arXiv subjects

Shao-Hsuan Wang

Publications and source records attributed to Shao-Hsuan Wang.

5 recordsLinked to original sources

arXiv2026

Bayesian sparse principal coordinates analysis with delta-tolerant linear approximation for microbiome data

Principal coordinates analysis (PCoA) is a standard exploratory tool for microbiome beta-diversity studies, but its axes are defined by pairwise dissimilarities and therefore do not directly identify the taxa driving an ordination. We propose Bayesian sparse principal coordinates analysis (BSPCoA), a post hoc framework that approximates the leading principal coordinates by a sparse linear surrogate in the observed taxa. A delta-tolerance diagnostic quantifies the discrepancy between the classical ordination and its best linear surrogate, clarifying when taxon-level interpretation is well supported. We place three-parameter beta normal global-local priors on the surrogate coefficients to induce row sparsity, obtain posterior uncertainty, and select influential taxa. The method reduces to sparse principal component analysis under Euclidean distance, while remaining applicable to ecologically meaningful dissimilarities such as Bray--Curtis and Hellinger distances. We conduct simulation studies to demonstrate that BSPCoA provides an approximately linear representation of the dominant ordination geometry while enhancing interpretability in sparse microbiome settings. In the Hadza gut microbiome data, the method produces an ordination close to that of classical PCoA while highlighting a parsimonious set of taxa associated with seasonal variation.

stat.ME↗

arXiv2025

A Bayesian Sparse Kronecker Product Decomposition Framework for Tensor Predictors with Mixed-Type Responses

Ultra-high-dimensional tensor predictors are increasingly common in neuroimaging and other biomedical studies, yet existing methods rarely integrate continuous, count, and binary responses in a single coherent model. We present a Bayesian Sparse Kronecker Product Decomposition (BSKPD) that represents each regression (or classification) coefficient tensor as a low-rank Kronecker product whose factors are endowed with element-wise Three-Parameter Beta-Normal shrinkage priors, yielding voxel-level sparsity and interpretability. Embedding Gaussian, Poisson, and Bernoulli outcomes in a unified exponential-family form, and combining the shrinkage priors with Polya-Gamma data augmentation, gives closed-form Gibbs updates that scale to full-resolution 3-D images. We prove posterior consistency and identifiability even when each tensor mode dimension grows subexponentially with the sample size, thereby extending high-dimensional Bayesian theory to mixed-type multivariate responses. Simulations and applications to ADNI and OASIS magnetic-resonance imaging datasets show that BSKPD delivers sharper signal recovery and lower predictive error than current low-rank or sparsity-only competitors while preserving scientific interpretability.

stat.ME↗

arXiv2024

Two-Step Mixed-Type Multivariate Bayesian Sparse Variable Selection with Shrinkage Priors

We introduce a Bayesian framework for mixed-type multivariate regression using continuous shrinkage priors. Our framework enables joint analysis of mixed continuous and discrete outcomes and facilitates variable selection from the $p$ covariates. Theoretical studies of Bayesian mixed-type multivariate response models have not been conducted previously and require more intricate arguments than the corresponding theory for univariate response models due to the correlations between the responses. In this paper, we investigate necessary and sufficient conditions for posterior contraction of our method when $p$ grows faster than sample size $n$. The existing literature on Bayesian high-dimensional asymptotics has focused only on cases where $p$ grows subexponentially with $n$. In contrast, we study the asymptotic regime where $p$ is allowed to grow exponentially in terms of $n$. We develop a novel two-step approach for variable selection which possesses the sure screening property and provably achieves posterior contraction even under exponential growth of $p$. We demonstrate the utility of our method through simulation studies and applications to real data, including a cancer genomics dataset where $n=174$ and $p=9183$. The R code to implement our method is available at https://github.com/raybai07/MtMBSP.

math.ST↗

arXiv2021

Two-stage dimension reduction for noisy high-dimensional images and application to Cryogenic Electron Microscopy

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an eigenvalue problem for the sample covariance matrix. We propose herein a two-stage dimension reduction (2SDR) method for image reconstruction from high-dimensional noisy image data. The first stage treats the image as a matrix, which is a tensor of order 2, and uses multilinear principal component analysis (MPCA) for matrix rank reduction and image denoising. The second stage vectorizes the reduced-rank matrix and achieves further dimension and noise reduction. Simulation studies demonstrate excellent performance of 2SDR, for which we also develop an asymptotic theory that establishes consistency of its rank selection. Applications to cryo-EM (cryogenic electronic microscopy), which has revolutionized structural biology, organic and medical chemistry, cellular and molecular physiology in the past decade, are also provided and illustrated with benchmark cryo-EM datasets. Connections to other contemporaneous developments in image reconstruction and high-dimensional statistical inference are also discussed.

eess.IV↗

arXiv2011

Estimate the Occurrence Rate of the DNA Palindromes

A DNA palindrome is a segment of double-stranded DNA sequence with inver- sion symmetry which may form secondary structures conferring significant biolog- ical functions ranging from RNA transcription to DNA replication. To test if the clusters of DNA palindromes distribute randomly is an interesting bioinformatic problem, where the occurrence rate of the DNA palindromes is a key estimator for setting up a test. The most commonly used statistics for estimating the occur- rence rate for scan statistics is the average rate. However, in our simulation, the average rate may double the null occurrence rate of DNA palindromes due to hot spot regions of 3000 bp's in a herpes virus genome. Here, we propose a formula to estimate the occurrence rate through an analytic derivation under a Markov assumption on DNA sequence. Our simulation study shows that the performance of this method has improved the accuracy and robustness against hot spots, as compared to the commonly used average rate. In addition, we derived analytical formula for the moment-generating functions of various statistics under a Markov model, enabling further calculations of p-values.

stat.AP↗