Probabilistic Systems with Hidden State and Unobservable Transitions
This work addresses a theoretical extension for probabilistic systems with hidden state, which is incremental as it builds directly on existing HMM methods.
The paper tackles the problem of extending Hidden Markov Models (HMMs) to include unobservable transitions, which complicates probability calculations due to ε-loops. It presents algorithms for determining the most probable explanation and parameter learning, generalizing the Viterbi and Baum-Welch algorithms.
We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable ε-transitions (also called null transitions), allowing state changes of which the observer is unaware. Due to the presence of ε-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.