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.
Highlights
A Hidden Markov Model (HMM) is a stochastic model of the dynamic process of two related random processes that evolve over time
We propose a sensitivity analysis algorithm for HMMs using a simplified matrix formulation directly from the model representation based on a recently proposed technique called the Coefficient-Matrix-Fill procedure [26]
Sensitivity analysis in HMMs is explained based on the assumption of proportional co-variation, and a univariate polynomial sensitivity function whose coefficients the proposed algorithm computes is defined
Summary
A Hidden Markov Model (HMM) is a stochastic model of the dynamic process of two related random processes that evolve over time. It directly utilizes the recursive probability expressions in an HMM It improves the computational complexity of applying the existing approaches for sensitivity analysis in Bayesian networks to HMMs. In [27], imprecise HMMs are presented as a tool for performing sensitivity analysis of HMMs. In this paper, we propose a sensitivity analysis algorithm for HMMs using a simplified matrix formulation directly from the model representation based on a recently proposed technique called the Coefficient-Matrix-Fill procedure [26]. The matrices (Initial, Transition, and Observation) where the corresponding model parameter θ varies are decomposed into the parts independent of and dependent on θ for mathematical convenience This enables us to compute the coefficients of the sensitivity function at each iteration in the recursive probability expression and implement the algorithm in a computer program. The paper is concluded with a summary of the results achieved and recommendations for future research works
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