F. Wood and M.J. BlackDeptartment of Computer Science,

Brown Univ, Providence, RI, USA

Modeling the joint activity of large populations of neurons is hard because of the dimensionality of the data. In populations of more than a few neurons, fully parametric models either suffer from over-smoothness (multi-dimensional Gaussian) or cannot model correlations between cells (independent joint Poisson, etc.). We suggest an energy based model (a Gibbs distribution) for joint firing activity and demonstrate its efficacy in modeling the firing rates of a large population of cells.

We used contrastive divergence to train a Gibbs distribution on the firing rates of a large population of neurons. This distribution was constructed so that marginals over particular 1-D linear projections of the learned distribution match empirical histograms of the training data along the same projections. The number of projections was optimized empirically. We found that random projection directions (random marginals) were sufficient to model the distribution well.

Preliminary results from modeling the firing rates of 4-6 cells (where computing the partition function was tractable) showed that this model fit test data better than both a full covariance Gaussian and a fully independent joint Poisson. We show measures of an unnormalized model fit to a large population of cells (>40) that suggest our model outperforms the others.

This model extends straightforwardly to any high-dimensionality joint distribution. For instance this approach can be used to model the error residual in a linear generative model of firing rates (in contrast to the normality assumption made in Kalman filtering). Decoding results using this generalized likelihood will be shown.

This work was supported by NIH-NINDS R01 NS 50967-01 as part of the NSF/NIH Collaborative Research in Computational Neuroscience Program.

Citation:Energy Based Models of Motor Cortical Population ActivityWood, F.and Black, M.

to appearSociety for Neuroscience, 2005. Online.

## Related Publications

Modeling neural population spiking activity with Gibbs distributions.Wood, F., Roth, S., and Black, M. J.,

to appear:Advances in Neural Information Processing Systems, 2005.

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