A simplified matrix formulation for sensitivity analysis of hidden Markov models

Abstract

In this paper, a new algorithm for sensitivity analysis of discrete hidden Markov models (HMMs) is proposed. Sensitivity analysis is a general technique for investigating the robustness of the output of a system model. Sensitivity analysis of probabilistic networks has recently been studied extensively. This has resulted in the development of mathematical relations between a parameter and an output probability of interest and also methods for establishing the effects of parameter variations on decisions. Sensitivity analysis in HMMs has usually been performed by taking small perturbations in parameter values and re-computing the output probability of interest. As recent studies show, the sensitivity analysis of an HMM can be performed using a functional relationship that describes how an output probability varies as the network's parameters of interest change. To derive this sensitivity function, existing Bayesian network algorithms have been employed for HMMs. These algorithms are computationally inefficient as the length of the observation sequence and the number of parameters increases. In this study, a simplified efficient matrix-based algorithm for computing the coefficients of the sensitivity function for all hidden states and all time steps is proposed and an example is presented.