Wald-Kernel: Learning to Aggregate Information for Sequential Inference

TL;DR

Wald-Kernel introduces a kernel-based method for learning sequential detectors from training data, enabling efficient and accurate binary hypothesis testing without known density functions, outperforming previous likelihood ratio estimation methods.

Contribution

The paper presents Wald-Kernel, a novel convex-optimization-based approach for learning sequential detectors directly from data, applicable when density functions are unknown.

Findings

Achieves lower average sampling cost than previous methods at the same error rate.

Effective on synthetic and real-world datasets.

Provides computationally efficient solutions for large-scale data.

Abstract

Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less samples in average. For a binary detection problem, it is well known that for known density functions accumulating the likelihood ratio statistics is time optimal under a fixed error rate constraint. This paper considers the problem of learning a binary sequential detector from training samples when density functions are unavailable. We formulate the problem as a constrained likelihood ratio estimation which can be solved efficiently through convex optimization by imposing Reproducing Kernel Hilbert Space (RKHS) structure on the log-likelihood ratio function. In addition, we provide a computationally efficient approximated solution for large scale data set. The proposed algorithm, namely Wald-Kernel, is tested on a synthetic data set and two real world data sets, together with previous approaches for likelihood ratio estimation. Our empirical results show that the classifier trained through the proposed technique achieves smaller average sampling cost than previous approaches proposed in the literature for the same error rate.