arXiv subjects

Gongjun Xu

Publications and source records attributed to Gongjun Xu.

At least 19 recordsLinked to original sources

arXiv2026

Genetic association testing with multivariate survival phenotypes under interval censoring

Set-based genetic association tests provide a powerful framework for detecting genetic effects on complex traits by jointly analyzing multiple genetic variants. Although set-based methods have been developed for interval-censored survival outcomes, existing approaches primarily focus on a single survival phenotype and therefore do not fully use information from multiple correlated outcomes. In this paper, we develop two Weighted V Tests for Multivariate Interval-Censored Data (WV-M-IC), extending the weighted V-statistic framework (Wu et al., 2021) to the joint analysis of multiple correlated interval-censored survival outcomes. The performance of these methods is evaluated through simulation studies, showing that the proposed approaches can provide power gains compared with single-outcome analyses. We apply the proposed methods to the ZOE 2.0 study to investigate dental caries progression in children.

stat.ME↗

arXiv2026

Conditional-Independence-Regularized Distributional Autoencoders for Mixed-Type Data

Mixed-type data containing both numerical and categorical variables arise in many scientific and real-world applications. Existing representation learning and generative modeling approaches typically focus either on reconstruction accuracy or unconditional data generation, but often fail to recover the full conditional distribution of the data while preserving interpretable structural relationships between heterogeneous variable types. In this work, we introduce Conditional-Independence-Regularized Distributional Autoencoders, a framework for learning low-dimensional representations of mixed-type data through conditional distribution matching and structural regularization. Our method combines an energy-score-based objective for numerical variables, a likelihood-based objective for categorical variables, and an auxiliary conditional independence regularization term encouraging the learned representation to capture the dependence between numerical and categorical components. We provide theoretical analysis showing that the optimal representation balances unexplained numerical variability, conditional entropy of categorical variables, and residual conditional dependence. Empirically, the proposed method achieves strong performance on both synthetic and real-world datasets, substantially improving categorical distribution recovery, achieving competitive overall conditional distribution recovery, and preserving mixed-type dependence structure. The code has been made available at GitHub.

stat.ME↗

arXiv2026

Statistical analysis of block structured latent variable models

This paper studies block structured latent variable models, in which observed variables are grouped into distinct blocks based on their relationships with the underlying latent variables. These block structures are prevalent in various fields such as psychology, education, economics, and genetics. Despite their widespread applications, the fundamental statistical properties of these models remain largely unexplored. In this work, we present a comprehensive statistical analysis of the block structured latent variable models. In particular, we first derive conditions for model identifiability across various block designs. Furthermore, we investigate the maximum likelihood estimation under these identifiability constraints. To accommodate these intricate constraints associated with various block configurations, we introduce a Lagrangian-type formulation for the constrained nonconvex optimization problem and show that its optimum coincides with that of the original problem. This formulation serves as a critical tool for understanding the behavior of the constrained estimator under various block structures. Building on that, we establish sharp non-asymptotic error bounds and asymptotic distributions of the constrained maximum likelihood estimator. We also propose a computational framework to obtain the estimator and establish theoretical properties for the algorithm output. Our theoretical findings are validated through simulation studies and empirical data analyses.

stat.ME↗

arXiv2026

Stochastic Sensitivity Analysis for Matched Observational Studies

Sensitivity analysis asks how strong unmeasured confounding needs to be to explain away an observational study's conclusion. The conventional approach in matched studies conducts inference conditional upon the potential outcomes as well as both observed and unobserved confounders, and then finds the worst-case distribution for the conditional treatment assignments across all possible realizations of the unobserved confounder. The resulting worst-case allocation imagines strong, near perfect, correlations between the potential outcomes and hidden bias. We propose a stochastic sensitivity analysis that instead targets inference conditional upon potential outcomes and observed confounders while treating the hidden confounders as random with unknown conditional laws. Rather than finding the worst-case realizations for the hidden confounders, we instead determine the worst-case conditional law over a broad class of distributions. This preserves the adversarial spirit of sensitivity analysis while allowing for imperfect alignment between hidden bias and potential outcomes to a degree controlled by a scalar sensitivity parameter. We consider restrictions to both an interpretable class with no parametric assumptions and a Bernoulli class of conditional laws. Design sensitivity calculations and real-data demonstrations illustrate that allowing for even a small degree of stochasticity can materially increase reported robustness to hidden bias relative to the conventional approach.

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arXiv2026

Efficient Synthetic Network Generation via Latent Embedding Reconstruction

Network data are ubiquitous across the social sciences, biology, and information systems. Generating realistic synthetic network data has broad applications from network simulation to scientific discovery. However, many existing black-box approaches for network generation tend to overfit observed data while overlooking characteristic network structure, and incur substantial computational overhead at scale. These practical challenges call for synthetic network generation methods that are both efficient and capable of capturing structural properties of networks. In this paper, we introduce Synthetic Network Generation via Latent Embedding Reconstruction (SyNGLER), a general and efficient framework for synthetic network generation that builds on latent space network models. Given an observed network, SyNGLER first learns low-dimensional latent node embeddings via a latent space network model and then reconstructs the latent space by building a distribution-free generator over these embeddings. For generation, SyNGLER first samples (or resamples) node embeddings from the generator in the latent space and then produces synthetic networks using the latent space network model. Through the latent space framework, SyNGLER preserves unique characteristics in networks such as sparsity and node degree heterogeneity, while allowing for efficient training with lower computational cost than many existing deep architectures. We provide theoretical guarantees by developing consistency results on the distance between the true and synthetic edge distributions. Empirical studies further demonstrate the effectiveness of SyNGLER, which efficiently produces networks that better preserve key network characteristics such as network moments and degree distributions compared with existing approaches. Code is available at https://github.com/FeifanJiang/syngler.

stat.ML↗

arXiv2026

Theoretical Analysis of Engression and Reverse Markov Engression

Engression is a recently proposed and effective framework for conditional distribution learning. Its multi-step Reverse Markov extension further improves generative flexibility by decomposing complex conditional sampling into sequential reverse transitions. Despite their strong empirical performance, rigorous finite-sample statistical guarantees for these methods remain unavailable. In this paper, under deep neural network parameterizations, we establish nonasymptotic convergence bounds for Engression by directly controlling the Energy Distance between the learned and target conditional distributions. For the Reverse Markov framework, we further develop an Energy-Distance-based chain rule that enables a rigorous analysis of error propagation across reverse steps. Our analysis yields corresponding excess-risk bounds that are near-optimal up to logarithmic factors relative to the classical minimax rate over a general H\"older class.

stat.ME↗

arXiv2026

Multidimensional Item Response Theory under General Latent Distributions

Multidimensional item response theory (MIRT) provides an important psychometric framework for modeling how multiple latent traits jointly influence observed item responses. In most existing estimation procedures, the latent trait distribution is assumed to be Gaussian. Although computationally convenient, this assumption can be restrictive in many applications where the latent distribution exhibits skewness, heavy tails, or multimodality. More importantly, misspecifying the latent distribution may bias the estimation of item parameters and latent traits. To address this limitation, we propose a data-driven flow-based framework for MIRT models that can capture a broad class of non-Gaussian latent distributions. The proposed approach represents the latent distribution as an invertible transformation of a simple base distribution. For efficient estimation, we further introduce a conditional flow as a function of both the observed response and the noise to approximate the posterior distribution. Under this framework, the item parameters, latent distribution, and posterior approximation can be learned jointly. Comprehensive simulation studies show that the proposed method improves item-parameter and latent-trait recovery when the true latent distribution is non-normal. An application to a personality dataset further illustrates the practical utility of the proposed framework for modeling complex latent trait distributions in large-scale data.

stat.ME↗

arXiv2026

Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation

Nonconvex methods have emerged as a dominant approach for low-rank matrix estimation, a problem that arises widely in machine learning and AI for learning and representing high-dimensional data. Existing analyses for these methods often require additional regularization to mitigate nonconvexity, even though such regularization is often unnecessary in practice. Moreover, most analyses rely on problem-specific arguments that are difficult to generalize to more complex settings. In this paper, we develop a theoretical framework for studying nonconvex procedures across a broad class of low-rank matrix estimation problems. Rather than focusing on a specific model, we reveal a fundamental mechanism that explains why nonconvex procedures can behave well in low-rank estimation. Our key device is a {\it benign regularizer} that does not alter the original update rule, but yields an equivalent locally strongly convex formulation of the algorithm. This perspective uncovers a disguised convexity inherent in the nonconvex procedure and provides a new route to theoretical guarantees for nonconvex low-rank matrix estimation.

stat.ML↗

arXiv2026

Inference on Generalized Latent Variable Models with High-Dimensional Responses and Covariates

Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on latent variables that capture key unobserved characteristics. To draw statistical inferences on covariate effects while accounting for latent variables, we consider a high-dimensional generalized latent variable model that accommodates mixed-type responses and allows for flexible dependence between covariates and latent variables, which is more suitable for many real-world applications than existing methods that either rely on a linear regression form or restricted assumptions on the dependence between covariates and latent variables. We develop an alternating algorithm that iteratively updates the regression parameters and the latent variables, transforming an intractable nonconvex problem into a sequence of tractable convex subproblems. Theoretically, we provide algorithmic guarantees by establishing statistical consistency of the resulting estimator and deriving an error bound for it. Further, building on this estimator, we construct a debiased estimator for the covariate effect and establish its asymptotic normality. The effectiveness of the proposed method is demonstrated through an application to evaluating the fairness of the Programme for International Student Assessment (PISA).

stat.ME↗

arXiv2026

Beyond Vintage Rotation: Bias-Free Sparse Representation Learning with Oracle Inference

Learning low-dimensional latent representations is a central topic in statistics and machine learning, and rotation methods have long been used to obtain sparse and interpretable representations. Despite nearly a century of widespread use across many fields, rigorous guarantees for valid inference for the learned representation remain lacking. In this paper, we identify a surprisingly prevalent phenomenon that suggests a reason for this gap: for a broad class of vintage rotations, the resulting estimators exhibit a non-estimable bias. Because this bias is independent of the data, it fundamentally precludes the development of valid inferential procedures, including the construction of confidence intervals and hypothesis testing. To address this challenge, we propose a novel bias-free rotation method within a general representation learning framework based on latent variables. We establish an oracle inference property for the learned sparse representations: the estimators achieve the same asymptotic variance as in the ideal setting where the latent variables are observed. To bridge the gap between theory and computation, we develop an efficient computational framework and prove that its output estimators retain the same oracle property. Our results provide a rigorous inference procedure for the rotated estimators, yielding statistically valid and interpretable representation learning. Code for implementing the proposed method is available at the GitHub repository: https://github.com/chengyu06/Folomin.git.

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arXiv2026

Unfolding and Fusion: Debiased Inference for Generalized Multilayer Latent Space Models

Multilayer networks have become increasingly ubiquitous across diverse scientific fields, yet their inferential theory remains underdeveloped. We propose a flexible latent space model for directed multilayer networks with various edge types, where each node has sender and receiver latent positions capturing its sending and receiving behaviors, together with layer-varying out- and in-degree parameters and layer-specific connection matrices. Through nonlinear link functions, the model induces a Tucker low-rank tensor structure in which the structural latent spaces are intertwined with the degree-effect subspaces, creating challenges for estimation and inference. To address these challenges, we develop a novel unfolding and fusion method, coupled with two-sided centering to partial out degree effects. We establish consistency and asymptotic normality for the latent-position estimators. For the connection matrices, we uncover a non-negligible second-order bias induced by fusing two separately estimated unfolding components, derive its explicit representation, and construct a feasible plug-in correction. The resulting debiased estimator is asymptotically normal. Together, these results enable confidence regions for latent positions and tests of whether two network layers share the same structure. Extensive simulation studies validate the proposed method, and a real-world data analysis demonstrates its practical utility.

stat.ME↗

arXiv2025

A Latent Variable Framework for Scaling Laws in Large Language Models

We propose a statistical framework built on latent variable modeling for scaling laws of large language models (LLMs). Our work is motivated by the rapid emergence of numerous new LLM families with distinct architectures and training strategies, evaluated on an increasing number of benchmarks. This heterogeneity makes a single global scaling curve inadequate for capturing how performance varies across families and benchmarks. To address this, we propose a latent variable modeling framework in which each LLM family is associated with a latent variable that captures the common underlying features in that family. An LLM's performance on different benchmarks is then driven by its latent skills, which are jointly determined by the latent variable and the model's own observable features. We develop an estimation procedure for this latent variable model and establish its statistical properties. We also design efficient numerical algorithms that support estimation and various downstream tasks. Empirically, we evaluate the approach on 12 widely used benchmarks from the Open LLM Leaderboard (v1/v2).

stat.AP↗

arXiv2025

Bridging Human and LLM Judgments: Understanding and Narrowing the Gap

Large language models are increasingly used as judges (LLM-as-a-judge) to evaluate model outputs at scale, but their assessments often diverge systematically from human judgments. We present Bridge, a unified statistical framework that explicitly bridges human and LLM evaluations under both absolute scoring and pairwise comparison paradigms. Bridge posits a latent human preference score for each prompt-response pair and models LLM deviations as linear transformations of covariates that capture sources of discrepancies. This offers a simple and principled framework for refining LLM ratings and characterizing systematic discrepancies between humans and LLMs. We provide an efficient fitting algorithm with asymptotic guarantees for statistical inference. Using six LLM judges and two benchmarks (BigGen Bench and Chatbot Arena), Bridge achieves higher agreement with human ratings (accuracy, calibration, and KL divergence) and exposes systematic human-LLM gaps.

cs.LG↗

arXiv2025

Identifiability and Inference for Generalized Latent Factor Models

Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and social sciences. Ensuring the identifiability of latent factors and the loading matrix is essential for the model's estimability and interpretability, and various identifiability conditions have been employed by practitioners. However, fundamental statistical inference issues for latent factors and factor loadings under commonly used identifiability conditions remain largely unaddressed, especially for correlated factors and/or non-orthogonal loading matrix. In this work, we focus on the maximum likelihood estimation for generalized factor models and establish statistical inference properties under popularly used identifiability conditions. The developed theory is further illustrated through numerical simulations and an application to a personality assessment dataset.

stat.ME↗

arXiv2025

Recurrent Event Analysis with Ordinary Differential Equations

This paper introduces a general framework for analyzing recurrent event data by modeling the conditional mean function of the recurrent event process as the solution to an Ordinary Differential Equation (ODE). This approach not only accommodates a wide range of semi-parametric recurrent event models, including both non-homogeneous Poisson processes (NHPPs) and non-Poisson processes, but also is scalable and easy-to-implement. Based on this framework, we propose a Sieve Maximum Pseudo-Likelihood Estimation (SMPLE) method, employing the NHPP as a working model. We establish the consistency and asymptotic normality of the proposed estimator, demonstrating that it achieves semi-parametric efficiency when the NHPP working model is valid. Furthermore, we develop an efficient resampling procedure to estimate the asymptotic covariance matrix. To assess the statistical efficiency and computational scalability of the proposed method, we conduct extensive numerical studies, including simulations under various settings and an application to a real-world dataset analyzing risk factors associated with Intensive Care Unit (ICU) readmission frequency.

stat.ME↗

arXiv2025

Accounting for Measurement Bias: A New Framework for Reliable Country Ranking in Large-Scale Educational Assessments

International Large-scale Assessments (ILSAs), such as the Program for International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS), are cornerstone tools for global educational research and policy-making. By benchmarking educational quality and performance trends, these assessments enable countries to evaluate and share effective pedagogical structures. Specifically, ILSAs employ Item Response Theory (IRT) models to rank countries by students' performance on cognitive items. However, measurement bias--arising from linguistic, cultural, and curricular differences--poses a significant threat to the statistical inference of IRT models and, consequently, the validity of the resulting rankings. Neglecting this bias can lead to systematic errors in parameter estimation, ultimately distorting national standings. To address this, we propose a novel method that avoids the restrictive assumptions typical of existing approaches, such as the prior identification of unbiased anchor items or designated reference groups. Our approach is computationally efficient and provides theoretical guarantees for the reliable recovery of group rankings. We apply this method to PISA 2022 data across the mathematics, science, and reading domains, yielding corrected performance rankings and insights into the survey's measurement-bias structures.

stat.ME↗

arXiv2025

Denoising Diffused Embeddings: a Generative Approach for Hypergraphs

Hypergraph data, which capture multi-way interactions among entities, are increasingly prevalent in the big data era. Generating new hyperlinks from an observed, usually high-dimensional hypergraph is an important yet challenging task with diverse applications in areas such as electronic health record analysis and biological research. This task is fraught with several challenges. The discrete nature of hyperlinks renders many existing generative models inapplicable. Additionally, powerful machine learning-based generative models often operate as black boxes, providing limited interpretability. Key structural characteristics of hypergraphs, including node degree heterogeneity and hyperlink sparsity, further complicate the modeling process and must be carefully addressed. To tackle these challenges, we propose Denoising Diffused Embeddings (DDE), a general and efficient generative modeling architecture for hypergraphs. DDE exploits low-rank structure in high-dimensional hypergraphs via a conditional hyperlink likelihood model that links discrete hyperlinks to a continuous latent embedding space and leverages a score-based diffusion model to reconstruct that space. Theoretically, we show that when true latent embeddings are accessible, DDE exactly reduces the task of generating new high-dimensional hyperlinks to generating new low-dimensional embeddings. Moreover, we analyze the implications of using estimated embeddings in DDE, revealing how hypergraph characteristics such as dimensionality, node degree heterogeneity, and hyperlink sparsity impact its generative performance. Simulation studies demonstrate the superiority of DDE over existing methods, in terms of both computational efficiency and generative performance. Furthermore, an application to a symptom co-occurrence hypergraph derived from electronic medical records uncovers interesting findings and highlights the advantages of DDE.

stat.ME↗

arXiv2024

Quantile Mediation Analytics

Mediation analytics help examine if and how an intermediate variable mediates the influence of an exposure variable on an outcome of interest. Quantiles, rather than the mean, of an outcome are scientifically relevant to the comparison among specific subgroups in practical studies. Albeit some empirical studies available in the literature, there lacks a thorough theoretical investigation of quantile-based mediation analysis, which hinders practitioners from using such methods to answer important scientific questions. To address this significant technical gap, in this paper, we develop a quantile mediation analysis methodology to facilitate the identification, estimation, and testing of quantile mediation effects under a hypothesized directed acyclic graph. We establish two key estimands, quantile natural direct effect (qNDE) and quantile natural indirect effect (qNIE), in the counterfactual framework, both of which have closed-form expressions. To overcome the issue that the null hypothesis of no mediation effect is composite, we establish a powerful adaptive bootstrap method that is shown theoretically and numerically to achieve a proper type I error control. We illustrate the proposed quantile mediation analysis methodology through both extensive simulation experiments and a real-world dataset in that we investigate the mediation effect of lipidomic biomarkers for the influence of exposure to phthalates on early childhood obesity clinically diagnosed by 95\% percentile of body mass index.

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