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Original Research ARTICLE

This article is part of a Research Topic

Statistical physics of pairwise probability models

Yasser Roudi¹*, Erik Aurell^2,3 and John A. Hertz^1,4

NORDITA, Stockholm, Sweden

Department of Computational Biology, AlbaNova University Centre, Stockholm, Sweden

ACCESS Linnaeus Centre, KTH-Royal Institute of Technology, Stockholm, Sweden

The Niels Bohr Institute, Copenhagen University, Copenhagen, Denmark

Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data: knowledge of the mean values and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying and using pairwise models. We build on our previous work on the subject and study the relation between different methods for fitting these models and evaluating their quality. In particular, using data from simulated cortical networks we study how the quality of various approximate methods for inferring the parameters in a pairwise model depends on the time bin chosen for binning the data. We also study the effect of the size of the time bin on the model quality itself, again using simulated data. We show that using finer time bins increases the quality of the pairwise model. We offer new ways of deriving the expressions reported in our previous work for assessing the quality of pairwise models.

Keywords:

pairwise model, inverse ising problem, maximum entropy distribution, inference

Citation:

Roudi Y, Aurell E and Hertz JA (2009). Statistical physics of pairwise probability models. Front. Comput. Neurosci. 3:22. doi: 10.3389/neuro.10.022.2009

Received:

25 April 2009;

Paper pending published:

21 July 2009;

Accepted:

02 October 2009;

Published online:

17 November 2009.

Edited by:

Hava T. Siegelmann, University of Massachusetts Amherst, USA

Reviewed by:

Boshiyuki Tanaka, Kyoto University, Japan
Lenka Zdeborova, Los Alamos National Laboratory, USA

© 2009 Roudi, Aurell and Hertz. This is an open-access article subject to an exclusive license agreement between the authors and the Frontiers Research Foundation, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are credited.

*Correspondence:

Yasser Roudi, NORDITA, Roslagstullsbacken 23, 106 91 Stockholm, Sweden. e-mail: yasserroudi@googlemail.com