arXiv subjects

Pixu Shi

Publications and source records attributed to Pixu Shi.

10 recordsLinked to original sources

arXiv2026

Panel Flow Matching: A Generative Approach to Learning Distributions of Longitudinal Data

Learning distributions of longitudinal data is central to tasks such as visualization, completion, classification, and synthetic data generation, but it remains statistically challenging because longitudinal observations are often irregular, sparse, and collected from only a limited number of subjects. To address this, we develop a novel generative framework, termed panel flow matching (PFM), for learning longitudinal distributions by pooling information across time via a continuous panel flow model. PFM combines a forward flow-matching step with a backward kernel-fitting step, yielding a flexible and data-adaptive approach for capturing complex distributional structures. We apply PFM to estimate panel densities, namely the cross-sectional densities of longitudinal data, and establish statistical guarantees under irregular and sparse sampling designs. Under this, PFM naturally supports tasks including longitudinal completion, synthetic data generation, and classification, without requiring a preliminary dimension-reduction step to handle data irregularity. Extensive simulations demonstrate that PFM outperforms existing methods across these tasks. We further apply PFM to a vaginal microbiome longitudinal dataset from 188 pregnancies labeled as term or preterm, where it improves classification accuracy and reveals time-varying distributional differences between the two groups.

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arXiv2026

Associating High-Dimensional Longitudinal Datasets through an Efficient Cross-Covariance Decomposition

Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem that arises across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the complex, time-varying cross-covariance structure coupled with high dimensionality, which complicates both model formulation and statistical estimation. To address these challenges, we propose a new framework, termed Functional-Aggregated Cross-covariance Decomposition (FACD), tailored for canonical cross-covariance analysis between paired high-dimensional longitudinal datasets through a statistically efficient and theoretically grounded procedure. Unlike existing methods that are often limited to low-dimensional data or rely on explicit parametric modeling of temporal dynamics, FACD adaptively learns temporal structure by aggregating signals across features and naturally accommodates variable selection to identify the most relevant features associated across datasets. We establish statistical guarantees for FACD and demonstrate its advantages over existing approaches through extensive simulation studies. Finally, we apply FACD to a longitudinal multi-omic human study, revealing blood molecules with time-varying associations across omic layers during acute exercise.

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arXiv2024

Functional-SVD for Heterogeneous Trajectories: Case Studies in Health

Trajectory data, including time series and longitudinal measurements, are increasingly common in health-related domains such as biomedical research and epidemiology. Real-world trajectory data frequently exhibit heterogeneity across subjects such as patients, sites, and subpopulations, yet many traditional methods are not designed to accommodate such heterogeneity in data analysis. To address this, we propose a unified framework, termed Functional Singular Value Decomposition (FSVD), for statistical learning with heterogeneous trajectories. We establish the theoretical foundations of FSVD and develop a corresponding estimation algorithm that accommodates noisy and irregular observations. We further adapt FSVD to a wide range of trajectory-learning tasks, including dimension reduction, factor modeling, regression, clustering, and data completion, while preserving its ability to account for heterogeneity, leverage inherent smoothness, and handle irregular sampling. Through extensive simulations, we demonstrate that FSVD-based methods consistently outperform existing approaches across these tasks. Finally, we apply FSVD to a COVID-19 case-count dataset and electronic health record datasets, showcasing its effective performance in global and subgroup pattern discovery and factor analysis.

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arXiv2024

Supervised low-rank approximation of high-dimensional multivariate functional data via tensor decomposition

Motivated by the challenges of analyzing high-dimensional ($p \gg n$) sequencing data from longitudinal microbiome studies, where samples are collected at multiple time points from each subject, we propose supervised functional tensor singular value decomposition (SupFTSVD), a novel dimensionality reduction method that leverages auxiliary information in the dimensionality reduction of high-dimensional functional tensors. Although multivariate functional principal component analysis is a natural choice for dimensionality reduction of multivariate functional data, it becomes computationally burdensome in high-dimensional settings. Low-rank tensor decomposition is a feasible alternative and has gained popularity in recent literature, but existing methods in this realm are often incapable of simultaneously utilizing the temporal structure of the data and subject-level auxiliary information. SupFTSVD overcomes these limitations by generating low-rank representations of high-dimensional functional tensors while incorporating subject-level auxiliary information and accounting for the functional nature of the data. Moreover, SupFTSVD produces low-dimensional representations of subjects, features, and time, as well as subject-specific trajectories, providing valuable insights into the biological significance of variations within the data. In simulation studies, we demonstrate that our method achieves notable improvement in tensor approximation accuracy and loading estimation by utilizing auxiliary information. Finally, we applied SupFTSVD to two longitudinal microbiome studies where biologically meaningful patterns in the data were revealed.

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arXiv2023

Guaranteed Functional Tensor Singular Value Decomposition

This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular modes. The problem is motivated by high-order longitudinal data analysis. Our model assumes the observed data to be a random realization of an approximate CP low-rank functional tensor measured on a discrete time grid. Incorporating tensor algebra and the theory of Reproducing Kernel Hilbert Space (RKHS), we propose a novel RKHS-based constrained power iteration with spectral initialization. Our method can successfully estimate both singular vectors and functions of the low-rank structure in the observed data. With mild assumptions, we establish the non-asymptotic contractive error bounds for the proposed algorithm. The superiority of the proposed framework is demonstrated via extensive experiments on both simulated and real data.

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arXiv2021

High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis

In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the classic log-contrast model is often used where read counts are normalized into compositions. However, zero read counts and the randomness in covariates remain critical issues. In this article, we introduce a surprisingly simple, interpretable, and efficient method for the estimation of compositional data regression through the lens of a novel high-dimensional log-error-in-variable regression model. The proposed method provides both corrections on sequencing data with possible overdispersion and simultaneously avoids any subjective imputation of zero read counts. We provide theoretical justifications with matching upper and lower bounds for the estimation error. The merit of the procedure is illustrated through real data analysis and simulation studies.

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arXiv2018

Generalized Linear Models with Linear Constraints for Microbiome Compositional Data

Motivated by regression analysis for microbiome compositional data, this paper considers generalized linear regression analysis with compositional covariates, where a group of linear constraints on regression coefficients are imposed to account for the compositional nature of the data and to achieve subcompositional coherence. A penalized likelihood estimation procedure using a generalized accelerated proximal gradient method is developed to efficiently estimate the regression coefficients. A de-biased procedure is developed to obtain asymptotically unbiased and normally distributed estimates, which leads to valid confidence intervals of the regression coefficients. Simulations results show the correctness of the coverage probability of the confidence intervals and smaller variances of the estimates when the appropriate linear constraints are imposed. The methods are illustrated by a microbiome study in order to identify bacterial species that are associated with inflammatory bowel disease (IBD) and to predict IBD using fecal microbiome.

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arXiv2017

A Model for Paired-Multinomial Data and Its Application to Analysis of Data on a Taxonomic Tree

In human microbiome studies, sequencing reads data are often summarized as counts of bacterial taxa at various taxonomic levels specified by a taxonomic tree. This paper considers the problem of analyzing two repeated measurements of microbiome data from the same subjects. Such data are often collected to assess the change of microbial composition after certain treatment, or the difference in microbial compositions across body sites. Existing models for such count data are limited in modeling the covariance structure of the counts and in handling paired multinomial count data. A new probability distribution is proposed for paired-multinomial count data, which allows flexible covariance structure and can be used to model repeatedly measured multivariate count data. Based on this distribution, a test statistic is developed for testing the difference in compositions based on paired multinomial count data. The proposed test can be applied to the count data observed on a taxonomic tree in order to test difference in microbiome compositions and to identify the subtrees with different subcompositions. Simulation results indicate that proposed test has correct type 1 errors and increased power compared to some commonly used methods. An analysis of an upper respiratory tract microbiome data set is used to illustrate the proposed methods.

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arXiv2016

Regression Analysis for Microbiome Compositional Data

One important problem in microbiome analysis is to identify the bacterial taxa that are associated with a response, where the microbiome data are summarized as the composition of the bacterial taxa at different taxonomic levels. This paper considers regression analysis with such compositional data as covariates. In order to satisfy the subcompositional coherence of the results, linear models with a set of linear constraints on the regression coefficients are introduced. Such models allow regression analysis for subcompositions and include the log-contrast model for compositional covariates as a special case. A penalized estimation procedure for estimating the regression coefficients and for selecting variables under the linear constraints is developed. A method is also proposed to obtain de-biased estimates of the regression coefficients that are asymptotically unbiased and have a joint asymptotic multivariate normal distribution. This provides valid confidence intervals of the regression coefficients and can be used to obtain the $p$-values. Simulation results show the validity of the confidence intervals and smaller variances of the de-biased estimates when the linear constraints are imposed. The proposed methods are applied to a gut microbiome data set and identify four bacterial genera that are associated with the body mass index after adjusting for the total fat and caloric intakes.

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arXiv2013

Methods to Calculate the Upper Bound of Gini Coefficient Based on Grouped Data and the Result for China

Determining an upper bound, particularly the optimal upper bound of the Gini coefficient when dealing with grouped data without specified income brackets, remains an important and open question. In this paper, we introduce an efficient algorithm to calculate the exact optimal upper bound of the Gini coefficient with provable guarantees. To exemplify these methods, we also offer computed results for the Gini coefficients of urban and rural China spanning the years 2003 to 2008.

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