arXiv subjects

Ray Bai

Publications and source records attributed to Ray Bai.

At least 19 recordsLinked to original sources

arXiv2026

BiSSLB: Binary Spike-and-Slab Lasso Biclustering

Biclustering is a powerful unsupervised learning technique for simultaneously identifying coherent subsets of rows and columns in a data matrix, thus revealing local patterns that may not be apparent in global analyses. However, most biclustering methods are developed for continuous data and are not applicable for binary datasets such as single-nucleotide polymorphism (SNP) or protein-protein interaction (PPI) data. Existing biclustering algorithms for binary data often struggle to recover biclustering patterns under noise, face scalability issues, and/or bias the final results towards biclusters of a particular size or characteristic. We propose a Bayesian method for biclustering binary datasets called Binary Spike-and-Slab Lasso Biclustering (BiSSLB). Our method is robust to noise and allows for overlapping biclusters of various sizes without prior knowledge of the noise level or bicluster characteristics. BiSSLB is based on a logistic matrix factorization model with spike-and-slab priors on the latent spaces. We further incorporate an Indian Buffet Process (IBP) prior to automatically determine the number of biclusters from the data. We develop a novel coordinate ascent algorithm with proximal steps which allows for scalable computation. The performance of our proposed approach is assessed through simulations and two real applications on HapMap SNP and Homo Sapiens PPI data, where BiSSLB is shown to outperform other state-of-the-art binary biclustering methods when the data is very noisy.

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arXiv2026

BVSIMC: Bayesian Variable Selection-Guided Inductive Matrix Completion for Improved and Interpretable Drug Discovery

Recent advances in drug discovery have demonstrated that incorporating side information (e.g., chemical properties about drugs and genomic information about diseases) often greatly improves prediction performance. However, these side features can vary widely in relevance and are often noisy and high-dimensional. We propose Bayesian Variable Selection-Guided Inductive Matrix Completion (BVSIMC), a new Bayesian model that enables variable selection from side features in drug discovery. By learning sparse latent embeddings, BVSIMC improves both predictive accuracy and interpretability. We validate our method through simulation studies and two drug discovery applications: 1) prediction of drug resistance in Mycobacterium tuberculosis, and 2) prediction of new drug-disease associations in computational drug repositioning. On both synthetic and real data, BVSIMC outperforms several other state-of-the-art methods in terms of prediction. In our two real examples, BVSIMC further reveals the most clinically meaningful side features.

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arXiv2025

A Monotone Single-Index Modal Regression Powered by Deep Neural Networks for Non-Gaussian Periodontal Data

Pocket depth (PD) is a widely used biomarker for diagnosing risk of periodontal disease (PrD). However, PD typically exhibits skewness and heavy-tailedness, and its relationship with clinical risk factors is often nonlinear. Motivated by PrD studies, this paper develops a robust single-index modal regression framework for analyzing skewed and heavy-tailed data. Our method has the following novel features: (a) a flexible two-piece scale Student-$t$ error distribution that generalizes both normal and two-piece scale normal distributions; (b) a neural network with guaranteed monotonicity constraints to estimate the unknown single-index function; and (c) theoretical \revone{support}, including model identifiability and a universal approximation theorem. Our single-index model combines the flexibility of neural networks and the two-piece scaled Student-$t$ distribution, delivering robust mode-based estimation that is resistant to outliers, while retaining clinical interpretability through parametric index coefficients. We demonstrate the performance of our method through simulation studies, and an application to PrD electronic health records obtained from the HealthPartners Institute of Minnesota. The proposed methodology is implemented in the \texttt{R} package \href{https://doi.org/10.32614/CRAN.package.DNNSIM}{\texttt{DNNSIM}}.

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arXiv2024

Neural-g: A Deep Learning Framework for Mixing Density Estimation

Mixing (or prior) density estimation is an important problem in machine learning and statistics, especially in empirical Bayes $g$-modeling where accurately estimating the prior is necessary for making good posterior inferences. In this paper, we propose neural-$g$, a new neural network-based estimator for $g$-modeling. Neural-$g$ uses a softmax output layer to ensure that the estimated prior is a valid probability density. Under default hyperparameters, we show that neural-$g$ is very flexible and capable of capturing many unknown densities, including those with flat regions, heavy tails, and/or discontinuities. In contrast, existing methods struggle to capture all of these prior shapes. We provide justification for neural-$g$ by establishing a new universal approximation theorem regarding the capability of neural networks to learn arbitrary probability mass functions. To accelerate convergence of our numerical implementation, we utilize a weighted average gradient descent approach to update the network parameters. Finally, we extend neural-$g$ to multivariate prior density estimation. We illustrate the efficacy of our approach through simulations and analyses of real datasets. A software package to implement neural-$g$ is publicly available at https://github.com/shijiew97/neuralG.

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arXiv2024

Fast Bootstrapping Nonparametric Maximum Likelihood for Latent Mixture Models

Estimating the mixing density of a latent mixture model is an important task in signal processing. Nonparametric maximum likelihood estimation is one popular approach to this problem. If the latent variable distribution is assumed to be continuous, then bootstrapping can be used to approximate it. However, traditional bootstrapping requires repeated evaluations on resampled data and is not scalable. In this letter, we construct a generative process to rapidly produce nonparametric maximum likelihood bootstrap estimates. Our method requires only a single evaluation of a novel two-stage optimization algorithm. Simulations and real data analyses demonstrate that our procedure accurately estimates the mixing density with little computational cost even when there are a hundred thousand observations.

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arXiv2024

A Unified Three-State Model Framework for Analysis of Treatment Crossover in Survival Trials

We present a unified three-state model (TSM) framework for evaluating treatment effects in clinical trials in the presence of treatment crossover. Researchers have proposed diverse methodologies to estimate the treatment effect that would have hypothetically been observed if treatment crossover had not occurred. However, there is little work on understanding the connections between these different approaches from a statistical point of view. The proposed TSM framework unifies existing methods, effectively identifying potential biases, model assumptions, and inherent limitations for each method. This can guide researchers in understanding when these methods are appropriate and choosing a suitable approach for their data. The TSM framework also facilitates the creation of new methods to adjust for confounding effects from treatment crossover. To illustrate this capability, we introduce a new imputation method that falls under its scope. Through simulation experiments, we demonstrate the performance of different approaches for estimating the treatment effects. Codes for implementing the methods within the TSM framework are available at https://github.com/JasonZhao111/TSM.

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arXiv2023

Sparse high-dimensional linear mixed modeling with a partitioned empirical Bayes ECM algorithm

High-dimensional longitudinal data is increasingly used in a wide range of scientific studies. To properly account for dependence between longitudinal observations, statistical methods for high-dimensional linear mixed models (LMMs) have been developed. However, few packages implementing these high-dimensional LMMs are available in the statistical software R. Additionally, some packages suffer from scalability issues. This work presents an efficient and accurate Bayesian framework for high-dimensional LMMs. We use empirical Bayes estimators of hyperparameters for increased flexibility and an Expectation-Conditional-Minimization (ECM) algorithm for computationally efficient maximum a posteriori probability (MAP) estimation of parameters. The novelty of the approach lies in its partitioning and parameter expansion as well as its fast and scalable computation. We illustrate Linear Mixed Modeling with PaRtitiOned empirical Bayes ECM (LMM-PROBE) in simulation studies evaluating fixed and random effects estimation along with computation time. A real-world example is provided using data from a study of lupus in children, where we identify genes and clinical factors associated with a new lupus biomarker and predict the biomarker over time. Supplementary materials are available online.

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arXiv2023

Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression

Sparse linear regression methods for high-dimensional data commonly assume that residuals have constant variance, which can be violated in practice. For example, Aphasia Quotient (AQ) is a critical measure of language impairment and informs treatment decisions, but it is challenging to measure in stroke patients. It is of interest to use high-resolution T2 neuroimages of brain damage to predict AQ. However, sparse regression models show marked evidence of heteroscedastic error even after transformations are applied. This violation of the homoscedasticity assumption can lead to bias in estimated coefficients, prediction intervals (PI) with improper length, and increased type I errors. Bayesian heteroscedastic linear regression models relax the homoscedastic error assumption but can enforce restrictive prior assumptions on parameters, and many are computationally infeasible in the high-dimensional setting. This paper proposes estimating high-dimensional heteroscedastic linear regression models using a heteroscedastic partitioned empirical Bayes Expectation Conditional Maximization (H-PROBE) algorithm. H-PROBE is a computationally efficient maximum a posteriori estimation approach that requires minimal prior assumptions and can incorporate covariates hypothesized to impact heterogeneity. We apply this method by using high-dimensional neuroimages to predict and provide PIs for AQ that accurately quantify predictive uncertainty. Our analysis demonstrates that H-PROBE can provide narrower PI widths than standard methods without sacrificing coverage. Narrower PIs are clinically important for determining the risk of moderate to severe aphasia. Additionally, through extensive simulation studies, we exhibit that H-PROBE results in superior prediction, variable selection, and predictive inference compared to alternative methods.

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arXiv2023

Generative Quantile Regression with Variability Penalty

Quantile regression and conditional density estimation can reveal structure that is missed by mean regression, such as multimodality and skewness. In this paper, we introduce a deep learning generative model for joint quantile estimation called Penalized Generative Quantile Regression (PGQR). Our approach simultaneously generates samples from many random quantile levels, allowing us to infer the conditional distribution of a response variable given a set of covariates. Our method employs a novel variability penalty to avoid the problem of vanishing variability, or memorization, in deep generative models. Further, we introduce a new family of partial monotonic neural networks (PMNN) to circumvent the problem of crossing quantile curves. A major benefit of PGQR is that it can be fit using a single optimization, thus bypassing the need to repeatedly train the model at multiple quantile levels or use computationally expensive cross-validation to tune the penalty parameter. We illustrate the efficacy of PGQR through extensive simulation studies and analysis of real datasets. Code to implement our method is available at https://github.com/shijiew97/PGQR.

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arXiv2022

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.

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arXiv2021

A Bayesian Selection Model for Correcting Outcome Reporting Bias With Application to a Meta-analysis on Heart Failure Interventions

Multivariate meta-analysis (MMA) is a powerful tool for jointly estimating multiple outcomes' treatment effects. However, the validity of results from MMA is potentially compromised by outcome reporting bias (ORB), or the tendency for studies to selectively report outcomes. Until recently, ORB has been understudied. Since ORB can lead to biased conclusions, it is crucial to correct the estimates of effect sizes and quantify their uncertainty in the presence of ORB. With this goal, we develop a Bayesian selection model to adjust for ORB in MMA. We further propose a measure for quantifying the impact of ORB on the results from MMA. We evaluate our approaches through a meta-evaluation of 748 bivariate meta-analyses from the Cochrane Database of Systematic Reviews. Our model is motivated by and applied to a meta-analysis of interventions on hospital readmission and quality of life for heart failure patients. In our analysis, the relative risk (RR) of hospital readmission for the intervention group changes from a significant decrease (RR: 0.931, 95% confidence interval [CI]: 0.862-0.993) to a statistically nonsignificant effect (RR: 0.955, 95% CI: 0.876-1.051) after adjusting for ORB. This study demonstrates that failing to account for ORB can lead to different conclusions in a meta-analysis.

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arXiv2021

Quantifying patient and neighborhood risks for stillbirth and preterm birth in Philadelphia with a Bayesian spatial model

Stillbirth and preterm birth are major public health challenges. Using a Bayesian spatial model, we quantified patient-specific and neighborhood risks of stillbirth and preterm birth in the city of Philadelphia. We linked birth data from electronic health records at Penn Medicine hospitals from 2010 to 2017 with census-tract-level data from the United States Census Bureau. We found that both patient-level characteristics (e.g. self-identified race/ethnicity) and neighborhood-level characteristics (e.g. violent crime) were significantly associated with patients' risk of stillbirth or preterm birth. Our neighborhood analysis found that higher-risk census tracts had 2.68 times the average risk of stillbirth and 2.01 times the average risk of preterm birth compared to lower-risk census tracts. Higher neighborhood rates of women in poverty or on public assistance were significantly associated with greater neighborhood risk for these outcomes, whereas higher neighborhood rates of college-educated women or women in the labor force were significantly associated with lower risk. Several of these neighborhood associations were missed by the patient-level analysis. These results suggest that neighborhood-level analyses of adverse pregnancy outcomes can reveal nuanced relationships and, thus, should be considered by epidemiologists. Our findings can potentially guide place-based public health interventions to reduce stillbirth and preterm birth rates.

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arXiv2020

Spike-and-Slab Meets LASSO: A Review of the Spike-and-Slab LASSO

High-dimensional data sets have become ubiquitous in the past few decades, often with many more covariates than observations. In the frequentist setting, penalized likelihood methods are the most popular approach for variable selection and estimation in high-dimensional data. In the Bayesian framework, spike-and-slab methods are commonly used as probabilistic constructs for high-dimensional modeling. Within the context of linear regression, Rockova and George (2018) introduced the spike-and-slab LASSO (SSL), an approach based on a prior which provides a continuum between the penalized likelihood LASSO and the Bayesian point-mass spike-and-slab formulations. Since its inception, the spike-and-slab LASSO has been extended to a variety of contexts, including generalized linear models, factor analysis, graphical models, and nonparametric regression. The goal of this paper is to survey the landscape surrounding spike-and-slab LASSO methodology. First we elucidate the attractive properties and the computational tractability of SSL priors in high dimensions. We then review methodological developments of the SSL and outline several theoretical developments. We illustrate the methodology on both simulated and real datasets.

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arXiv2020

Bayesian Group Regularization in Generalized Linear Models with a Continuous Spike-and-Slab Prior

We study Bayesian group-regularized estimation in high-dimensional generalized linear models (GLMs) under a continuous spike-and-slab prior. Our framework covers both canonical and non-canonical link functions and subsumes logistic, Poisson, negative binomial, and Gaussian regression with group sparsity. We obtain the minimax L2 convergence rate for both a maximum a posteriori (MAP) estimator and the full posterior distribution under our prior. Our theoretical results thus justify the use of the posterior mode as a point estimator. The posterior distribution also contracts at the same rate as the MAP estimator, an attractive feature of our approach which is not the case for the group lasso. For computation, we propose expectation-maximization (EM) and Markov chain Monte Carlo (MCMC) algorithms. We illustrate our method through simulations and a real data application on predicting human immunodeficiency virus (HIV) drug resistance from protein sequences.

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arXiv2020

A Robust Bayesian Copas Selection Model for Quantifying and Correcting Publication Bias

The validity of conclusions from meta-analysis is potentially threatened by publication bias. Most existing procedures for correcting publication bias assume normality of the study-specific effects that account for between-study heterogeneity. However, this assumption may not be valid, and the performance of these bias correction procedures can be highly sensitive to departures from normality. Further, there exist few measures to quantify the magnitude of publication bias based on selection models. In this paper, we address both of these issues. First, we explore the use of heavy-tailed distributions for the study-specific effects within a Bayesian hierarchical framework. The deviance information criterion (DIC) is used to determine the appropriate distribution to use for conducting the final analysis. Second, we develop a new measure to quantify the magnitude of publication bias based on Hellinger distance. Our measure is easy to interpret and takes advantage of the estimation uncertainty afforded naturally by the posterior distribution. We illustrate our proposed approach through simulation studies and meta-analyses on lung cancer and antidepressants. To assess the prevalence of publication bias, we apply our method to 1500 meta-analyses of dichotomous outcomes in the Cochrane Database of Systematic Reviews. Our methods are implemented in the publicly available R package RobustBayesianCopas.

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arXiv2020

VCBART: Bayesian trees for varying coefficients

The linear varying coefficient models posits a linear relationship between an outcome and covariates in which the covariate effects are modeled as functions of additional effect modifiers. Despite a long history of study and use in statistics and econometrics, state-of-the-art varying coefficient modeling methods cannot accommodate multivariate effect modifiers without imposing restrictive functional form assumptions or involving computationally intensive hyperparameter tuning. In response, we introduce VCBART, which flexibly estimates the covariate effect in a varying coefficient model using Bayesian Additive Regression Trees. With simple default settings, VCBART outperforms existing varying coefficient methods in terms of covariate effect estimation, uncertainty quantification, and outcome prediction. We illustrate the utility of VCBART with two case studies: one examining how the association between later-life cognition and measures of socioeconomic position vary with respect to age and socio-demographics and another estimating how temporal trends in urban crime vary at the neighborhood level. An R package implementing VCBART is available at https://github.com/skdeshpande91/VCBART

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arXiv2019

Scalable high-dimensional Bayesian varying coefficient models with unknown within-subject covariance

Nonparametric varying coefficient (NVC) models are useful for modeling time-varying effects on responses that are measured repeatedly for the same subjects. When the number of covariates is moderate or large, it is desirable to perform variable selection from the varying coefficient functions. However, existing methods for variable selection in NVC models either fail to account for within-subject correlations or require the practitioner to specify a parametric form for the correlation structure. In this paper, we introduce the nonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesian high-dimensional NVC models. Through the introduction of functional random effects, our method allows for flexible modeling of within-subject correlations without needing to specify a parametric covariance function. We further propose several scalable optimization and Markov chain Monte Carlo (MCMC) algorithms. For variable selection, we propose an Expectation Conditional Maximization (ECM) algorithm to rapidly obtain maximum a posteriori (MAP) estimates. Our ECM algorithm scales linearly in the total number of observations $N$ and the number of covariates $p$. For uncertainty quantification, we introduce an approximate MCMC algorithm that also scales linearly in both $N$ and $p$. We demonstrate the scalability, variable selection performance, and inferential capabilities of our method through simulations and a real data application. These algorithms are implemented in the publicly available R package NVCSSL on the Comprehensive R Archive Network.

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arXiv2019

Spike-and-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models

We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the first nonparametric variant of the spike-and-slab lasso methodology. Our model simultaneously performs group selection and estimation, while our fully Bayes treatment of the mixture proportion allows for model complexity control and automatic self-adaptivity to different levels of sparsity. We develop theory to uniquely characterize the global posterior mode under the SSGL and introduce a highly efficient block coordinate ascent algorithm for maximum a posteriori (MAP) estimation. We further employ de-biasing methods to provide uncertainty quantification of our estimates. Thus, implementation of our model avoids the computational intensiveness of Markov chain Monte Carlo (MCMC) in high dimensions. We derive posterior concentration rates for both grouped linear regression and sparse GAMs when the number of covariates grows at nearly exponential rate with sample size. Finally, we illustrate our methodology through extensive simulations and data analysis.

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