Tensor Train Spectral Method for Learning of Hidden Markov Models (HMM)

2019 ◽  
Vol 19 (1) ◽  
pp. 93-99 ◽  
Author(s):  
Maxim A. Kuznetsov ◽  
Ivan V. Oseledets
Keyword(s):  
Probability Distribution ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Order Tensor ◽  
Spectral Learning ◽  
Frobenius Distance ◽  
Hidden States

AbstractWe propose a new algorithm for spectral learning of Hidden Markov Models (HMM). In contrast to the standard approach, we do not estimate the parameters of the HMM directly, but construct an estimate for the joint probability distribution. The idea is based on the representation of a joint probability distribution as an N-th-order tensor with low ranks represented in the tensor train (TT) format. Using TT-format, we get an approximation by minimizing the Frobenius distance between the empirical joint probability distribution and tensors with low TT-ranks with core tensors normalization constraints. We propose an algorithm for the solution of the optimization problem that is based on the alternating least squares (ALS) approach and develop its fast version for sparse tensors. The order of the tensor d is a parameter of our algorithm. We have compared the performance of our algorithm with the existing algorithm by Hsu, Kakade and Zhang proposed in 2009 and found that it is much more robust if the number of hidden states is overestimated.

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. 

scholarly journals Evaluation of Spectral Learning for the Identification of Hidden Markov Models

2015 ◽  
Vol 48 (28) ◽  
pp. 897-902 ◽  
Author(s):  
Robert Mattila ◽  
Cristian R. Rojas ◽  
Bo Wahlberg
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Spectral Learning

Extending hidden Markov models to allow conditioning on previous observations

2018 ◽  
Vol 16 (05) ◽  
pp. 1850019 ◽  
Author(s):  
Ioannis A. Tamposis ◽  
Margarita C. Theodoropoulou ◽  
Konstantinos D. Tsirigos ◽  
Pantelis G. Bagos
Keyword(s):  
Hidden Markov Models ◽  
Probabilistic Models ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Simple Extension ◽  
Computational Molecular Biology ◽  
Current State ◽  
Observation Sequence ◽  
Hidden States

Hidden Markov Models (HMMs) are probabilistic models widely used in computational molecular biology. However, the Markovian assumption regarding transition probabilities which dictates that the observed symbol depends only on the current state may not be sufficient for some biological problems. In order to overcome the limitations of the first order HMM, a number of extensions have been proposed in the literature to incorporate past information in HMMs conditioning either on the hidden states, or on the observations, or both. Here, we implement a simple extension of the standard HMM in which the current observed symbol (amino acid residue) depends both on the current state and on a series of observed previous symbols. The major advantage of the method is the simplicity in the implementation, which is achieved by properly transforming the observation sequence, using an extended alphabet. Thus, it can utilize all the available algorithms for the training and decoding of HMMs. We investigated the use of several encoding schemes and performed tests in a number of important biological problems previously studied by our team (prediction of transmembrane proteins and prediction of signal peptides). The evaluation shows that, when enough data are available, the performance increased by 1.8%–8.2% and the existing prediction methods may improve using this approach. The methods, for which the improvement was significant (PRED-TMBB2, PRED-TAT and HMM-TM), are available as web-servers freely accessible to academic users at www.compgen.org/tools/ .

scholarly journals FactorialHMM: Fast and exact inference in factorial hidden Markov models

2018 ◽  
Author(s):  
Regev Schweiger ◽  
Yaniv Erlich ◽  
Shai Carmi
Keyword(s):  
Hidden Markov Models ◽  
Posterior Probability ◽  
Markov Models ◽  
Hidden Markov ◽  
Cartesian Product ◽  
Exact Inference ◽  
Running Time ◽  
Time Scaling ◽  
Multiple Processes ◽  
Hidden States

MotivationHidden Markov models (HMMs) are powerful tools for modeling processes along the genome. In a standard genomic HMM, observations are drawn, at each genomic position, from a distribution whose parameters depend on a hidden state; the hidden states evolve along the genome as a Markov chain. Often, the hidden state is the Cartesian product of multiple processes, each evolving independently along the genome. Inference in these so-called Factorial HMMs has a naïve running time that scales as the square of the number of possible states, which by itself increases exponentially with the number of subchains; such a running time scaling is impractical for many applications. While faster algorithms exist, there is no available implementation suitable for developing bioinformatics applications.ResultsWe developed FactorialHMM, a Python package for fast exact inference in Factorial HMMs. Our package allows simulating either directly from the model or from the posterior distribution of states given the observations. Additionally, we allow the inference of all key quantities related to HMMs: (1) the (Viterbi) sequence of states with the highest posterior probability; (2) the likelihood of the data; and (3) the posterior probability (given all observations) of the marginal and pairwise state probabilities. The running time and space requirement of all procedures is linearithmic in the number of possible states. Our package is highly modular, providing the user with maximal flexibility for developing downstream applications.Availabilityhttps://github.com/regevs/factorialhmm

Equivalence of Linear Boltzmann Chains and Hidden Markov Models

1996 ◽  
Vol 8 (1) ◽  
pp. 178-181 ◽  
Author(s):  
David J. C. MacKay
Keyword(s):  
Probability Distribution ◽  
Markov Model ◽  
Hidden Markov Models ◽  
State Transition ◽  
Markov Models ◽  
Hidden Markov ◽  
Simple Condition ◽  
Transition Energies ◽  
State Sequence ◽  
The Relationship

Several authors have studied the relationship between hidden Markov models and “Boltzmann chains” with a linear or “time-sliced” architecture. Boltzmann chains model sequences of states by defining state-state transition energies instead of probabilities. In this note I demonstrate that under the simple condition that the state sequence has a mandatory end state, the probability distribution assigned by a strictly linear Boltzmann chain is identical to that assigned by a hidden Markov model.

Uncovering hidden states in African lion movement data using hidden Markov models

2019 ◽  
Vol 46 (4) ◽  
pp. 296
Author(s):  
Victoria L. Goodall ◽  
Sam M. Ferreira ◽  
Paul J. Funston ◽  
Nkabeng Maruping-Mzileni
Keyword(s):  
Hidden Markov Models ◽  
Management Practices ◽  
Markov Models ◽  
Hidden Markov ◽  
Suitable Model ◽  
Movement Rate ◽  
State Sequence ◽  
Direct Observations ◽  
Early Evening ◽  
Hidden States

Context Direct observations of animals are the most reliable way to define their behavioural characteristics; however, to obtain these observations is costly and often logistically challenging. GPS tracking allows finer-scale interpretation of animal responses by measuring movement patterns; however, the true behaviour of the animal during the period of observation is seldom known. Aims The aim of our research was to draw behavioural inferences for a lioness with a hidden Markov model and to validate the predicted latent-state sequence with field observations of the lion pride. Methods We used hidden Markov models to model the movement of a lioness in the Kruger National Park, South Africa. A three-state log-normal model was selected as the most suitable model. The model outputs are related to collected data by using an observational model, such as, for example, a distribution for the average movement rate and/or direction of movement that depends on the underlying model states that are taken to represent behavioural states of the animal. These inferred behavioural states are validated against direct observation of the pride’s behaviour. Key results Average movement rate provided a useful alternative for the application of hidden Markov models to irregularly spaced GPS locations. The movement model predicted resting as the dominant activity throughout the day, with a peak in the afternoon. The local-movement state occurred consistently throughout the day, with a decreased proportion during the afternoon, when more resting takes place, and an increase towards the early evening. The relocating state had three peaks, namely, during mid-morning, early evening and about midnight. Because of the differences in timing of the direct observations and the GPS locations, we had to compare point observations of the true behaviour with an interval prediction of the modelled behavioural state. In 75% of the cases, the model-predicted behaviour and the field-observed behaviour overlapped. Conclusions Our data suggest that the hidden Markov modelling approach is successful at predicting a realistic behaviour of lions on the basis of the GPS location coordinates and the average movement rate between locations. The present study provided a unique opportunity to uncover the hidden states and compare the true behaviour with the inferred behaviour from the predicted state sequence. Implications Our results illustrated the potential of using hidden Markov models with movement rate as an input to understand carnivore behavioural patterns that could inform conservation management practices.

scholarly journals Analysis of multimodal Bayesian nonparametric autoregressive hidden Markov models for process monitoring in robotic contact tasks

2019 ◽  
Vol 16 (2) ◽  
pp. 172988141983484 ◽  
Author(s):  
Hongmin Wu ◽  
Yisheng Guan ◽  
Juan Rojas
Keyword(s):  
Stochastic Process ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Observation Model ◽  
Vector Autoregressive ◽  
Hidden States ◽  
Contact Tasks

Robot introspection aids robots to understand what they do and how they do it. Previous robot introspection techniques have often used parametric hidden Markov models or supervised learning techniques, implying that the number of hidden states or classes is defined a priori and fixed through the entire modeling process. Fixed parameterizations limit the modeling power of a process to properly encode the data. Furthermore, first-order Markov models are limited in their ability to model complex data sequences that represent highly dynamic behaviors as they assume observations are conditionally independent given the state. In this work, we contribute a Bayesian nonparametric autoregressive Hidden Markov model for the monitoring of robot contact tasks, which are characterized by complex dynamical data that are hard to model. We used a nonparametric prior that endows our hidden Markov models with an unbounded number of hidden states for a given robot skill (or subtask). We use a hierarchical Dirichlet stochastic process prior to learn an hidden Markov model with a switching vector autoregressive observation model of wrench signatures and end-effector pose for the manipulation contact tasks. The proposed scheme monitors both nominal skill execution and anomalous behaviors. Two contact tasks are used to measure the effectiveness of our approach: (i) a traditional pick-and-place task composed of four skills and (ii) a cantilever snap assembly task (also composed of four skills). The modeling performance or our approach was compared with other methods, and classification accuracy measures were computed for skill and anomaly identification. The hierarchical Dirichlet stochastic process prior to learn an hidden Markov model with a switching vector autoregressive observation model was shown to have excellent process monitoring performance with higher identification rates and monitoring ability.

scholarly journals Generalized Hidden Markov Models for Phylogenetic Comparative Datasets

2020 ◽  
Author(s):  
James D. Boyko ◽  
Jeremy M. Beaulieu
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
R Package ◽  
List Type ◽  
Ancestral State ◽  
Rate Heterogeneity ◽  
Ancestral States ◽  
The Difference ◽  
Hidden States

AbstractHidden Markov models (HMM) have emerged as an important tool for understanding the evolution of characters that take on discrete states. Their flexibility and biological sensibility make them appealing for many phylogenetic comparative applications.Previously available packages placed unnecessary limits on the number of observed and hidden states that can be considered when estimating transition rates and inferring ancestral states on a phylogeny.To address these issues, we expanded the capabilities of the R package corHMM to handle n-state and n-character problems and provide users with a streamlined set of functions to create custom HMMs for any biological question of arbitrary complexity.We show that increasing the number of observed states increases the accuracy of ancestral state reconstruction. We also explore the conditions for when an HMM is most effective, finding that an HMM is an appropriate model when the degree of rate heterogeneity is moderate to high.Finally, we demonstrate the importance of these generalizations by reconstructing the phyllotaxy of the ancestral angiosperm flower. Partially contradicting previous results, we find the most likely state to be a whorled perianth, whorled androecium, whorled gynoecium. The difference between our analysis and previous studies was that our modeling explicitly allowed for the correlated evolution of several flower characters.

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