scholarly journals An Efficient Algorithm for Estimating State Sequences in Imprecise Hidden Markov Models

2014 ◽  
Vol 50 ◽  
pp. 189-233 ◽  
Author(s):  
J. De Bock ◽  
G. De Cooman
Keyword(s):  
Hidden Markov Models ◽  
Character Recognition ◽  
Optical Character Recognition ◽  
Markov Models ◽  
Hidden Markov ◽  
Exact Algorithm ◽  
Mass Function ◽  
The State ◽  
Model Parameters ◽  
State Sequence

We present an efficient exact algorithm for estimating state sequences from outputs or observations in imprecise hidden Markov models (iHMMs). The uncertainty linking one state to the next, and that linking a state to its output, is represented by a set of probability mass functions instead of a single such mass function. We consider as best estimates for state sequences the maximal sequences for the posterior joint state model conditioned on the observed output sequence, associated with a gain function that is the indicator of the state sequence. This corresponds to and generalises finding the state sequence with the highest posterior probability in (precise-probabilistic) HMMs, thereby making our algorithm a generalisation of the one by Viterbi. We argue that the computational complexity of our algorithm is at worst quadratic in the length of the iHMM, cubic in the number of states, and essentially linear in the number of maximal state sequences. An important feature of our imprecise approach is that there may be more than one maximal sequence, typically in those instances where its precise-probabilistic counterpart is sensitive to the choice of prior. For binary iHMMs, we investigate experimentally how the number of maximal state sequences depends on the model parameters. We also present an application in optical character recognition, demonstrating that our algorithm can be usefully applied to robustify the inferences made by its precise-probabilistic counterpart.

The State of the Art of Hidden Markov Models for Predictive Maintenance of Diesel Engines

2017 ◽  
Vol 33 (8) ◽  
pp. 2765-2779 ◽  
Author(s):  
António Simões ◽  
José Manuel Viegas ◽  
José Torres Farinha ◽  
Inácio Fonseca
Keyword(s):  
Hidden Markov Models ◽  
Diesel Engines ◽  
Markov Models ◽  
State Of The Art ◽  
Hidden Markov ◽  
The State ◽  
Predictive Maintenance

HIDDEN MARKOV MODELS IN TEXT RECOGNITION

1995 ◽  
Vol 09 (06) ◽  
pp. 925-958 ◽  
Author(s):  
J.C. ANIGBOGU ◽  
A. BELAÏD
Keyword(s):  
Hidden Markov Models ◽  
Character Recognition ◽  
Markov Models ◽  
Hidden Markov ◽  
Majority Vote ◽  
The Other ◽  
Distance Measures ◽  
Original Form ◽  
Verification Methods ◽  
Font Identification

A multi-level multifont character recognition is presented. The system proceeds by first delimiting the context of the characters. As a way of enhancing system performance, typographical information is extracted and used for font identification before actual character recognition is performed. This has the advantage of sure character identification as well as text reproduction in its original form. The font identification is based on decision trees where the characters are automatically arranged differently in confusion classes according to the physical characteristics of fonts. The character recognizers are built around the first and second order hidden Markov models (HMM) as well as Euclidean distance measures. The HMMs use the Viterbi and the Extended Viterbi algorithms to which enhancements were made. Also present is a majority-vote system that polls the other systems for “advice” before deciding on the identity of a character. Among other things, this last system is shown to give better results than each of the other systems applied individually. The system finally uses combinations of stochastic and dictionary verification methods for word recognition and error-correction.

scholarly journals Bayesian selection of Hidden Markov models for multi-dimensional ion channel data

2020 ◽  
Author(s):  
Jan Münch ◽  
Fabian Paul ◽  
Ralf Schmauder ◽  
Klaus Benndorf
Keyword(s):  
Hidden Markov Models ◽  
Cross Validation ◽  
Markov Models ◽  
Hidden Markov ◽  
Conformational Dynamics ◽  
Kinetic Scheme ◽  
Rate Equations ◽  
Model Parameters ◽  
Limited Information ◽  
Daunting Task

AbstractInferring the complex conformational dynamics of ion channels from ensemble currents is a daunting task due to limited information in the data leading to poorly determined model inference and selection. We address this problem with a parallelized Kalman filter for specifying Hidden Markov Models for current and fluorescence data. We demonstrate the flexibility of this Bayesian network by including different noises distributions. The accuracy of the parameter estimation is increased by tenfold compared to fitting Rate Equations. Furthermore, adding orthogonal fluorescence data increases the accuracy of the model parameters by up to two orders of magnitude. Additional prior information alleviates parameter unidenfiability for weakly informative data. We show that with Rate Equations a reliable detection of the true kinetic scheme requires cross validation. In contrast, our algorithm avoids overfitting by automatically switching of rates (continuous model expansion), by cross-validation, by applying the ‘widely applicable information criterion’ or variance-based model selection.

Exploring More Representative States of Hidden Markov Model in Optical Character Recognition: A Clustering-Based Model Pre-Training Approach

2015 ◽  
Vol 29 (03) ◽  
pp. 1550014 ◽  
Author(s):  
Zhiwei Jiang ◽  
Xiaoqing Ding ◽  
Liangrui Peng ◽  
Changsong Liu
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Character Recognition ◽  
Optical Character Recognition ◽  
Hidden Markov ◽  
Recognition Performance ◽  
Optimization Methods ◽  
Model Parameters ◽  
Model Structure ◽  
Training Approach

Hidden Markov Model (HMM) is an effective method to describe sequential signals in many applications. As to model estimation issue, common training algorithm only focuses on the optimization of model parameters. However, model structure influences system performance as well. Although some structure optimization methods are proposed, they are usually implemented as an independent module before parameter optimization. In this paper, the clustering feature of states in HMM is discussed through comparing the mechanism of Quadratic Discriminant Function (QDF) classifier and HMM. Then, through the clustering effect of Viterbi training and Baum–Welch training, a novel clustering-based model pre-training approach is proposed. It can optimize model parameters and model structure by turns, until the representative states of all models are explored. Finally, the proposed approach is evaluated on two typical OCR applications, printed and handwritten Arabic text line recognition. And it is compared with some other optimization methods. The improvement of character recognition performance proves the proposed approach can make more precise state allocation. And the representative states are benefit to HMM decoding.

scholarly journals Handling underlying discrete variables with bivariate mixed hidden Markov models in NONMEM

2019 ◽  
Vol 46 (6) ◽  
pp. 591-604 ◽  
Author(s):  
A. Brekkan ◽  
S. Jönsson ◽  
M. O. Karlsson ◽  
E. L. Plan
Keyword(s):  
Hidden Markov Models ◽  
Transition Rate ◽  
Markov Models ◽  
Drug Effect ◽  
Hidden Markov ◽  
Transition Probability ◽  
Hidden Variables ◽  
Model Parameters ◽  
Patient Reported ◽  
Parameter Precision

Abstract Non-linear mixed effects models typically deal with stochasticity in observed processes but models accounting for only observed processes may not be the most appropriate for all data. Hidden Markov models (HMMs) characterize the relationship between observed and hidden variables where the hidden variables can represent an underlying and unmeasurable disease status for example. Adding stochasticity to HMMs results in mixed HMMs (MHMMs) which potentially allow for the characterization of variability in unobservable processes. Further, HMMs can be extended to include more than one observation source and are then multivariate HMMs. In this work MHMMs were developed and applied in a chronic obstructive pulmonary disease example. The two hidden states included in the model were remission and exacerbation and two observation sources were considered, patient reported outcomes (PROs) and forced expiratory volume (FEV1). Estimation properties in the software NONMEM of model parameters were investigated with and without random and covariate effect parameters. The influence of including random and covariate effects of varying magnitudes on the parameters in the model was quantified and a power analysis was performed to compare the power of a single bivariate MHMM with two separate univariate MHMMs. A bivariate MHMM was developed for simulating and analysing hypothetical COPD data consisting of PRO and FEV1 measurements collected every week for 60 weeks. Parameter precision was high for all parameters with the exception of the variance of the transition rate dictating the transition from remission to exacerbation (relative root mean squared error [RRMSE] > 150%). Parameter precision was better with higher magnitudes of the transition probability parameters. A drug effect was included on the transition rate probability and the precision of the drug effect parameter improved with increasing magnitude of the parameter. The power to detect the drug effect was improved by utilizing a bivariate MHMM model over the univariate MHMM models where the number of subject required for 80% power was 25 with the bivariate MHMM model versus 63 in the univariate MHMM FEV1 model and > 100 in the univariate MHMM PRO model. The results advocates for the use of bivariate MHMM models when implementation is possible.

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