Occam factors and model independent Bayesian learning of continuous distributions

Ilya Nemenman, William Bialek

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

Learning of a smooth but nonparametric probability density can be regularized using methods of quantum field theory. We implement a field theoretic prior numerically, test its efficacy, and show that the data and the phase space factors arising from the integration over the model space determine the free parameter of the theory (“smoothness scale”) self-consistently. This persists even for distributions that are atypical in the prior and is a step towards a model independent theory for learning continuous distributions. Finally, we point out that a wrong parametrization of a model family may sometimes be advantageous for small data sets.

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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