Learning to detect an oddball target

TL;DR

This paper introduces an asymptotically optimal sequential detection policy for identifying an odd Poisson process among similar ones, with applications to visual search experiments and neuronal dissimilarity indices.

Contribution

It proposes a generalized likelihood ratio based sequential policy that satisfies false detection constraints and is asymptotically optimal, with applications to neuroscience data.

Findings

The policy is asymptotically optimal as false detection probability approaches zero.

The neuronal dissimilarity index correlates strongly with behavioral data.

The new index performs worse than some existing indices under certain conditions.

Abstract

We consider the problem of detecting an odd process among a group of Poisson point processes, all having the same rate except the odd process. The actual rates of the odd and non-odd processes are unknown to the decision maker. We consider a time-slotted sequential detection scenario where, at the beginning of each slot, the decision maker can choose which process to observe during that time slot. We are interested in policies that satisfy a given constraint on the probability of false detection. We propose a generalised likelihood ratio based sequential policy which, via suitable thresholding, can be made to satisfy the given constraint on the probability of false detection. Further, we show that the proposed policy is asymptotically optimal in terms of the conditional expected stopping time among all policies that satisfy the constraint on the probability of false detection. The asymptotic is as the probability of false detection is driven to zero. We apply our results to a particular visual search experiment studied recently by neuroscientists. Our model suggests a neuronal dissimilarity index for the visual search task. The neuronal dissimilarity index, when applied to visual search data from the particular experiment, correlates strongly with the behavioural data. However, the new dissimilarity index performs worse than some previously proposed neuronal dissimilarity indices. We explain why this may be attributed to the experiment conditons.