On the Sequential Probability Ratio Test in Hidden Markov Models

TL;DR

This paper analyzes the Sequential Probability Ratio Test in Hidden Markov Models, linking its execution time to Lyapunov exponents and providing complexity results for model identification tasks.

Contribution

It establishes theoretical relationships between test execution time and Lyapunov exponents, and offers complexity analysis for the Sequential Probability Ratio Test in HMMs.

Findings

Execution time relates to Lyapunov exponents of random matrix systems.

Provides complexity bounds for the Sequential Probability Ratio Test.

Links between model identification accuracy and system dynamics.

Abstract

We consider the Sequential Probability Ratio Test applied to Hidden Markov Models. Given two Hidden Markov Models and a sequence of observations generated by one of them, the Sequential Probability Ratio Test attempts to decide which model produced the sequence. We show relationships between the execution time of such an algorithm and Lyapunov exponents of random matrix systems. Further, we give complexity results about the execution time taken by the Sequential Probability Ratio Test.