scholarly journals Variational Beta Process Hidden Markov Models with Shared Hidden States for Trajectory Recognition

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1290
Author(s):  
Jing Zhao ◽  
Yi Zhang ◽  
Shiliang Sun ◽  
Haiwei Dai
Keyword(s):  
Dirichlet Process ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Beta Process ◽  
Shared Information ◽  
Long Time ◽  
Real World Datasets ◽  
Hidden States

Hidden Markov model (HMM) is a vital model for trajectory recognition. As the number of hidden states in HMM is important and hard to be determined, many nonparametric methods like hierarchical Dirichlet process HMMs and Beta process HMMs (BP-HMMs) have been proposed to determine it automatically. Among these methods, the sampled BP-HMM models the shared information among different classes, which has been proved to be effective in several trajectory recognition scenes. However, the existing BP-HMM maintains a state transition probability matrix for each trajectory, which is inconvenient for classification. Furthermore, the approximate inference of the BP-HMM is based on sampling methods, which usually takes a long time to converge. To develop an efficient nonparametric sequential model that can capture cross-class shared information for trajectory recognition, we propose a novel variational BP-HMM model, in which the hidden states can be shared among different classes and each class chooses its own hidden states and maintains a unified transition probability matrix. In addition, we derive a variational inference method for the proposed model, which is more efficient than sampling-based methods. Experimental results on a synthetic dataset and two real-world datasets show that compared with the sampled BP-HMM and other related models, the variational BP-HMM has better performance in trajectory recognition.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models

2018 ◽  
Vol 28 (5) ◽  
pp. 1552-1563 ◽  
Author(s):  
Tunny Sebastian ◽  
Visalakshi Jeyaseelan ◽  
Lakshmanan Jeyaseelan ◽  
Shalini Anandan ◽  
Sebastian George ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Markov Chain ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Passage Time ◽  
Transition Probability Matrix ◽  
Ordinal Logistic Regression ◽  
The Mean

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as ‘Low’, ‘Moderate’ and ‘High’ with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

scholarly journals On modifications to the Poisson-triggered hidden Markov paradigm through partitioned empirical recurrence rates ratios and its applications to natural hazards monitoring

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Moinak Bhaduri
Keyword(s):  
Natural Hazards ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Conditional Distributions ◽  
Recurrence Rates ◽  
State Dependent ◽  
Risk Period

Abstract Hidden Markov models (HMMs), especially those with a Poisson density governing the latent state-dependent emission probabilities, have enjoyed substantial and undeniable success in modeling natural hazards. Classifications among these hazards, induced through quantifiable properties such as varying intensities or geographic proximities, often exist, enabling the creation of an empirical recurrence rates ratio (ERRR), a smoothing statistic that is gradually gaining currency in modeling literature due to its demonstrated ability in unearthing interactions. Embracing these tools, this study puts forth a refreshing monitoring alternative where the unobserved state transition probability matrix in the likelihood of the Poisson based HMM is replaced by the observed transition probabilities of a discretized ERRR. Analyzing examples from Hawaiian volcanic and West Atlantic hurricane interactions, this work illustrates how the discretized ERRR may be interpreted as an observed version of the unobserved hidden Markov chain that generates one of the two interacting processes. Surveying different facets of traditional inference such as global state decoding, hidden state predictions, one-out conditional distributions, and implementing related computational algorithms, we find that the latest proposal estimates the chances of observing a high-risk period, one threatening several hazards, more accurately than its established counterpart. Strongly intuitive and devoid of forbidding technicalities, the new prescription launches a vision of surer forecasts and stands versatile enough to be applicable to other types of hazard monitoring (such as landslides, earthquakes, floods), especially those with meager occurrence probabilities.

scholarly journals Sensitivity of hidden Markov models

2005 ◽  
Vol 42 (03) ◽  
pp. 632-642 ◽  
Author(s):  
Alexander Yu. Mitrophanov ◽  
Alexandre Lomsadze ◽  
Mark Borodovsky
Keyword(s):  
Markov Chain ◽  
Hidden Markov Models ◽  
Stochastic Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Initial Distribution ◽  
Transition Probability Matrix ◽  
Perturbation Bound ◽  
Semi Markov Processes

We derive a tight perturbation bound for hidden Markov models. Using this bound, we show that, in many cases, the distribution of a hidden Markov model is considerably more sensitive to perturbations in the emission probabilities than to perturbations in the transition probability matrix and the initial distribution of the underlying Markov chain. Our approach can also be used to assess the sensitivity of other stochastic models, such as mixture processes and semi-Markov processes.

scholarly journals Sensitivity of hidden Markov models

2005 ◽  
Vol 42 (3) ◽  
pp. 632-642 ◽  
Author(s):  
Alexander Yu. Mitrophanov ◽  
Alexandre Lomsadze ◽  
Mark Borodovsky
Keyword(s):  
Markov Chain ◽  
Hidden Markov Models ◽  
Stochastic Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Initial Distribution ◽  
Transition Probability Matrix ◽  
Perturbation Bound ◽  
Semi Markov Processes

We derive a tight perturbation bound for hidden Markov models. Using this bound, we show that, in many cases, the distribution of a hidden Markov model is considerably more sensitive to perturbations in the emission probabilities than to perturbations in the transition probability matrix and the initial distribution of the underlying Markov chain. Our approach can also be used to assess the sensitivity of other stochastic models, such as mixture processes and semi-Markov processes.

An MEWMA-based segmental multivariate hidden Markov model for degradation assessment and prediction

2021 ◽  
pp. 1748006X2199052
Author(s):  
Yaping Li ◽  
Enrico Zio ◽  
Ershun Pan
Keyword(s):  
Markov Models ◽  
Hidden Markov ◽  
Average Run Length ◽  
Moving Average ◽  
Model Parameters ◽  
Current Time ◽  
Multivariate Processes ◽  
Industrial Systems ◽  
Hidden States ◽  
Multivariate Signals

Degradation is an unavoidable phenomenon in industrial systems. Hidden Markov models (HMMs) have been used for degradation modeling. In particular, segmental HMMs have been developed to model the explicit relationship between degradation signals and hidden states. However, existing segmental HMMs deal only with univariate cases, whereas in real systems, signals from various sensors are collected simultaneously, which makes it necessary to adapt the segmental HMMs to deal with multivariate processes. Also, to make full use of the information from the sensors, it is important to differentiate stable signals from deteriorating ones, but there is no good way for this, especially in multivariate processes. In this paper, the multivariate exponentially weighted moving average (MEWMA) control chart is employed to identify deteriorating multivariate signals. Specifically, the MEWMA statistic is used as a comprehensive indicator for differentiating multivariate observations. Likelihood Maximization is used to estimate the model parameters. To avoid underflow, the forward and backward probabilities are normalized. In order to assess degradation, joint probabilities are defined and derived. Further, the occurrence probability of each degradation state at the current time, as well as in the future, is derived. The Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset of NASA is employed for comparative analysis. In terms of degradation assessment and prediction, the proposed model performs very well in general. By sensitivity analysis, we show that in order to improve further the performance of the method, the weight of the chart should be set relatively small, whereas the method is not sensitive to the change of the in-control average run length (ARL).

A Nonstationary Hidden Markov Model with Approximately Infinitely-Long Time-Dependencies

2016 ◽  
Vol 25 (05) ◽  
pp. 1640001 ◽  
Author(s):  
Sotirios Chatzis ◽  
Dimitrios Kosmopoulos ◽  
George Papadourakis
Keyword(s):  
Markov Models ◽  
Hidden Markov ◽  
Mean Field ◽  
Sequential Data ◽  
First Order ◽  
Order Markov Chain ◽  
Inference Algorithms ◽  
Unrealistic Assumption ◽  
Long Time ◽  
Time Dependencies

Hidden Markov models (HMMs) are a popular approach for modeling sequential data, typically based on the assumption of a first-order Markov chain. In other words, only one-step back dependencies are modeled which is a rather unrealistic assumption in most applications. In this paper, we propose a method for postulating HMMs with approximately infinitely-long time-dependencies. Our approach considers the whole history of model states in the postulated dependencies, by making use of a recently proposed nonparametric Bayesian method for modeling label sequences with infinitely-long time dependencies, namely the sequence memoizer. We manage to derive training and inference algorithms for our model with computational costs identical to simple first-order HMMs, despite its entailed infinitely-long time-dependencies, by employing a mean-field-like approximation. The efficacy of our proposed model is experimentally demonstrated.

Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

2021 ◽  
Author(s):  
Jin Zhu ◽  
Kai Xia ◽  
Geir E Dullerud
Keyword(s):  
Linear Systems ◽  
Controller Design ◽  
Hidden Markov ◽  
Transition Probability ◽  
Original System ◽  
Transition Probability Matrix ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Weighting Matrix ◽  
Markov Jump Linear Systems

Abstract This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

scholarly journals Dynamic Transactions Between News Frames and Sociopolitical Events: An Integrative, Hidden Markov Model Approach

2020 ◽  
Vol 70 (3) ◽  
pp. 335-355 ◽  
Author(s):  
Frederic R Hopp ◽  
Jacob T Fisher ◽  
René Weber
Keyword(s):  
Markov Models ◽  
Hidden Markov ◽  
News Coverage ◽  
News Frames ◽  
Macro Scale ◽  
News Event ◽  
Hidden States ◽  
Research Domains ◽  
Integrated Study ◽  
Model Approach

Abstract A central goal of news research is to understand the interplay between news coverage and sociopolitical events. Although a great deal of work has elucidated how events drive news coverage, and how in turn news coverage influences societal outcomes, integrative systems-level models of the reciprocal interchanges between these two processes are sparse. Herein, we present a macro-scale investigation of the dynamic transactions between news frames and events using Hidden Markov Models (HMMs), focusing on morally charged news frames and sociopolitical events. Using 3,501,141 news records discussing 504,759 unique events, we demonstrate that sequences of frames and events can be characterized in terms of “hidden states” containing distinct moral frame and event relationships, and that these “hidden states” can forecast future news frames and events. This work serves to construct a path toward the integrated study of the news-event cycle across multiple research domains.

scholarly journals Use of Hidden Markov Models to Identify Background States Behind Risks of Cerebral Infarction and Ischemic Heart Disease

2017 ◽  
Vol 9 (1) ◽  
pp. 24
Author(s):  
Hiroshi Morimoto
Keyword(s):  
Heart Disease ◽  
Ischemic Heart Disease ◽  
Human Health ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Meteorological Factors ◽  
Hidden Markov ◽  
Weather Patterns ◽  
Weather And Human Health ◽  
Hidden States

Cold exposure is often said to trigger the incidence of cerebral infarctions and ischemic heart disease. This association between weather and human health has attracted considerable interest, and has been explored using standard statistical techniques such as regression models. Meteorological factors, such as temperature, are controlled by background systems, notably weather patterns. Therefore, it is reasonable to posit that the incidence of diseases is similarly influenced by a background system. The aim of this paper was to identify and construct these respective background systems. Possible background states or "hidden states", behind the incidence of diseases were derived using the EM and Viterbi algorithms with in the framework of hidden Markov models (HMM). A self-organizing map (SOM) enabled identification of weather patterns, considered as background states behind meteorological factors. These background states were then compared, and the hidden states behind the incidence of diseases were identified by six weather patterns. This finding indicates new evidence of the links between weather and human health, shedding light on the association between changes in the weather and the onset of disease. 

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