A short introduction to observable operator models of discrete stochastic processes
نویسنده
چکیده
The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afford both mathematical simplicity and algorithmic efficiency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic representation of stationary, discrete stochastic processes. It is shown how any such process can be uniquely characterized by its abstract observable operators, yielding an abstract OOM of the process. All in all, observable operators open a lucid, general, and computationally extremely powerful avenue to discrete stochastic processes.
منابع مشابه
A short introduction to observable operator models of stochastic processes
The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afford both mathematical simplicity and algorithmic efficiency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic represent...
متن کاملDiscrete-time, discrete-valued observable operator models: a tutorial
This tutorial gives a basic yet rigorous introduction to observable operator models (OOMs). OOMs are a recently discovered class of models of stochastic processes. They are mathematically simple in that they require only concepts from elementary linear algebra. The linear algebra nature gives rise to an efficient, consistent, unbiased, constructive learning procedure for estimating models from ...
متن کاملObservable Operator Models for Discrete Stochastic Time Series
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 observab...
متن کاملNote on Negative Probabilities and Observable Processes
Amathematical framework for observable processes is introduced via the model of systems whose states may be time dependent and described by possibly ”negative probabilities”. The model generalizes and includes the linearly dependent models or observable operator models for classical discrete stochastic processes. Within this model a general convergence result for finite-dimensional processes, w...
متن کاملUsing a new modified harmony search algorithm to solve multi-objective reactive power dispatch in deterministic and stochastic models
The optimal reactive power dispatch (ORPD) is a very important problem aspect of power system planning and is a highly nonlinear, non-convex optimization problem because consist of both continuous and discrete control variables. Since the power system has inherent uncertainty, hereby, this paper presents both of the deterministic and stochastic models for ORPD problem in multi objective and sin...
متن کامل