Hierarchical Continuous Time Hidden Markov Model, with Application in Zero-Inflated Accelerometer Data

Wearable devices including accelerometers are increasingly being used to collect high-frequency human activity data in situ. There is tremendous potential to use such data to inform medical decision making and public health policies. However, modeling such data is challenging as they are high-dimensional, heterogeneous, and subject to informative missingness, e.g., zero readings when the device is removed by the participant. We propose a flexible and extensible continuous-time hidden Markov model to extract meaningful activity patterns from human accelerometer data. To facilitate estimation with massive data we derive an efficient learning algorithm that exploits the hierarchical structure of the parameters indexing the proposed model. We also propose a bootstrap procedure for interval estimation. The proposed methods are illustrated using data from the 2003–2004 and 2005–2006 National Health and Nutrition Examination Survey.

[1]  L. Ferrucci,et al.  Quantifying the lifetime circadian rhythm of physical activity: a covariate-dependent functional approach. , 2015, Biostatistics.

[2]  I. Pigeot,et al.  Using Hidden Markov Models to Improve Quantifying Physical Activity in Accelerometer Data – A Simulation Study , 2014, PloS one.

[3]  S. Anderssen,et al.  Accelerometer-determined physical activity in adults and older people. , 2012, Medicine and science in sports and exercise.

[4]  K. Evenson.  Towards an Understanding of Change in Physical Activity from Pregnancy Through Postpartum. , 2011, Psychology of sport and exercise.

[5]  Michael F. Leitzmann,et al.  Associations of Objectively Assessed Physical Activity and Sedentary Time with All-Cause Mortality in US Adults: The NHANES Study , 2015, PloS one.

[6]  Graham A Colditz,et al.  Youth recall and TriTrac accelerometer estimates of physical activity levels. , 2004, Medicine and science in sports and exercise.

[7]  Jeffrey S. Morris,et al.  Journal of the American Statistical Association Using Wavelet-based Functional Mixed Models to Characterize Population Heterogeneity in Accelerometer Profiles Using Wavelet-based Functional Mixed Models to Characterize Population Heterogeneity in Accelerometer Profiles: a Case Study , 2022 .

[8]  Daphne Koller,et al.  Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks , 2005, UAI.

[9]  Sung-Bae Cho,et al.  Human activity recognition using smartphone sensors with two-stage continuous hidden Markov models , 2014, 2014 10th International Conference on Natural Computation (ICNC).

[10]  Zhi-Quan Luo,et al.  On the linear convergence of the alternating direction method of multipliers , 2012, Mathematical Programming.

[11]  R. Pyke.  Markov Renewal Processes with Finitely Many States , 1961 .

[12]  K. Izawa,et al.  Effect of accelerometer-based feedback on physical activity in hospitalized patients with ischemic stroke: a randomized controlled trial , 2018, Clinical rehabilitation.

[13]  Xiang Wang,et al.  Unsupervised learning of disease progression models , 2014, KDD.

[14]  R. Pyke.  Markov renewal processes: Definitions and preliminary properties , 1961 .

[15]  L. Mâsse,et al.  Physical activity in the United States measured by accelerometer. , 2008, Medicine and science in sports and exercise.

[16]  Garik Markarian,et al.  Self management of chronic disease using mobile devices and Bluetooth monitors , 2007, BODYNETS.

[17]  Wendy Robertson,et al.  Utility of Accelerometers to Measure Physical Activity in Children Attending an Obesity Treatment Intervention , 2010, Journal of obesity.

[18]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[19]  Kelly R Evenson,et al.  Patterns of objectively measured physical activity in the United States. , 2008, Medicine and science in sports and exercise.

[20]  Alessandro Tognetti,et al.  CAPTURE AND CLASSIFICATION OF BODY POSTURE AND GESTURE USING WEARABLE KINESTHETIC SYSTEMS , 2005 .

[21]  A. Albert.  Estimating the Infinitesimal Generator of a Continuous Time, Finite State Markov Process , 1962 .

[22]  Le Song,et al.  Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression , 2015, NIPS.

[23]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[24]  Eric Moulines,et al.  Inference in hidden Markov models , 2010, Springer series in statistics.

[25]  Dylan S. Small,et al.  HIDDEN MARKOV MODELS FOR ALCOHOLISM TREATMENT TRIAL DATA , 2010, 1010.1410.

[26]  Jeff Gill,et al.  Missing value imputation for physical activity data measured by accelerometer , 2018, Statistical methods in medical research.

[27]  Christoph Busch,et al.  Using Hidden Markov Models for accelerometer-based biometric gait recognition , 2011, 2011 IEEE 7th International Colloquium on Signal Processing and its Applications.

[28]  Jindong Tan,et al.  Real-time Daily Activity Classification with Wireless Sensor Networks using Hidden Markov Model , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[29]  Song Yang,et al.  Imputation of missing data when measuring physical activity by accelerometry. , 2005, Medicine and science in sports and exercise.

[30]  Qing Ling,et al.  On the Linear Convergence of the ADMM in Decentralized Consensus Optimization , 2013, IEEE Transactions on Signal Processing.

[31]  Eric Moulines,et al.  Inference in Hidden Markov Models (Springer Series in Statistics) , 2005 .

[32]  R. Douc,et al.  Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime , 2004, math/0503681.

[33]  Gareth M. James,et al.  Hidden Markov Models for Longitudinal Comparisons , 2005 .

[34]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[35]  B. Marcus,et al.  Accelerometer use in a physical activity intervention trial. , 2010, Contemporary clinical trials.

[36]  R. Altman.  Mixed Hidden Markov Models , 2007 .

[37]  Ana-Maria Staicu,et al.  The Use of Functional Data Analysis to Evaluate Activity in a Spontaneous Model of Degenerative Joint Disease Associated Pain in Cats , 2017, PloS one.