Using response models to study coding strategies in monkey visual cortex

Decoding spike trains instant by instant using order statistics and the mixture-of-Poissons model

In the brain, spike trains are generated in time and presumably also interpreted as they unfold in time. Recent work (Oram et al., 1999; Baker and Lemon, 2000) suggests that in several areas of the monkey brain, individual spike times carry information because they reflect an underlying rate variation. Constructing a model based on this stochastic structure allows us to apply order statistics to decode spike trains instant by instant as spikes arrive or do not. Order statistics are time-consuming to compute in the general case. We demonstrate that data from neurons in primary visual cortex are well fit by a mixture of Poisson processes; in this special case, our computations are substantially faster. In these data, spike timing contributed information beyond that available from the spike count throughout the trial. At the end of the trial, a decoder based on the mixture-of-Poissons model correctly decoded about three times as many trials as expected by chance, compared with approximately twice as many as expected by chance using the spike count only. If our model perfectly described the spike trains, and enough data were available to estimate model parameters, then our Bayesian decoder would be optimal. For four-fifths of the sets of stimulus-elicited responses, the observed spike trains were consistent with the mixture-of-Poissons model. Most of the error in estimating stimulus probabilities is attributable to not having enough data to specify the parameters of the model rather than to misspecification of the model itself.

Assessing the encoding of stimulus attributes with rapid sequences of stimulus events

In a preceding paper (M. Eger and R. Eckhorn, J. Comput. Neurosci., 2002) we have published a three step method for the quantification of transinformation in multi-input and -output neuronal systems. Here we present an extension that applies to rapid series of transient stimuli and thus, fills the gap between the discrete and continuous stimulation paradigm. While the three step method potentially captures all stimulus aspects, the present approach quantifies the discriminability of selected attributes of discrete stimuli and thus, assesses their encoding. Based on simulated and recorded data we investigate the performance of the implemented algorithm. Our approach is illustrated by analyses of neuronal population activity from the visual cortex of the cat, evoked by electrical stimuli of the retina.

Consistency of encoding in monkey visual cortex

Are different kinds of stimuli (for example, different classes of geometric images or naturalistic images) encoded differently by visual cortex, or are the principles of encoding the same for all stimuli? We examine two response properties: (1) the range of spike counts that can be elicited from a neuron in epochs representative of short periods of fixation (up to 400 msec), and (2) the relation between mean and variance of spike counts elicited by different stimuli, that together characterize the information processing capabilities of a neuron using the spike count code. In monkey primary visual cortex (V1) complex cells, we examine responses elicited by static stimuli of four kinds (photographic images, bars, gratings, and Walsh patterns); in area TE of inferior temporal cortex, we examine responses elicited by static stimuli in the sample, nonmatch, and match phases of a delayed match-to-sample task. In each area, the ranges of mean spike counts and the relation between mean and variance of spike counts elicited are sufficiently similar across experimental conditions that information transmission is unaffected by the differences across stimulus set or behavioral conditions [although in 10 of 27 (37%) of the V1 neurons there are statistically significant but small differences, the median difference in transmitted information for these neurons was 0.9%]. Encoding therefore appears to be consistent across experimental conditions for neurons in both V1 and TE, and downstream neurons could decode all incoming signals using a single set of rules.

Using response models to estimate channel capacity for neuronal classification of stationary visual stimuli using temporal coding

Both spike count and temporal modulation are known to carry information about which of a set of stimuli elicited a response; but how much information temporal modulation adds remains a subject of debate. This question usually is addressed by examining the results of a particular experiment that depend on the specific stimuli used. Developing a response model allows us to ask how much more information is carried by the best use of response strength and temporal modulation together (that is, the channel capacity using a code incorporating both) than by the best use of spike count alone (the channel capacity using the spike count code). This replaces dependence on a particular data set with dependence on the accuracy of the model. The model is constructed by finding statistical rules obeyed by all the observed responses and assuming that responses to stimuli not presented in our experiments obey the same rules. We assume that all responses within the observed dynamic range, even if not elicited by a stimulus in our experiment, could be elicited by some stimulus. The model used here is based on principal component analysis and includes both response strength and a coarse (+/-10 ms) representation of temporal modulation. Temporal modulation at finer time scales carries little information about the identity of stationary visual stimuli (although it may carry information about stimulus motion or change), and we present evidence that, given its variability, it should not be expected to do so. The model makes use of a linear relation between the logarithms of mean and variance of responses, similar to the widely seen relation between mean and variance of spike count. Responses are modeled using truncated Gaussian distributions. The amount of stimulus-related information carried by spike count in our data are 0.35 and 0.31 bits in primary visual and inferior temporal cortices, respectively, rising to 0.52 and 0.37 bits for the two-principal-component code. The response model estimates that the channel capacity is 1.1 and 1.4 bits, respectively, using the spike count only, rising to 2.0 and 2.2 bits using two principal components. Thus using this representation of temporal modulation is nearly equivalent to adding a second independent cell using the spike count code. This is much more than estimated using transmitted information but far less than would be expected if all degrees of freedom provided by the individual spike times carried independent information.