Event:

Maximum-entropy models have been successfully applied to neuronal data, from areas as diverse as the retina, the hippocampus or the cortex. The activity of a neuron is hereby abstracted to be binary, either "on" or "off", depending on whether the neuron has spiked at least once in a given time bin or not. This representation is, despite the success of the approach, a major drawback. It does not only limit the statistics that can be matched, but also prevents capturing the neurons’ behavior when the firing rate is high, that is when the amount of transmitted information is large.

The family of spike-count models we are suggesting provides a solution to both of these caveats. We allow the single-neuron variable to be a natural number, not limited to 0 and 1 . In addition, we model the interaction between neurons by Ising-like couplings, which allows capturing the pairwise covariances of the data, like in a maximum-entropy approach (with given correlations). Inserting a concrete form for the single-neuron model, we infer the model parameters using Monte-Carlo and mean-field methods.

This allows to faithfully parameterize the measured probability distribution of neuronal activities, which we use to estimate the corresponding entropy and eventually the mutual information between the neural activity and the stimulus. This is a well-established approach when using the binary representation of neural activity - which comes with the limits highlighted before. Our approach, however, allows to flexibly choose the time-bin size in dependence of the data without losing information by clipping spike counts. Furthermore, using the diagrammatic framework recently developed in Kühn & van Wijland 2023 allows us to directly obtain the mutual information from measured quantities, avoiding biases due to the fitting of a specific model.