EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies

2018 ◽  
Vol 35 (1-2) ◽  
pp. 51-72 ◽  
Author(s):  
Camilla Damian ◽  
Zehra Eksi ◽  
Rüdiger Frey
Keyword(s):  
Markov Model ◽  
Em Algorithm ◽  
Credit Risk ◽  
Hidden Markov Model ◽  
Point Process ◽  
Gaussian Noise ◽  
Goodness Of Fit ◽  
Markov Models ◽  
Hidden Markov ◽  
Process Observation

AbstractIn this paper we study parameter estimation via the Expectation Maximization (EM) algorithm for a continuous-time hidden Markov model with diffusion and point process observation. Inference problems of this type arise for instance in credit risk modelling. A key step in the application of the EM algorithm is the derivation of finite-dimensional filters for the quantities that are needed in the E-Step of the algorithm. In this context we obtain exact, unnormalized and robust filters, and we discuss their numerical implementation. Moreover, we propose several goodness-of-fit tests for hidden Markov models with Gaussian noise and point process observation. We run an extensive simulation study to test speed and accuracy of our methodology. The paper closes with an application to credit risk: we estimate the parameters of a hidden Markov model for credit quality where the observations consist of rating transitions and credit spreads for US corporations.

scholarly journals The Application of Baum-Welch Algorithm in Multistep Attack

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yanxue Zhang ◽  
Dongmei Zhao ◽  
Jinxing Liu
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov Models ◽  
Viterbi Algorithm ◽  
Markov Models ◽  
Hidden Markov ◽  
Simulation Experiments ◽  
Forward Algorithm ◽  
Better Than

The biggest difficulty of hidden Markov model applied to multistep attack is the determination of observations. Now the research of the determination of observations is still lacking, and it shows a certain degree of subjectivity. In this regard, we integrate the attack intentions and hidden Markov model (HMM) and support a method to forecasting multistep attack based on hidden Markov model. Firstly, we train the existing hidden Markov model(s) by the Baum-Welch algorithm of HMM. Then we recognize the alert belonging to attack scenarios with the Forward algorithm of HMM. Finally, we forecast the next possible attack sequence with the Viterbi algorithm of HMM. The results of simulation experiments show that the hidden Markov models which have been trained are better than the untrained in recognition and prediction.

scholarly journals Confidence Intervals for the Mixture Transition Distribution (MTD) Model and Other Markovian Models

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 351
Author(s):  
André Berchtold
Keyword(s):  
Markov Chains ◽  
Markov Model ◽  
Em Algorithm ◽  
Hidden Markov Model ◽  
Confidence Intervals ◽  
Hidden Markov ◽  
Simple Calculation ◽  
Standard Methods ◽  
Transition Distribution ◽  
Simulation Results

The Mixture Transition Distribution (MTD) model used for the approximation of high-order Markov chains does not allow a simple calculation of confidence intervals, and computationnally intensive methods based on bootstrap are generally used. We show here how standard methods can be extended to the MTD model as well as other models such as the Hidden Markov Model. Starting from existing methods used for multinomial distributions, we describe how the quantities required for their application can be obtained directly from the data or from one run of the E-step of an EM algorithm. Simulation results indicate that when the MTD model is estimated reliably, the resulting confidence intervals are comparable to those obtained from more demanding methods.

Remaining Useful Life Estimation Based on a Segmental Hidden Markov Model With Continuous Observations

2017 ◽  
Author(s):  
Zhen Chen ◽  
Tangbin Xia ◽  
Ershun Pan
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Goodness Of Fit ◽  
Hidden Markov ◽  
Remaining Useful Life ◽  
Likelihood Method ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Useful Life ◽  
Hidden States

In this paper, a segmental hidden Markov model (SHMM) with continuous observations, is developed to tackle the problem of remaining useful life (RUL) estimation. The proposed approach has the advantage of predicting the RUL and detecting the degradation states simultaneously. As the observation space is discretized into N segments corresponding to N hidden states, the explicit relationship between actual degradation paths and the hidden states can be depicted. The continuous observations are fitted by Gaussian, Gamma and Lognormal distribution, respectively. To select a more suitable distribution, model validation metrics are employed for evaluating the goodness-of-fit of the available models to the observed data. The unknown parameters of the SHMM can be estimated by the maximum likelihood method with the complete data. Then a recursive method is used for RUL estimation. Finally, an illustrate case is analyzed to demonstrate the accuracy and efficiency of the proposed method. The result also suggests that SHMM with observation probability distribution which is closer to the real data behavior may be more suitable for the prediction of RUL.

scholarly journals Utilizing Gaze Behavior for Inferring Task Transitions Using Abstract Hidden Markov Models

2016 ◽  
Vol 19 (58) ◽  
pp. 1
Author(s):  
Daniel Fernando Tello Gamarra
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Hand Movement ◽  
Gaze Behavior ◽  
Improved Method ◽  
The Relationship

We demonstrate an improved method for utilizing observed gaze behavior and show that it is useful in inferring hand movement intent during goal directed tasks. The task dynamics and the relationship between hand and gaze behavior are learned using an Abstract Hidden Markov Model (AHMM). We show that the predicted hand movement transitions occur consistently earlier in AHMM models with gaze than those models that do not include gaze observations.

scholarly journals A Hidden Markov Model for the Linguistic Analysis of the Voynich Manuscript

2019 ◽  
Vol 24 (1) ◽  
pp. 14 ◽  
Author(s):  
Luis Acedo
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Mathematical Linguistics ◽  
Underlying Structure ◽  
Internal States ◽  
Consonant Sounds

Hidden Markov models are a very useful tool in the modeling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden Markov model to analyze the underlying structure of an ancient and complex manuscript, known as the Voynich manuscript, which remains undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscripts, we train the network by means of the α and β -pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices to compare with known languages concerning the frequency of consonant andvowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript.

Hidden Markov model interpretations of neural networks

2000 ◽  
Vol 23 (4) ◽  
pp. 494-495
Author(s):  
Ingmar Visser
Keyword(s):  
Neural Networks ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Distributed Representations ◽  
Hidden Layer

Page's manifesto makes a case for localist representations in neural networks, one of the advantages being ease of interpretation. However, even localist networks can be hard to interpret, especially when at some hidden layer of the network distributed representations are employed, as is often the case. Hidden Markov models can be used to provide useful interpretable representations.

scholarly journals Five-year trajectories of multimorbidity patterns in an elderly Mediterranean population using Hidden Markov Models

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Concepción Violán ◽  
Sergio Fernández-Bertolín ◽  
Marina Guisado-Clavero ◽  
Quintí Foguet-Boreu ◽  
Jose M. Valderas ◽  
...  
Keyword(s):  
Primary Care ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Markov Models ◽  
Cox Regression ◽  
Hidden Markov ◽  
Population Based ◽  
Specific Pattern ◽  
Mediterranean Population ◽  
Primary Care Population

Abstract This study aimed to analyse the trajectories and mortality of multimorbidity patterns in patients aged 65 to 99 years in Catalonia (Spain). Five year (2012–2016) data of 916,619 participants from a primary care, population-based electronic health record database (Information System for Research in Primary Care, SIDIAP) were included in this retrospective cohort study. Individual longitudinal trajectories were modelled with a Hidden Markov Model across multimorbidity patterns. We computed the mortality hazard using Cox regression models to estimate survival in multimorbidity patterns. Ten multimorbidity patterns were originally identified and two more states (death and drop-outs) were subsequently added. At baseline, the most frequent cluster was the Non-Specific Pattern (42%), and the least frequent the Multisystem Pattern (1.6%). Most participants stayed in the same cluster over the 5 year follow-up period, from 92.1% in the Nervous, Musculoskeletal pattern to 59.2% in the Cardio-Circulatory and Renal pattern. The highest mortality rates were observed for patterns that included cardio-circulatory diseases: Cardio-Circulatory and Renal (37.1%); Nervous, Digestive and Circulatory (31.8%); and Cardio-Circulatory, Mental, Respiratory and Genitourinary (28.8%). This study demonstrates the feasibility of characterizing multimorbidity patterns along time. Multimorbidity trajectories were generally stable, although changes in specific multimorbidity patterns were observed. The Hidden Markov Model is useful for modelling transitions across multimorbidity patterns and mortality risk. Our findings suggest that health interventions targeting specific multimorbidity patterns may reduce mortality in patients with multimorbidity.

SENTENCE LIPREADING USING HIDDEN MARKOV MODEL WITH INTEGRATED GRAMMAR

2001 ◽  
Vol 15 (01) ◽  
pp. 161-176 ◽  
Author(s):  
KEREN YU ◽  
XIAOYI JIANG ◽  
HORST BUNKE
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov Models ◽  
Systematic Approach ◽  
Markov Models ◽  
Hidden Markov ◽  
E Mail

In this paper, we describe a systematic approach to the lipreading of whole sentences. A vocabulary of elementary words is considered. Based on the vocabulary, we define a grammar that generates a set of legal sentences. Our lipreading approach is based on a combination of the grammar with hidden Markov models (HMMs). Two different experiments were conducted. In the first experiment a set of e-mail commands is considered, while the set of sentences in the second experiment is given by all English integer numbers up to one million. Both experiments showed promising results, regarding the difficulty of the considered task.

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