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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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| 3. |
- 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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| 4. |
- Tyrcha, Joanna, et al.
(författare)
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Spike pattern distributions in model cortical networks
- 2008
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Ingår i: COSYNE-Computational and Systems Neuroscience 2008, Salt Lake City.
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Konferensbidrag (populärvet., debatt m.m.)abstract
- We can learn something about coding in large populations of neurons from models of the spike pattern distributions constructed from data. In our work, we do this for data generated from computational models of local cortical networks. This permits us to explore how features of the neuronal and synaptic properties of the network are related to those of the spike pattern distribution model. We employ the approach of Schneidman et al [1] and model this distribution by a Sherrington-Kirkpatrick (SK) model: P[S] = Z-1exp(½ΣijJijSiSj+ΣihiSi). In the work reported here, we analyze spike records from a simple model of a cortical column in a high-conductance state for two different cases: one with stationary tonic firing and the other with a rapidly time-varying input that produces rapid variations in firing rates. The average cross-correlation coefficient in the former is an order of magnitude smaller than that in the latter.To estimate the parameters Jij and hi we use a technique [2] based on inversion of the Thouless-Anderson-Palmer equations from spin glass theory. We have performed these fits for groups of neurons of sizes from 12 to 200 for tonic firing and from 6 to 800 for the case of the rapidly time-varying “stimulus”. The first two figures show that the distributions of Jij’s in the two cases are quite similar, both growing slightly narrower with increasing N. They are also qualitatively similar to those found by Schneidman et al and by Tkačik et al [3] for data from retinal networks. As in their work, it does not appear to be necessary to include higher order couplings. The means, which are much smaller than the standard deviations, also decrease with N, and the one for tonic firing is less than half that for the stimulus-driven network.However, the models obtained never appear to be in a spin glass phase for any of the sizes studied, in contrast to the finding of Tkačik et al, who reported spin glass behaviour at N=120. This is shown in the third figure panel. The x axis is 1/J, where J = N1/2std(Jij) and the y axis is H/J, where H is the total “field” N-1Σi(hi+ΣjJij‹Sj›). The green curve marks the Almeida-Thouless line separating the normal and spin glass phases in this parameter plane. All our data, for N ≤800 (the number of excitatory neurons in the originally-simulated network), lie in the normal region, and extrapolation from our results predicts spin glass behaviour only for N>5000.[1] E. Schneidman et al., Nature 440 1007-1012 (2006)[2] T. Tanaka, Phys Rev E 58 2302-2310 (1998); H. J. Kappen and F. B Rodriguez, Neural Comp 10 1137-1156 (1998)[3] G. Tkačik et al., arXiv:q-bio.NC/0611072 v1 (2006)
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| 5. |
- Tyrcha, Joanna, et al.
(författare)
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Testing Algorithms for Extracting Functional Connectivity from Spike Data
- 2008
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Ingår i: 1st INCF Congress of Neuroinformatics: Databasing and Modeling the Brain.
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Konferensbidrag (populärvet., debatt m.m.)abstract
- We can learn something about how large neuronal networks function from models of their spike pattern distributions constructed from data. We do this using the approach introduced by Schneidman et al [1], modeling this distribution by an Ising model: P[S] = Z-1exp(ΣJijSiSj + ΣihiSi). In the work reported here, we explore the accuracy of two algorithms for extracting the model parameters Jij and hi by testing them on data generated by networks in which these parameters are known.Both algorithms use, as input, the firing rates and mutual correlations of the neurons in the network. The first algorithm is straightforward Boltzmann learning. It will yield the parameters correctly if the input statistics are known exactly,but it may be very slow to converge. The second, very fast, algorithm [2] is based on inversion of the Thouless-Anderson-Palmer equations from spin glass theory. It is derived from a small-Jij expansion, but it is in principle correct for all Jij when the network is infinitely large and densely connected.In practice, however, the rates and correlations used as inputs to the algorithms are estimates based on a finite number of measurements. Therefore, there will be errors in the extracted model parameters. Errors will also occur if the data are incomplete, i.e., if the rates and correlations are not measured for all neurons or all pairs. This case is highly relevant to the experimental situation, since in practice it is only possible to record from a small fraction of the neurons in a network.Two particular kinds of error statistics are of special interest: variances of the differences between true and extracted parameters, and variances of the differences between parameters extracted for two independent sets of training data. We study the relation between the two, since the first is what we are interested in but only the second can be computed in the realistic situation, where we do not know the parameters a priori. We also examine the variance of the difference between the true and extracted correlations.Finally, we apply the algorithms to the data of Schneidman et al from salamander retinal ganglion neurons.References--------------------------------------------------------------------------------1. E Schneidman et al, Nature 440 1007-1012 (2006); G Tkacik et al, arXiv:q-bio.NC/0611072 (2006)2. T Tanaka, Phys Rev E 58 2302-2310 (1998); H J Kappen and F B Rodriguez, Neural Comp 10 1137-1156 (1998)
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