The Query/Hit Model for Sequential Hypothesis Testing

TL;DR

This paper introduces the Query/Hit learning model for sequential hypothesis testing, where two agents communicate via queries and responses to efficiently detect hypotheses under constraints, with theoretical analysis and empirical validation.

Contribution

It proposes the Q/H model, characterizes the error exponent, and introduces the DSSA querying strategy using neural mutual information estimation.

Findings

DSSA outperforms baselines in error probability and detection time.

The model effectively handles real-world datasets like mouse movements and user interactions.

Theoretical error exponent analysis guides efficient query selection.

Abstract

This work introduces the Query/Hit (Q/H) learning model. The setup consists of two agents. One agent, Alice, has access to a streaming source, while the other, Bob, does not have direct access to the source. Communication occurs through sequential Q/H pairs: Bob sends a sequence of source symbols (queries), and Alice responds with the waiting time until each query appears in the source stream (hits). This model is motivated by scenarios with communication, computation, and privacy constraints that limit real-time access to the source. The error exponent for sequential hypothesis testing under the Q/H model is characterized, and a querying strategy, the Dynamic Scout-Sentinel Algorithm (DSSA), is proposed. The strategy employs a mutual information neural estimator to compute the error exponent associated with each query and to select the query with the highest efficiency. Extensive empirical evaluations on both synthetic and real-world datasets -- including mouse movement trajectories, typesetting patterns, and touch-based user interactions -- are provided to evaluate the performance of the proposed strategy in comparison with baselines, in terms of probability of error, query choice, and time-to-detection.