arXiv subjects

Chengqian Xian

Publications and source records attributed to Chengqian Xian.

4 recordsLinked to original sources

arXiv2026

Variational Inference for Functional Data Clustering via Dirichlet Process Mixtures with Correlated Errors

We propose a Bayesian model-based approach for clustering functional data with an unknown number of clusters and temporally correlated observations. Cluster-specific mean functions are represented using B-spline basis expansions, while within-curve dependence is modeled through an Ornstein--Uhlenbeck covariance structure. A truncated Dirichlet process mixture is used to infer the effective number of clusters, and a variational EM algorithm is developed for efficient posterior approximation. Simulation studies show that the proposed method performs well under both correctly specified and misspecified mean-function settings and compares favorably with several existing functional clustering methods. Comparisons with MCMC indicate that the variational approximation yields consistent clustering and parameter estimates but at substantially lower computational cost. An application to Canadian daily temperature curves further demonstrates the practical usefulness of the method in identifying interpretable functional clusters while accounting for temporal dependence.

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arXiv2024

Fast variational Bayesian inference for correlated survival data: an application to invasive mechanical ventilation duration analysis

Correlated survival data are prevalent in various clinical settings and have been extensively discussed in literature. One of the most common types of correlated survival data is clustered survival data, where the survival times from individuals in a cluster are associated. Our study is motivated by invasive mechanical ventilation data from different intensive care units (ICUs) in Ontario, Canada, forming multiple clusters. The survival times from patients within the same ICU cluster are correlated. To address this association, we introduce a shared frailty log-logistic accelerated failure time model that accounts for intra-cluster correlation through a cluster-specific random intercept. We present a novel, fast variational Bayes (VB) algorithm for parameter inference and evaluate its performance using simulation studies varying the number of clusters and their sizes. We further compare the performance of our proposed VB algorithm with the h-likelihood method and a Markov Chain Monte Carlo (MCMC) algorithm. The proposed algorithm delivers satisfactory results and demonstrates computational efficiency over the MCMC algorithm. We apply our method to the ICU ventilation data from Ontario to investigate the ICU site random effect on ventilation duration.

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arXiv2023

Variational Bayesian analysis of survival data using a log-logistic accelerated failure time model

The log-logistic regression model is one of the most commonly used accelerated failure time (AFT) models in survival analysis, for which statistical inference methods are mainly established under the frequentist framework. Recently, Bayesian inference for log-logistic AFT models using Markov chain Monte Carlo (MCMC) techniques has also been widely developed. In this work, we develop an alternative approach to MCMC methods and infer the parameters of the log-logistic AFT model via a mean-field variational Bayes (VB) algorithm. A piecewise approximation technique is embedded in deriving the VB algorithm to achieve conjugacy. The proposed VB algorithm is evaluated and compared with typical frequentist inferences and MCMC inference using simulated data under various scenarios. A publicly available dataset is employed for illustration. We demonstrate that the proposed VB algorithm can achieve good estimation accuracy and has a lower computational cost compared with MCMC methods.

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arXiv2023

Clustering Functional Data via Variational Inference

Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at discrete points. Among different kinds of functional data analyses, clustering analysis aims to determine underlying groups of curves in the dataset when there is no information on the group membership of each individual curve. In this work, we propose a new model-based approach for clustering and smoothing functional data simultaneously via variational inference. We derive coordinate ascent mean-field variational Bayes algorithms to approximate the posterior distribution of our model parameters by finding the variational distribution with the smallest Kullback-Leibler divergence to the posterior. The performance of our proposed method is evaluated using simulated data and publicly available datasets.

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