Exact inferences in a neural implementation of a hidden Markov model.

Published

Journal Article

From first principles, we derive a quadratic nonlinear, first-order dynamical system capable of performing exact Bayes-Markov inferences for a wide class of biologically plausible stimulus-dependent patterns of activity while simultaneously providing an online estimate of model performance. This is accomplished by constructing a dynamical system that has solutions proportional to the probability distribution over the stimulus space, but with a constant of proportionality adjusted to provide a local estimate of the probability of the recent observations of stimulus-dependent activity-given model parameters. Next, we transform this exact equation to generate nonlinear equations for the exact evolution of log likelihood and log-likelihood ratios and show that when the input has low amplitude, linear rate models for both the likelihood and the log-likelihood functions follow naturally from these equations. We use these four explicit representations of the probability distribution to argue that, in contrast to the arguments of previous work, the dynamical system for the exact evolution of the likelihood (as opposed to the log likelihood or log-likelihood ratios) not only can be mapped onto a biologically plausible network but is also more consistent with physiological observations.

Full Text

Duke Authors

Cited Authors

  • Beck, JM; Pouget, A

Published Date

  • May 2007

Published In

Volume / Issue

  • 19 / 5

Start / End Page

  • 1344 - 1361

PubMed ID

  • 17381269

Pubmed Central ID

  • 17381269

International Standard Serial Number (ISSN)

  • 0899-7667

Digital Object Identifier (DOI)

  • 10.1162/neco.2007.19.5.1344

Language

  • eng

Conference Location

  • United States