Large and Small Deviations for Statistical Sequence Matching

TL;DR

This paper analyzes the statistical sequence matching problem, providing theoretical performance guarantees for the generalized likelihood ratio test (GLRT) and demonstrating its optimality in large and small deviations regimes, with extensions to unknown match counts.

Contribution

It offers a comprehensive theoretical analysis of GLRT for sequence matching, including optimality proofs and extensions to unknown match scenarios, improving upon prior results.

Findings

Explicit characterization of mismatch and false reject tradeoffs

Proof of GLRT optimality under Neyman-Pearson criterion

Strengthening of previous results for single-sequence databases

Abstract

We revisit the problem of statistical sequence matching between two databases of sequences initiated by Unnikrishnan (TIT 2015) and derive theoretical performance guarantees for the generalized likelihood ratio test (GLRT). We first consider the case where the number of matched pairs of sequences between the databases is known. In this case, the task is to accurately find the matched pairs of sequences among all possible matches between the sequences in the two databases. We analyze the performance of the GLRT by Unnikrishnan and explicitly characterize the tradeoff between the mismatch and false reject probabilities under each hypothesis in both large and small deviations regimes. Furthermore, we demonstrate the optimality of Unnikrishnan's GLRT test under the generalized Neyman-Person criterion for both regimes and illustrate our theoretical results via numerical examples. Subsequently, we generalize our achievability analyses to the case where the number of matched pairs is unknown, and an additional error probability needs to be considered. When one of the two databases contains a single sequence, the problem of statistical sequence matching specializes to the problem of multiple classification introduced by Gutman (TIT 1989). For this special case, our result for the small deviations regime strengthens previous result of Zhou, Tan and Motani (Information and Inference 2020) by removing unnecessary conditions on the generating distributions.