The VCdimension of a class of multiples of the primes, and a connection to AdaBoost
Abstract
We discuss the VCdimension of a class of multiples of integers and primes (equivalently indicator functions) and demonstrate connections to prime counting functions. Additionally, we prove limit theorems for the behavior of an empirical risk minimization rule as well as the weights assigned to the output hypothesis in AdaBoost for these "primeidentifying" indicator functions, when we sample $m_n$ i.i.d. points uniformly from the integers $\{2, \dots, n\}$.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 arXiv:
 arXiv:2208.06442
 Bibcode:
 2022arXiv220806442T
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Combinatorics;
 Mathematics  Probability;
 11B25;
 68Q32;
 60F15
 EPrint:
 9 pages, 0 figures