Learning to Aggregate Information for Sequential Inferences

We consider the problem of training a binary sequential classifier under an error rate constraint. It is well known that for known densities, accumulating the likelihood ratio statistics is time optimal under a fixed error rate constraint. For the case of unknown densities, we formulate the learning for sequential detection problem as a constrained density ratio estimation problem. Specifically, we show that the problem can be posed as a convex optimization problem using a Reproducing Kernel Hilbert Space representation for the log-density ratio function. The proposed binary sequential classifier is tested on synthetic data set and UC Irvine human activity recognition data set, together with previous approaches for density ratio estimation. Our empirical results show that the classifier trained through the proposed technique achieves smaller average sampling cost than previous classifiers proposed in the literature for the same error rate.