arXiv subjects

Hunter Chase

Publications and source records attributed to Hunter Chase.

4 recordsLinked to original sources

arXiv2023

Applications of Littlestone dimension to query learning and to compression

In this paper we give several applications of Littlestone dimension. The first is to the model of \cite{angluin2017power}, where we extend their results for learning by equivalence queries with random counterexamples. Second, we extend that model to infinite concept classes with an additional source of randomness. Third, we give improved results on the relationship of Littlestone dimension to classes with extended $d$-compression schemes, proving a strong version of a conjecture of \cite{floyd1995sample} for Littlestone dimension.

cs.LG↗

arXiv2019

Bounds in Query Learning

We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful enough to enough to give new and very short proofs of the efficient learnability of several prominent examples (e.g. regular languages and regular $\omega$-languages), in some cases also producing new bounds on the number of queries. In the setting of equivalence plus membership queries, we give an algorithm which learns a class in polynomially many queries whenever any such algorithm exists. We also study equivalence query learning in a randomized model, producing new bounds on the expected number of queries required to learn an arbitrary concept. Many of the techniques and notions of dimension draw inspiration from or are related to notions from model theory, and these connections are explained. We also use techniques from query learning to mildly improve a result of Laskowski regarding compression schemes.

cs.LG↗

arXiv2018

Model theory and combinatorics of banned sequences

We set up a general context in which one can prove Sauer-Shelah type lemmas. We apply our general results to answer a question of Bhaskar and give a slight improvement to a result of Malliaris and Terry. We also prove a new Sauer-Shelah type lemma in the context of op-rank, a notion of Guingona and Hill.

math.LO↗

arXiv2018

Model Theory and Machine Learning

About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory (NIP) and machine learning (PAC-learnability). The following years saw a fruitful exchange of ideas between PAC learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between \emph{stability} and learnability in various settings of \emph{online learning.} In particular, this gives many new examples of mathematically interesting classes which are learnable in the online setting.

math.LO↗