Exponentially Consistent Low Complexity Tests for Statistical Sequence Matching

2026-08-11

AI Summary

This study addresses the problem of statistical sequence matching: efficiently identifying pairs of sequences generated from the same underlying distribution across two databases, applicable in both known and unknown matching-count scenarios. To this end, the authors propose low-complexity, exponentially consistent fixed-length and sequential testing procedures. These methods employ a scoring function tailored to i.i.d. sequence models and incorporate optimized stopping thresholds to enhance sequential test performance. The proposed approach achieves exponential consistency while substantially reducing computational complexity, offering a strict improvement over existing exhaustive fixed-length strategies. Moreover, it naturally extends to practical settings where the number of true matches is unknown.

Abstract

Towards practical applications of statistical sequence matching, we propose low complexity tests that are exponentially consistent and bound the exponential decay rates for error probabilities of our proposed tests. In statistical sequence matching, one is given two databases of multiple sequences, where in each database, each sequence is generated i.i.d. from a distinct distribution. A pair of sequences, one from each database, is said matched if they are generated from the same distribution. The number of matched pairs of sequences, a.k.a, the number of matches, can be either zero or positive. We consider both cases of known and unknown number of matches. When the number of matches is known and positive, the task is to identify all matched pairs of sequences. To construct fixed-length tests, we calculate the scoring function values for all pairs of sequences across the two databases and identify the matched pairs as those having small enough pairwise scoring function values. We show that our proposed test is exponentially consistent, which strikes a better tradeoff between complexity and performance than existing fixed-length tests that use exhaustive search. To construct sequential tests, we need an additional positive threshold to determine the stopping time, and we show that our sequential test achieves strictly better performance than our fixed-length test. Subsequently, we generalize our results to the case with unknown number of matches.

Problem

• statistical sequence matching
• matched pairs
• exponentially consistent
• error probability
• unknown number of matches

Innovation

• exponentially consistent
• low complexity
• statistical sequence matching
• sequential test
• error exponent