Abstract

Event Abstract Back to Event A decoder-based spike train metric for analyzing the neural code in the retina Spike trains of retinal ganglion cells exhibit variability in response to repeated presentations of the same stimulus. Thus the exact timing and configuration of spikes is not enitrely relevant for visual signaling. Here, based on a Bayesian decoder, we devise a spike train metric [1] which measures the distinguishability of two given sets of spike trains, and allows for quantifying the importance of different spikes and spike patterns in encoding stimuli. The decoder is based on a generalized linear model (GLM) which accurately predicts how a group of neurons transform stimuli (spatiotemporal contrast fields) into spikes, and accounts for history dependencies and interactions between cells. The model has been fit to multi-electrode recordings from macaque retina [2]. Given the observed spike trains, the decoded stimulus may be obtained by maximizing the posterior probability arising from the GLM. We define the distance between two spike trains to be the metric distance between their associated decoded stimuli. This metric is entirely determined by the properties of the GLM, the stimulus ensemble, and the stimulus metric, and has no free parameters of its own. Direct calculation of this metric would seem to require computation time that scales quadratically with stimulus duration, rendering it essentially unusable. But by exploiting the likelihood concavity and temporal quasi-locality of the GLM, and properties of banded matrices, we have devised a novel method for finding the posterior maximum in a computational time that scales linearly with the stimulus duration. Because the Bayesian decoder is nonlinear, the stimulus information encoded by a spike is not fixed and depends on its context. We use our metric to define two types of costs associated with spike-train variability, in the spirit of [1]. For each spike, we define its addition/removal cost to be the distance between two spike trains differing only in the presence of that spike, and define its jitter sensitivity to be the distance accrued per unit time shift of that spike, in the limit of small shifts. We studied the statistics of these quantities and the factors influencing them (the local firing rate, synchrony with spikes in neighboring cells, etc.) in the recorded data. The decoder nonlinearity results in large variations in these quantities across spikes; by contrast, a linear decoder would yield constant values. Moreover, we found that the relative cost of spike shifts vs. removals and additions exhibits less variability; on average jittering a spike time by 10\pm2 ms was equivalent to removing it. Finally, we show that small lossy compressions of spike trains, which coarse grain the (collective or single spike) degrees of freedom optimally according to relevance, are dictated by the local limit of our metric. As an example, for nearly synchronous spikes in neighboring cells, the optimal compression retains the relative timing information with higher resolution than the average (absolute) timing. Interestingly, compression based on a linear decoder would coarse grain both degrees of freedom equally.

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