288 pp. per issue
6 x 9, illustrated
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Neural Computation

June 1, 2000, Vol. 12, No. 6, Pages 1371-1398
(doi: 10.1162/089976600300015411)
© 2000 Massachusetts Institute of Technology
Observable Operator Models for Discrete Stochastic Time Series
Article PDF (330.32 KB)

A widely used class of models for stochastic systems is hidden Markov models. Systems that can be modeled by hidden Markov models are a proper subclass of linearly dependent processes, a class of stochastic systems known from mathematical investigations carried out over the past four decades. This article provides a novel, simple characterization of linearly dependent processes, called observable operator models. The mathematical properties of observable operator models lead to a constructive learning algorithm for the identification of linearly dependent processes. The core of the algorithm has a time complexity of O (N + nm3), where N is the size of training data, n is the number of distinguishable outcomes of observations, and m is model state-space dimension.