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Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques…

We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives…

Statistics Theory · Mathematics 2014-10-27 Elisabeth Gassiat , Judith Rousseau

Hidden Markov models (HMMs) are commonly used to model animal movement data and infer aspects of animal behavior. An HMM assumes that each data point from a time series of observations stems from one of $N$ possible states. The states are…

This paper presents a new and flexible prognostics framework based on a higher order hidden semi-Markov model (HOHSMM) for systems or components with unobservable health states and complex transition dynamics. The HOHSMM extends the basic…

Applications · Statistics 2020-02-14 Ying Liao , Yisha Xiang , Min Wang

Hidden Markov Models (HMMs) are powerful tools for modeling sequential data, where the underlying states evolve in a stochastic manner and are only indirectly observable. Traditional HMM approaches are well-established for linear sequences,…

Machine Learning · Statistics 2024-06-05 Farzan Vafa , Sahand Hormoz

This work aims at providing a new model for time series classification based on learning from just one example. We assume that time series can be well characterized as a parametric random process, a sort of Hidden semi-Markov Model…

Machine Learning · Statistics 2022-11-18 Adrián Pérez Herrero , Paulo Félix Lamas , Jesús María Rodríguez Presedo

Use of accelerometers is now widespread within animal biotelemetry as they provide a means of measuring an animal's activity in a meaningful and quantitative way where direct observation is not possible. In sequential acceleration data…

In a clinical trial of a treatment for alcoholism, a common response variable of interest is the number of alcoholic drinks consumed by each subject each day, or an ordinal version of this response, with levels corresponding to abstinence,…

Applications · Statistics 2010-10-08 Kenneth E. Shirley , Dylan S. Small , Kevin G. Lynch , Stephen A. Maisto , David W. Oslin

Motivated by Hubert's segmentation procedure we discuss the application of hidden Markov models (HMM) to the segmentation of hydrological and enviromental time series. We use a HMM algorithm which segments time series of several hundred…

Computational Engineering, Finance, and Science · Computer Science 2011-11-09 Ath. Kehagias

We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled…

Applications · Statistics 2015-05-20 Ruth King , Roland Langrock

The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we…

Systems and Control · Electrical Eng. & Systems 2025-06-10 Dongyan Sui , Haotian Pu , Siyang Leng , Stefan Vlaski

The formalism of state estimation and hidden Markov models (HMMs) can simplify and clarify the discussion of stochastic thermodynamics in the presence of feedback and measurement errors. After reviewing the basic formalism, we use it to…

Statistical Mechanics · Physics 2015-11-13 John Bechhoefer

Recommender systems are widely used for suggesting books, education materials, and products to users by exploring their behaviors. In reality, users' preferences often change over time, leading to studies on time-dependent recommender…

Information Retrieval · Computer Science 2024-12-17 Haidong Zhang , Wancheng Ni , Xin Li , Yiping Yang

Hidden Markov models (HMMs) are widely applied in studies where a discrete-valued process of interest is observed indirectly. They have for example been used to model behaviour from human and animal tracking data, disease status from…

Methodology · Statistics 2025-05-22 Théo Michelot

This paper is concerned with the computational complexity of learning the Hidden Markov Model (HMM). Although HMMs are some of the most widely used tools in sequential and time series modeling, they are cryptographically hard to learn in…

Machine Learning · Computer Science 2024-02-27 Sham M. Kakade , Akshay Krishnamurthy , Gaurav Mahajan , Cyril Zhang

Modeling continuous-time physiological processes that manifest a patient's evolving clinical states is a key step in approaching many problems in healthcare. In this paper, we develop the Hidden Absorbing Semi-Markov Model (HASMM): a…

Artificial Intelligence · Computer Science 2016-12-28 Ahmed M. Alaa , Mihaela van der Schaar

The conformational kinetics of enzymes can be reliably revealed when they are governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate especially in the case of conformational states that are hardly distinguishable.…

Quantitative Methods · Quantitative Biology 2009-02-05 A. Kovalev , N. Zarrabi , F. Werz , M. Boersch , Z. Ristic , H. Lill , D. Bald , C. Tietz , J. Wrachtrup

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed,…

Systems and Control · Electrical Eng. & Systems 2020-07-10 Kaikai Zheng , Dawei Shi , Ling Shi

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…

Methodology · Statistics 2020-10-29 Sina Mews , Roland Langrock , Marius Ötting , Houda Yaqine , Jost Reinecke

Hidden Markov models (HMMs) are popular time series model in many fields including ecology, economics and genetics. HMMs can be defined over discrete or continuous time, though here we only cover the former. In the field of movement ecology…

Quantitative Methods · Quantitative Biology 2018-06-29 Vianey Leos-Barajas , Théo Michelot