The Forward Procedure for HSMMs based on Expected Duration

• Published in: IEEE signal processing letters 2016-08, Vol.23 (8), p.1116-1120
• Main Authors: Lemeire, Jan, Cartella, Francesco
• Format: Article
• Language: English
• Subjects: Approximation; Approximation error; Dynamic models; Error analysis; Forward procedure; Hidden Markov models; hidden semi Markov models (HSMMs); Indexes; Informatics; Mathematical analysis; Mathematical model; Mathematical models; Permissible error; semimarkov models; Signal processing; Tracking; Uncertainty
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2016.2583483

For dynamic models, the forward procedure is used to calculate the probability of an observation sequence for a given model. For hidden semiMarkov models (HSMMs), the calculation can be approximated by keeping a track of the expected state duration instead of the distribution. The update equation for the expected duration proposed by Azimi et al.[1] is, however, wrong. The experiments presented by Azimi et al.[1] did not reveal the error, since for the presented cases, the state duration does not play a role in the probabilities. We propose a better equation for updating the expected duration. It nevertheless remains an approximation for calculating the probability of observation sequences. We analyze the assumptions to show under which conditions the approximation errors become important. Experiments show that the approximation is only reasonable for left-to-right HSMMs. As we focus on a specific sub class of HSMMs, we derive specialized equations from the general form for the exact calculation of the forward variable.