2024

1. Am. Stat.

   

   Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation

   Xinkai Zhou, Qiang Heng, Eric C. Chi, and Hua Zhou

   The American Statistician, 2024

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   This article advocates proximal Markov chain Monte Carlo (ProxMCMC) as a flexible and general Bayesian inference framework for constrained or regularized estimation. Originally introduced in the Bayesian imaging literature, ProxMCMC employs the Moreau-Yosida envelope for a smooth approximation of the total-variation regularization term, fixes variance and regularization strength parameters as constants, and uses the Langevin algorithm for the posterior sampling. We extend ProxMCMC to be fully Bayesian by providing data-adaptive estimation of all parameters including the regularization strength parameter. More powerful sampling algorithms such as Hamiltonian Monte Carlo are employed to scale ProxMCMC to high-dimensional problems. Analogous to the proximal algorithms in optimization, ProxMCMC offers a versatile and modularized procedure for conducting statistical inference on constrained and regularized problems. The power of ProxMCMC is illustrated on various statistical estimation and machine learning tasks, the inference of which is traditionally considered difficult from both frequentist and Bayesian perspectives.

   @article{zhou2022proximal,
     author = {Zhou, Xinkai and Heng, Qiang and Chi, Eric C. and Zhou, Hua},
     title = {Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation},
     journal = {The American Statistician},
     volume = {0},
     number = {0},
     pages = {1--12},
     year = {2024},
     publisher = {Taylor \& Francis},
     doi = {10.1080/00031305.2024.2308821},
   }

2023

1. arXiv

   

   Analysis of Active/Inactive Patterns in the NHANES Data using Generalized Multilevel Functional Principal Component Analysis

   Xinkai Zhou, Julia Wrobel, Ciprian M. Crainiceanu, and Andrew Leroux

   arXiv preprint arXiv:2311.14054, 2023

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   Between 2011 and 2014 NHANES collected objectively measured physical activity data using wrist-worn accelerometers for tens of thousands of individuals for up to seven days. Here we analyze the minute-level indicators of being active, which can be viewed as binary (because there is an active indicator at every minute), multilevel (because there are multiple days of data for each study participant), functional (because within-day data can be viewed as a function of time) data. To extract within- and between-participant directions of variation in the data, we introduce Generalized Multilevel Functional Principal Component Analysis (GM-FPCA), an approach based on the dimension reduction of the linear predictor. Scores associated with specific patterns of activity are shown to be strongly associated with time to death. Extensive simulation studies indicate that GM-FPCA provides accurate estimation of model parameters, is computationally stable, and is scalable in the number of study participants, visits, and observations within visits. R code for implementing the method is provided.

   @article{zhou2023gmfpca,
     title = {Analysis of Active/Inactive Patterns in the NHANES Data using Generalized Multilevel Functional Principal Component Analysis},
     author = {Zhou, Xinkai and Wrobel, Julia and Crainiceanu, Ciprian M. and Leroux, Andrew},
     year = {2023},
     journal = {arXiv preprint arXiv:2311.14054},
   }

2022

1. Stat. Anal. Data Min.

   

   Bag of little bootstraps for massive and distributed longitudinal data

   Xinkai Zhou, Jin J Zhou, and Hua Zhou

   Statistical Analysis and Data Mining: The ASA Data Science Journal, 2022

   Abs Bib HTML Code

   Linear mixed models are widely used for analyzing longitudinal datasets, and the inference for variance component parameters relies on the bootstrap method. However, health systems and technology companies routinely generate massive longitudinal datasets that make the traditional bootstrap method infeasible. To solve this problem, we extend the highly scalable bag of little bootstraps method for independent data to longitudinal data and develop a highly efficient Julia package MixedModelsBLB.jl. Simulation experiments and real data analysis demonstrate the favorable statistical performance and computational advantages of our method compared to the traditional bootstrap method. For the statistical inference of variance components, it achieves 200 times speedup on the scale of 1 million subjects (20 million total observations), and is the only currently available tool that can handle more than 10 million subjects (200 million total observations) using desktop computers.

   @article{zhou2022blb,
     title = {Bag of little bootstraps for massive and distributed longitudinal data},
     author = {Zhou, Xinkai and Zhou, Jin J and Zhou, Hua},
     journal = {Statistical Analysis and Data Mining: The ASA Data Science Journal},
     volume = {15},
     number = {3},
     pages = {314--321},
     year = {2022},
     publisher = {Wiley Online Library},
   }