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Neurons within a population are strongly correlated, but how to simplycapture these correlations is still a matter of debate. Recent studies haveshown that the activity of each cell is influenced by the population rate,defined as the summed activity of all neurons in the population. However, anexplicit, tractable model for these interactions is still lacking. Here webuild a probabilistic model of population activity that reproduces the firingrate of each cell, the distribution of the population rate, and the linearcoupling between them. This model is tractable, meaning that its parameters canbe learned in a few seconds on a standard computer even for large populationrecordings. We inferred our model for a population of 160 neurons in thesalamander retina. In this population, single-cell firing rates depended inunexpected ways on the population rate. In particular, some cells had apreferred population rate at which they were most likely to fire. These complexdependencies could not be explained by a linear coupling between the cell andthe population rate. We designed a more general, still tractable model thatcould fully account for these non-linear dependencies. We thus provide a simpleand computationally tractable way to learn models that reproduce the dependenceof each neuron on the population rate.

A tractable method for describing complex couplings between neurons and population rate