TitleOccam factors and model independent Bayesian learning of continuous distributions.
Publication TypeJournal Article
Year of Publication2002
AuthorsNemenman, I, Bialek, W
JournalPhys Rev E Stat Nonlin Soft Matter Phys
Issue2 Pt 2
Date Published2002 Feb

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.

Alternate JournalPhys Rev E Stat Nonlin Soft Matter Phys