Observable operator models for discrete stochastic time series.

H Jaeger

doi:10.1162/089976600300015411

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PubMed · 10935718

Observable operator models for discrete stochastic time series.

H Jaeger

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Abstract

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.

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Linear Models Markov Chains Neural Networks, Computer Stochastic Processes Time Journal Article Research Support, Non-U.S. Gov't

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BibTeX RIS

H Jaeger. 2000. Observable operator models for discrete stochastic time series.. https://doi.org/10.1162/089976600300015411

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