert},
  journal= {arXiv preprint arXiv:1406.1111},
  year   = {2014}
}
R2 v1 2026-06-22T04:30:45.545Z