Neural dissimilarity indices that predict oddball detection in behaviour

Neuroscientists have recently shown that images that are difficult to find in visual search elicit similar patterns of firing across a population of recorded neurons. The $L^{1}$ distance between firing rate vectors associated with two images was strongly correlated with the inverse of decision time in behaviour. But why should decision times be correlated with $L^{1}$ distance? What is the decision-theoretic basis? In our decision theoretic formulation, we modeled visual search as an active sequential hypothesis testing problem with switching costs. Our analysis suggests an appropriate neuronal dissimilarity index which correlates equally strongly with the inverse of decision time as the $L^{1}$ distance. We also consider a number of other possibilities such as the relative entropy (Kullback-Leibler divergence) and the Chernoff entropy of the firing rate distributions. A more stringent test of equality of means, which would have provided a strong backing for our modeling fails for our proposed as well as the other already discussed dissimilarity indices. However, test statistics from the equality of means test, when used to rank the indices in terms of their ability to explain the observed results, places our proposed dissimilarity index at the top followed by relative entropy, Chernoff entropy and the $L^{1}$ indices. Computations of the different indices requires an estimate of the relative entropy between two Poisson point processes. An estimator is developed and is shown to have near unbiased performance for almost all operating regions.