Active Inference for Binary Symmetric Hidden Markov Models

TL;DR

This paper develops an analytical method for active MAP inference in binary symmetric Hidden Markov Models, optimizing label selection to improve state estimation accuracy based on model parameters.

Contribution

It introduces a closed-form solution for active inference in binary symmetric HMMs, linking expected error reduction to model parameters and optimal label selection strategies.

Findings

Derived a closed-form solution for active inference in binary symmetric HMMs

Identified optimal label selection schemes for error reduction

Connected active inference strategies to uncertainty reduction principles

Abstract

We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for the case of binary symmetric HMMs, and obtain a closed form solution that relates the expected error reduction to model parameters under the specified active inference scheme. We then use this solution to determine most optimal active inference scheme in terms of error reduction, and examine the relation of those schemes to heuristic principles of uncertainty reduction and solution unicity.