Machine Learning

, Volume 37, Issue 3, pp 355–363

Some PAC-Bayesian Theorems

  • David A. McAllester

DOI: 10.1023/A:1007618624809

Cite this article as:
McAllester, D.A. Machine Learning (1999) 37: 355. doi:10.1023/A:1007618624809


This paper gives PAC guarantees for “Bayesian” algorithms—algorithms that optimize risk minimization expressions involving a prior probability and a likelihood for the training data. PAC-Bayesian algorithms are motivated by a desire to provide an informative prior encoding information about the expected experimental setting but still having PAC performance guarantees over all IID settings. The PAC-Bayesian theorems given here apply to an arbitrary prior measure on an arbitrary concept space. These theorems provide an alternative to the use of VC dimension in proving PAC bounds for parameterized concepts.

Bayesian inference model selection risk minimization PAC MDL 
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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • David A. McAllester
    • 1
  1. 1.AT&T Labs-ResearchFlorham ParkUSA

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