Learning and generalization with the information Bottleneck

Ohad Shamir, Sivan Sabato, Naftali Tishby

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations


The Information Bottleneck is an information theoretic framework that finds concise representations for an 'input' random variable that are as relevant as possible for an 'output' random variable. This framework has been used successfully in various supervised and unsupervised applications. However, its learning theoretic properties and justification remained unclear as it differs from standard learning models in several crucial aspects, primarily its explicit reliance on the joint input-output distribution. In practice, an empirical plug-in estimate of the underlying distribution has been used, so far without any finite sample performance guarantees. In this paper we present several formal results that address these difficulties. We prove several finite sample bounds, which show that the information bottleneck can provide concise representations with good generalization, based on smaller sample sizes than needed to estimate the underlying distribution. The bounds are non-uniform and adaptive to the complexity of the specific model chosen. Based on these results, we also present a preliminary analysis on the possibility of analyzing the information bottleneck method as a learning algorithm in the familiar performance-complexity tradeoff framework. In addition, we formally describe the connection between the information bottleneck and minimal sufficient statistics.

Original languageEnglish
Pages (from-to)92-107
Number of pages16
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5254 LNAI
StatePublished - 1 Dec 2008
Externally publishedYes
Event19th International Conference on Algorithmic Learning Theory, ALT 2008 - Budapest, Hungary
Duration: 13 Oct 200816 Oct 2008

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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