On Error and Compression Rates for Prototype Rules

Omer Kerem, Roi Weiss

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study the close interplay between error and compression in the non-parametric multiclass classification setting in terms of prototype learning rules. We focus in particular on a recently proposed compression-based learning rule termed OptiNet. Beyond its computational merits, this rule has been recently shown to be universally consistent in any metric instance space that admits a universally consistent rule—the first learning algorithm known to enjoy this property. However, its error and compression rates have been left open. Here we derive such rates in the case where instances reside in Euclidean space under commonly posed smoothness and tail conditions on the data distribution. We first show that OptiNet achieves non-trivial compression rates while enjoying near minimax-optimal error rates. We then proceed to study a novel general compression scheme for further compressing prototype rules that locally adapts to the noise level without sacrificing accuracy. Applying it to OptiNet, we show that under a geometric margin condition, further gain in the compression rate is achieved. Experimental results comparing the performance of the various methods are presented.

Original languageEnglish
Title of host publicationAAAI-23 Technical Tracks 7
EditorsBrian Williams, Yiling Chen, Jennifer Neville
Pages8228-8236
Number of pages9
ISBN (Electronic)9781577358800
StatePublished - 27 Jun 2023
Event37th AAAI Conference on Artificial Intelligence, AAAI 2023 - Washington, United States
Duration: 7 Feb 202314 Feb 2023

Publication series

NameProceedings of the 37th AAAI Conference on Artificial Intelligence, AAAI 2023
Volume37

Conference

Conference37th AAAI Conference on Artificial Intelligence, AAAI 2023
Country/TerritoryUnited States
CityWashington
Period7/02/2314/02/23

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