Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance
Information Theory
2015-06-11 v2 Machine Learning
math.IT
Probability
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.
Keywords
Cite
@article{arxiv.1210.2613,
title = {Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance},
author = {Vittorio Perduca and Gregory Nuel},
journal= {arXiv preprint arXiv:1210.2613},
year = {2015}
}