Using a doubly-stochastic model to analyze neuronal activity in the visual cortex
Goris, Robbe L T, Simoncelli, Eero P and Movshon, J Anthony.
Published in Cosyne Abstracts, 2012.
Sensory neurons encode information probabilistically: repeated stimulus presentations elicit variable firing. This variability is often described using a cascade model, in which spikes arise from a Poisson process whose rate is a deterministic function of the stimulus. However, it has recently been shown that time-dependent rate variability is a wide-spread phenomenon in cortex (Churchland et al 2010, 2011). Consequently, the Poisson noise model commonly underestimates the variability of visual cortical recordings, which can lead to systematic errors in inferring neuronal characteristics. We measured responses to a variety of stimuli in visual cortex in anesthetized and alert monkeys. The fluctuations in neural responsiveness that typically occur over the timescale of these experiments are significantly greater than predicted by a Poisson model - estimated Fano factors as high as 10 occur in the acute preparation. We propose a doubly stochastic model, in which the stimulus-driven firing rate is modulated according to a stimulus-independent gamma-distributed random variable. This fluctuating rate generates spikes according to a Poisson process. Fitting the resulting mixture of Poisson processes to neural data reveals that the model is statistically superior for all neurons, and therefore provides an improved framework for analyzing neuronal tuning. The framework offers two further advantages over existing methods. First, it provides a natural means of estimating and tracking fluctuations in responsiveness (state changes) that occur during the course of an experiment. Second, it offers an efficient and accurate estimate of the upper bound on discrimination performance that can be supported by each neuron. Application of this new method can substantially improve the analysis of neuronal data, both in fitting explicit models and in assessing the limits of neuronal performance. Analysis of the contrast response function of a V1 cell (acute preparation). Stimuli were presented for one second, (40 repetitions). a, Mean firing rate as a function of stimulus contrast. Error bars indicate the 95% C.I.. The dotted line illustrates baseline activity; colored lines the best fitting (and indistinguishable) NakaRushton functions under the assumption of Poisson noise (green) and a doubly-stochastic process (red). b, Estimated Fano factor as a function of mean firing rate (black circles) compared with predicted values of the two models. c, Negative log likelihood of the entire data set and its expected distribution under the Poisson noise model. The negative log likelihood of the data is far outside the expected range, indicating a poor fit. d, Same as c for the doubly-stochastic model, which describes the data much better. e, One potential cause of state changes is rapid response-driven adaptation. Such mechanism would evoke a negative relation between firing rate and the Z-score of the subsequent spike count. We see no such effect for this neuron. f, An estimate of the comparatively slow fluctuations in responsiveness. g, This cell's neurometric function in a 2-AFC contrast discrimination experiment estimated from the raw data (white circles), the Poisson noise model (green line) and the doubly-stochastic model (red line).