Evaluating State-of-the-Art Classification Models Against Bayes Optimality

Ryan Theisen, Huan Wang, Lav R. Varshney, Caiming Xiong, Richard Socher

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Evaluating the inherent difficulty of a given data-driven classification problem is important for establishing absolute benchmarks and evaluating progress in the field. To this end, a natural quantity to consider is the Bayes error, which measures the optimal classification error theoretically achievable for a given data distribution. While generally an intractable quantity, we show that we can compute the exact Bayes error of generative models learned using normalizing flows. Our technique relies on a fundamental result, which states that the Bayes error is invariant under invertible transformation. Therefore, we can compute the exact Bayes error of the learned flow models by computing it for Gaussian base distributions, which can be done efficiently using Holmes-Diaconis-Ross integration. Moreover, we show that by varying the temperature of the learned flow models, we can generate synthetic datasets that closely resemble standard benchmark datasets, but with almost any desired Bayes error. We use our approach to conduct a thorough investigation of state-of-the-art classification models, and find that in some — but not all — cases, these models are capable of obtaining accuracy very near optimal. Finally, we use our method to evaluate the intrinsic "hardness" of standard benchmark datasets.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
EditorsMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
PublisherNeural information processing systems foundation
Pages9367-9377
Number of pages11
ISBN (Electronic)9781713845393
StatePublished - 2021
Event35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
Duration: Dec 6 2021Dec 14 2021

Publication series

NameAdvances in Neural Information Processing Systems
Volume12
ISSN (Print)1049-5258

Conference

Conference35th Conference on Neural Information Processing Systems, NeurIPS 2021
CityVirtual, Online
Period12/6/2112/14/21

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Fingerprint

Dive into the research topics of 'Evaluating State-of-the-Art Classification Models Against Bayes Optimality'. Together they form a unique fingerprint.

Cite this