Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance

TL;DR

This paper introduces a method to quantify the influence of individual observations on hidden states in HMMs using Kullback-Leibler distance, with an efficient algorithm for outlier detection.

Contribution

The paper presents a novel approach to measure observation influence in HMMs via KLD and provides a linear complexity algorithm for practical computation.

Findings

Effective outlier detection in HMM data series

Efficient algorithm with linear complexity

Quantitative influence measurement of observations

Abstract

We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting outliers in HMM data series.