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Computer Science > Machine Learning

arXiv:2205.13871 (cs)
[Submitted on 27 May 2022]

Title:Probabilistic Systems with Hidden State and Unobservable Transitions

Authors:Rebecca Bernemann, Barbara König, Matthias Schaffeld, Torben Weis
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Abstract:We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable {\epsilon}-transitions (also called null transitions), allowing state changes of which the observer is unaware. Due to the presence of {\epsilon}-loops this additional feature complicates the theory and requires to carefully set up the corresponding probability space and random variables. In particular we present an algorithm for determining the most probable explanation given an observation (a generalization of the Viterbi algorithm for HMMs) and a method for parameter learning that adapts the probabilities of a given model based on an observation (a generalization of the Baum-Welch algorithm). The latter algorithm guarantees that the given observation has a higher (or equal) probability after adjustment of the parameters and its correctness can be derived directly from the so-called EM algorithm.
Subjects: Machine Learning (cs.LG); Distributed, Parallel, and Cluster Computing (cs.DC); Logic in Computer Science (cs.LO)
ACM classes: G.3
Cite as: arXiv:2205.13871 [cs.LG]
  (or arXiv:2205.13871v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2205.13871

Submission history

From: Barbara König [view email]
[v1] Fri, 27 May 2022 10:06:04 UTC (32 KB)
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