A filter based encoding model for mouse retinal ganglion cells

We adopt a system theoretic approach and explore the model of retinal ganglion cells as linear filters followed by a maximum-likelihood Bayesian predictor. We evaluate the model by using cross-validation, i.e., first the model parameters are estimated using a training set, and then the prediction error is computed (by comparing the stochastic rate predicted by the model with the rate code of the response) for a test set. As in system identification theory, we present spatially uniform stimuli to the retina, whose temporal intensity is drawn independently from a Gaussian distribution, and we simultaneously record the spike trains from multiple neurons. The optimal linear filter for each cell is obtained by maximizing the mutual information between the filtered stimulus values and the output of the cell (as measured in terms of a stochastic rate code). Our results show that the model presented in this paper performs well on the test set, and it outperforms the identity Bayesian model and the traditional linear model. Moreover, in order to reduce the number of optimal filters needed for prediction, we cluster the cells based on the filters' shapes, and use the cluster consensus filters to predict the firing rates of all neurons in the same class. We obtain almost the same performance with these cluster filters. These results provide hope that filter-based retinal prosthetics might be an effective and feasible idea.