scholarly journals A recursive learning algorithm for model reduction of Hidden Markov Models

2011 ◽  
Author(s):  
Kun Deng ◽  
Prashant G. Mehta ◽  
Sean P. Meyn ◽  
Mathukumalli Vidyasagar
Keyword(s):  
Model Reduction ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Learning Algorithm ◽  
Hidden Markov ◽  
Recursive Learning

scholarly journals Smooth On-Line Learning Algorithms for Hidden Markov Models

1994 ◽  
Vol 6 (2) ◽  
pp. 307-318 ◽  
Author(s):  
Pierre Baldi ◽  
Yves Chauvin
Keyword(s):  
Hidden Markov Models ◽  
Expectation Maximization ◽  
Markov Models ◽  
Learning Algorithm ◽  
Hidden Markov ◽  
Batch Mode ◽  
On Line ◽  
Maximization Algorithms ◽  
On Line Learning ◽  
Entropy Functions

A simple learning algorithm for Hidden Markov Models (HMMs) is presented together with a number of variations. Unlike other classical algorithms such as the Baum-Welch algorithm, the algorithms described are smooth and can be used on-line (after each example presentation) or in batch mode, with or without the usual Viterbi most likely path approximation. The algorithms have simple expressions that result from using a normalized-exponential representation for the HMM parameters. All the algorithms presented are proved to be exact or approximate gradient optimization algorithms with respect to likelihood, log-likelihood, or cross-entropy functions, and as such are usually convergent. These algorithms can also be casted in the more general EM (Expectation-Maximization) framework where they can be viewed as exact or approximate GEM (Generalized Expectation-Maximization) algorithms. The mathematical properties of the algorithms are derived in the appendix.

Observable Operator Models for Discrete Stochastic Time Series

2000 ◽  
Vol 12 (6) ◽  
pp. 1371-1398 ◽  
Author(s):  
Herbert Jaeger
Keyword(s):  
Hidden Markov Models ◽  
Stochastic Systems ◽  
Markov Models ◽  
Learning Algorithm ◽  
Hidden Markov ◽  
Training Data ◽  
Constructive Learning ◽  
Proper Subclass ◽  
Stochastic Time Series ◽  
Dependent Processes

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.

scholarly journals Observable Operator Models

2016 ◽  
Vol 36 (1) ◽  
Author(s):  
Ilona Spanczér
Keyword(s):  
Stochastic Processes ◽  
Hidden Markov Models ◽  
Linear Algebra ◽  
Markov Models ◽  
Learning Algorithm ◽  
Hidden Markov ◽  
New Approach ◽  
Efficient Learning ◽  
Better Than

This paper describes a new approach to model discrete stochastic processes, called observable operator models (OOMs). The OOMs were introduced by Jaeger as a generalization of hidden Markov models (HMMs). The theory of OOMs makes use of both probabilistic and linear algebraic tools, which has an important advantage: using the tools of linear algebra a very simple and efficient learning algorithm can be developed for OOMs. This seems to be better than the known algorithms for HMMs. This learningalgorithm is presented in detail in the second part of the article.

scholarly journals An IOHMM-Based Framework to Investigate Drift in Effectiveness of IoT-Based Systems

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 527
Author(s):  
Gérald Rocher ◽  
Stéphane Lavirotte ◽  
Jean-Yves Tigli ◽  
Guillaume Cotte ◽  
Franck Dechavanne
Keyword(s):  
Hidden Markov Models ◽  
Real World ◽  
Physical Environment ◽  
Smart Home ◽  
Markov Models ◽  
Learning Algorithm ◽  
Hidden Markov ◽  
Input Output ◽  
Design Time ◽  
Verification Techniques

IoT-based systems, when interacting with the physical environment through actuators, are complex systems difficult to model. Formal verification techniques carried out at design-time being often ineffective in this context, these systems have to be quantitatively evaluated for effectiveness at run-time, i.e., for the extent to which they behave as expected. This evaluation is achieved by confronting a model of the effects they should legitimately produce in different contexts to those observed in the field. However, this quantitative evaluation is not informative on the drifts in effectiveness, it does not help designers investigate their possible causes, increasing the time needed to resolve them. To address this problem, and assuming that models of legitimate behavior can be described by means of Input-Output Hidden Markov Models (IOHMMs), a novel generic unsupervised clustering-based IOHMM structure and parameters learning algorithm is developed. This algorithm is first used to learn a model of legitimate behavior. Then, a model of the observed behavior is learned from observations gathered in the field. A second algorithm builds a dissimilarity graph that makes clear structural and parametric differences between both models, thus providing guidance to designers to help them investigate possible causes of drift in effectiveness. The approach is validated on a real world dataset collected in a smart home.

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