arXiv subjects

Gongjun Xu

Publications and source records attributed to Gongjun Xu.

At least 37 records · Page 2Linked to original sources

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).

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arXiv2026

Hyperbolic Network Latent Space Model with Learnable Curvature

Network data is ubiquitous in various scientific disciplines, including sociology, economics, and neuroscience. Latent space models are often employed in network data analysis, but the geometric effect of latent space curvature remains a significant, unresolved issue. In this work, we propose a hyperbolic network latent space model with a learnable curvature parameter. We theoretically justify that learning the optimal curvature is essential to minimizing the embedding error across all hyperbolic embedding methods beyond network latent space models. A maximum-likelihood estimation strategy, employing manifold gradient optimization, is developed, and we establish the consistency and convergence rates for the maximum-likelihood estimators, both of which are technically challenging due to the non-linearity and non-convexity of the hyperbolic distance metric. We further demonstrate the geometric effect of latent space curvature and the superior performance of the proposed model through extensive simulation studies and an application using a Facebook friendship network.

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arXiv2026

Statistical Inference for Covariate-Adjusted and Interpretable Generalized Factor Model with Application to Testing Fairness

Latent variable models are popularly used to measure latent factors (e.g., abilities and personalities) from large-scale assessment data. Beyond understanding these latent factors, the covariate effect on responses controlling for latent factors is also of great scientific interest and has wide applications, such as evaluating the fairness of educational testing, where the covariate effect reflects whether a test question is biased toward certain individual characteristics (e.g., gender and race), taking into account their latent abilities. However, the large sample sizes and test lengths pose challenges to developing efficient methods and drawing valid inferences. Moreover, to accommodate the commonly encountered discrete responses, nonlinear latent factor models are often assumed, adding further complexity. To address these challenges, we consider a covariate-adjusted generalized factor model and develop novel and interpretable conditions to address the identifiability issue. Based on the identifiability conditions, we propose a joint maximum likelihood estimation method and establish estimation consistency and asymptotic normality results for the covariate effects. Furthermore, we derive estimation and inference results for latent factors and the factor loadings. We illustrate the finite sample performance of the proposed method through extensive numerical studies and an educational assessment dataset from the Programme for International Student Assessment (PISA).

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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.

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arXiv2025

A General Latent Embedding Approach for Modeling Non-uniform High-dimensional Sparse Hypergraphs with Multiplicity

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations, including their heavy reliance on uniformity restrictions for hyperlink orders and their inability to account for repeated observations of identical hyperlinks. In this work, we introduce a novel and general latent embedding approach that addresses these challenges through the integration of latent embeddings, vertex degree heterogeneity parameters, and an order-adjusting parameter. Theoretically, we investigate the identifiability conditions for the latent embeddings and associated parameters, and we establish the convergence rates of their estimators along with asymptotic distributions. Computationally, we employ a projected gradient ascent algorithm for parameter estimation. Comprehensive simulation studies demonstrate the effectiveness of the algorithm and validate the theoretical findings. Moreover, an application to a co-citation hypergraph illustrates the advantages of the proposed method.

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arXiv2025

Statistical Inference on Latent Space Models for Network Data

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on point estimation and prediction, leaving the statistical inference of latent space models an open question. This work aims to fill this gap by providing a general framework to analyze the theoretical properties of the maximum likelihood estimators. In particular, we establish the uniform consistency and asymptotic distribution results for the latent space models under different edge types and link functions. Furthermore, the proposed framework enables us to generalize our results to the dependent-edge and sparse scenarios. Our theories are supported by simulation studies and have the potential to be applied in downstream inferences, such as link prediction and network testing problems.

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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.

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arXiv2025

Consistency Theory of General Nonparametric Classification Methods in Cognitive Diagnosis

Cognitive diagnosis models have been popularly used in fields such as education, psychology, and social sciences. While parametric likelihood estimation is a prevailing method for fitting cognitive diagnosis models, nonparametric methodologies are attracting increasing attention due to their ease of implementation and robustness, particularly when sample sizes are relatively small. However, existing clustering consistency results of the nonparametric estimation methods often rely on certain restrictive conditions, which may not be easily satisfied in practice. In this article, the clustering consistency of the general nonparametric classification method is reestablished under weaker and more practical conditions.

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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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arXiv2024

tinyBenchmarks: evaluating LLMs with fewer examples

The versatility of large language models (LLMs) led to the creation of diverse benchmarks that thoroughly test a variety of language models' abilities. These benchmarks consist of tens of thousands of examples making evaluation of LLMs very expensive. In this paper, we investigate strategies to reduce the number of evaluations needed to assess the performance of an LLM on several key benchmarks. For example, we show that to accurately estimate the performance of an LLM on MMLU, a popular multiple-choice QA benchmark consisting of 14K examples, it is sufficient to evaluate this LLM on 100 curated examples. We release evaluation tools and tiny versions of popular benchmarks: Open LLM Leaderboard, MMLU, HELM, and AlpacaEval 2.0. Our empirical analysis demonstrates that these tools and tiny benchmarks are sufficient to reliably and efficiently reproduce the original evaluation results.

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arXiv2024

High-dimensional Factor Analysis for Network-linked Data

Factor analysis is a widely used statistical tool in many scientific disciplines, such as psychology, economics, and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor analysis remains an open problem. In this paper, we focus on high-dimensional factor analysis involving network-connected observations, and propose a generalized factor model with latent factors that account for both the network structure and the dependence structure among high-dimensional variables. These latent factors can be shared by the high-dimensional variables and the network, or exclusively applied to either of them. We develop a computationally efficient estimation procedure and establish asymptotic inferential theories. Notably, we show that by borrowing information from the network, the proposed estimator of the factor loading matrix achieves optimal asymptotic variance under much milder identifiability constraints than existing literature. Furthermore, we develop a hypothesis testing procedure to tackle the challenge of discerning the shared and individual latent factors' structure. The finite sample performance of the proposed method is demonstrated through simulation studies and a real-world dataset involving a statistician co-authorship network.

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arXiv2024

Sufficient and Necessary Conditions for the Identifiability of DINA Models with Polytomous Responses

Cognitive Diagnosis Models (CDMs) provide a powerful statistical and psychometric tool for researchers and practitioners to learn fine-grained diagnostic information about respondents' latent attributes. There has been a growing interest in the use of CDMs for polytomous response data, as more and more items with multiple response options become widely used. Similar to many latent variable models, the identifiability of CDMs is critical for accurate parameter estimation and valid statistical inference. However, the existing identifiability results are primarily focused on binary response models and have not adequately addressed the identifiability of CDMs with polytomous responses. This paper addresses this gap by presenting sufficient and necessary conditions for the identifiability of the widely used DINA model with polytomous responses, with the aim to provide a comprehensive understanding of the identifiability of CDMs with polytomous responses and to inform future research in this field.

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arXiv2024

Variational Estimation for Multidimensional Generalized Partial Credit Model

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap, this paper presents a novel Gaussian variational estimation algorithm for the multidimensional generalized partial credit model (MGPCM). The proposed algorithm demonstrates both fast and accurate performance, as illustrated through a series of simulation studies and two real data analyses.

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arXiv2023

A Note on Improving Variational Estimation for Multidimensional Item Response Theory

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational challenge of estimating MIRT models prohibits its wide use because many of the extant methods can hardly provide results in a realistic time frame when the number of dimensions, sample size, and test length are large. Instead, variational estimation methods, such as Gaussian Variational Expectation Maximization (GVEM) algorithm, have been recently proposed to solve the estimation challenge by providing a fast and accurate solution. However, results have shown that variational estimation methods may produce some bias on discrimination parameters during confirmatory model estimation, and this note proposes an importance weighted version of GVEM (i.e., IW-GVEM) to correct for such bias under MIRT models. We also use the adaptive moment estimation method to update the learning rate for gradient descent automatically. Our simulations show that IW-GVEM can effectively correct bias with modest increase of computation time, compared with GVEM. The proposed method may also shed light on improving the variational estimation for other psychometrics models.

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arXiv2023

High-Dimensional Inference for Generalized Linear Models with Hidden Confounding

Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured confounders associated with both the response and covariates, which can lead to invalidity of standard debiasing methods. This paper focuses on a generalized linear regression framework with hidden confounding and proposes a debiasing approach to address this high-dimensional problem, by adjusting for the effects induced by the unmeasured confounders. We establish consistency and asymptotic normality for the proposed debiased estimator. The finite sample performance of the proposed method is demonstrated through extensive numerical studies and an application to a genetic data set.

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arXiv2023

Incorporating External Risk Information with the Cox Model under Population Heterogeneity: Applications to Trans-Ancestry Polygenic Hazard Scores

Polygenic hazard score (PHS) models designed for European ancestry (EUR) individuals provide ample information regarding survival risk discrimination. Incorporating such information can improve the performance of risk discrimination in an internal small-sized non-EUR cohort. However, given that external EUR-based model and internal individual-level data come from different populations, ignoring population heterogeneity can introduce substantial bias. In this paper, we develop a Kullback-Leibler-based Cox model (CoxKL) to integrate internal individual-level time-to-event data with external risk scores derived from published prediction models, accounting for population heterogeneity. Partial-likelihood-based KL information is utilized to measure the discrepancy between the external risk information and the internal data. We establish the asymptotic properties of the CoxKL estimator. Simulation studies show that the integration model by the proposed CoxKL method achieves improved estimation efficiency and prediction accuracy. We applied the proposed method to develop a trans-ancestry PHS model for prostate cancer and found that integrating a previously published EUR-based PHS with an internal genotype data of African ancestry (AFR) males yielded considerable improvement on the prostate cancer risk discrimination.

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arXiv2023

Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying, estimating, and interpreting the parameters. In this article, we propose a new class of Dimension-Grouped MMMs (Gro-M$^3$s) for multivariate categorical data, which improve parsimony and interpretability. In Gro-M$^3$s, observed variables are partitioned into groups such that the latent membership is constant for variables within a group but can differ across groups. Traditional latent class models are obtained when all variables are in one group, while traditional MMMs are obtained when each variable is in its own group. The new model corresponds to a novel decomposition of probability tensors. Theoretically, we derive transparent identifiability conditions for both the unknown grouping structure and model parameters in general settings. Methodologically, we propose a Bayesian approach for Dirichlet Gro-M$^3$s to inferring the variable grouping structure and estimating model parameters. Simulation results demonstrate good computational performance and empirically confirm the identifiability results. We illustrate the new methodology through applications to a functional disability survey dataset and a personality test dataset.

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arXiv2023

Statistical Inference for Noisy Incomplete Binary Matrix

We consider the statistical inference for noisy incomplete binary (or 1-bit) matrix. Despite the importance of uncertainty quantification to matrix completion, most of the categorical matrix completion literature focuses on point estimation and prediction. This paper moves one step further toward the statistical inference for binary matrix completion. Under a popular nonlinear factor analysis model, we obtain a point estimator and derive its asymptotic normality. Moreover, our analysis adopts a flexible missing-entry design that does not require a random sampling scheme as required by most of the existing asymptotic results for matrix completion. Under reasonable conditions, the proposed estimator is statistically efficient and optimal in the sense that the Cramer-Rao lower bound is achieved asymptotically for the model parameters. Two applications are considered, including (1) linking two forms of an educational test and (2) linking the roll call voting records from multiple years in the United States Senate. The first application enables the comparison between examinees who took different test forms, and the second application allows us to compare the liberal-conservativeness of senators who did not serve in the Senate at the same time.

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