Statistical physics of pairwise probability models

TL;DR

This paper explores how tools from statistical physics can improve the understanding and evaluation of pairwise models in biological systems, especially neural data, by analyzing the effects of data binning on model quality.

Contribution

It introduces new methods for assessing pairwise model quality and investigates how data binning influences model inference and accuracy using simulated neural data.

Findings

Finer time bins improve pairwise model quality.

Different inference methods vary in effectiveness depending on bin size.

New expressions for model quality assessment are proposed.

Abstract

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 means 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.