The VC-dimension of a class of multiples of the primes, and a connection to AdaBoost

Andrew M Thomas

doi:10.48550/arxiv.2208.06442

Back

The VC-dimension of a class of multiples of the primes, and a connection to AdaBoost

Preprint

Open access

The VC-dimension of a class of multiples of the primes, and a connection to AdaBoost

Andrew M Thomas

ArXiv.org

Cornell University

08/12/2022

DOI: 10.48550/arxiv.2208.06442

Files and links (1)

url

https://doi.org/10.48550/arXiv.2208.06442View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We discuss the VC-dimension 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 "prime-identifying" indicator functions, when we sample mn i.i.d. points uniformly from the integers {2,…,n}.

Number Theory

Combinatorics

Probability

Details

Title: Subtitle: The VC-dimension of a class of multiples of the primes, and a connection to AdaBoost
Creators: Andrew M Thomas
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2208.06442
ISSN: 2331-8422
Publisher: Cornell University
Number of pages: 9
Language: English
Date posted: 08/12/2022
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9984446969602771

Metrics

15 Record Views