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- Roudi, Yasser, et al.
(författare)
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Ising model for neural data : Model quality and approximate methods for extracting functional connectivity
- 2009
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 79:5, s. 51915-
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Tidskriftsartikel (refereegranskat)abstract
- We study pairwise Ising models for describing the statistics of multineuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we extract the optimal couplings for subsets of size up to 200 neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with those found from Boltzmann learning. Two of these methods-inversion of the Thouless-Anderson-Palmer equations and an approximation proposed by Sessak and Monasson-are remarkably accurate. Using these approximations for larger subsets of neurons, we find that extracting couplings using data from a subset smaller than the full network tends systematically to overestimate their magnitude. This effect is described qualitatively by infinite-range spin-glass theory for the normal phase. We also show that a globally correlated input to the neurons in the network leads to a small increase in the average coupling. However, the pair-to-pair variation in the couplings is much larger than this and reflects intrinsic properties of the network. Finally, we study the quality of these models by comparing their entropies with that of the data. We find that they perform well for small subsets of the neurons in the network, but the fit quality starts to deteriorate as the subset size grows, signaling the need to include higher-order correlations to describe the statistics of large networks.
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- Roudi, Yasser, et al.
(författare)
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Statistical physics of pairwise probability models
- 2009
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Ingår i: Frontiers in Computational Neuroscience. - : Frontiers Media SA. - 1662-5188. ; 3, s. 22-
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Tidskriftsartikel (refereegranskat)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 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.
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