Stimulus-dependent maximum entropy models of neural population codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. To be able to infer a model for this distribution from large-scale neural recordings, we introduce a stimulus-dependent maximum entropy (SDME) model---a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. The model is able to capture the single-cell response properties as well as the correlations in neural spiking due to shared stimulus and due to effective neuron-to-neuron connections. Here we show that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. As a result, the SDME model gives a more accurate account of single cell responses and in particular outperforms uncoupled models in reproducing the distributions of codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like surprise and information transmission in a neural population.Comment: 11 pages, 7 figure

Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

We present a method to estimate Gibbs distributions with \textit{spatio-temporal} constraints on spike trains statistics. We apply this method to spike trains recorded from ganglion cells of the salamander retina, in response to natural movies. Our analysis, restricted to a few neurons, performs more accurately than pairwise synchronization models (Ising) or the 1-time step Markov models (\cite{marre-boustani-etal:09}) to describe the statistics of spatio-temporal spike patterns and emphasizes the role of higher order spatio-temporal interactions.Comment: To appear in J. Physiol. Pari