# Statistical Physics of Pairwise Probability Models

@article{Roudi2009StatisticalPO, title={Statistical Physics of Pairwise Probability Models}, author={Yasser Roudi and Erik Aurell and John A. Hertz}, journal={Frontiers in Computational Neuroscience}, year={2009}, volume={3} }

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…

## 118 Citations

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This work provides a perturbative approximation of the maximally expected bias when the true model is out of model class, and illustrates the results using numerical simulations of an Ising model; i.e. the second-order maximum entropy distribution on binary data.

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By introducing multiple analytic approximation methods to a state-space model of neural population activity, this work makes it possible to estimate dynamic pairwise interactions of up to 60 neurons and accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data.

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This work considers the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units and presents a class of models for which the analytical solution of this inverse problem can be obtained.

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This work provides a perturbative approximation of the maximally expected bias when the true model is out of model class, and illustrates the results using numerical simulations of an Ising model; i.e. the second-order maximum entropy distribution on binary data.

Spin glass models for a network of real neurons

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It is shown that Pairwise interactions between neurons account for observed higher-order correlations, and that for groups of 10 or more neurons pairwise interactions can no longer be regarded as small perturbations in an independent system.

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