arXiv subjects

Yunxiao Chen

Publications and source records attributed to Yunxiao Chen.

At least 19 recordsLinked to original sources

arXiv2026

Sparse Latent Class Analysis For Dichotomous Responses: Post-Estimation Refinement via Item-level Pseudo-Likelihood

Latent Class Analysis (LCA) is widely used to identify unobserved subgroups in social and behavioural sciences. A long-standing challenge for LCA is the interpretability of the latent classes, due to the high complexity of the estimated item response probability matrix. To address this, we propose a computationally efficient post-estimation refinement procedure that enhances model interpretability by a sparse model estimate. The method begins by estimating a classical, unrestricted, latent class model and determining the number of classes using the Bayesian information criterion (BIC). It is followed by a refinement step that further performs model selection on the item-specific response probabilities based on the initial estimate. This refinement penalises the number of distinct response probability levels per item, collapsing redundant levels to yield a sparse matrix that is significantly easier to interpret than those produced by classical LCA. We provide asymptotic theory showing that the proposed procedure consistently recovers the sparse pattern of the item response probabilities for each item, and further validate its performance through extensive simulations. The practical power of the proposed method is further illustrated via an application to survey data on social role performance, where it provides a parsimonious and clear characterisation of the resulting latent classes. The code for implementing the proposed method is publicly available at https://github.com/florence07/Sparse-LCA-Refinement.

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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

Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applications

Most statistical models for pairwise comparisons, including the Bradley-Terry (BT) and Thurstone models and many extensions, make a relatively strong assumption of stochastic transitivity. This assumption imposes the existence of an unobserved global ranking among all the players/teams/items and monotone constraints on the comparison probabilities implied by the global ranking. However, the stochastic transitivity assumption does not hold in many real-world scenarios of pairwise comparisons, especially games involving multiple skills or strategies. As a result, models relying on this assumption can have suboptimal predictive performance. In this paper, we propose a general family of statistical models for pairwise comparison data without a stochastic transitivity assumption, substantially extending the BT and Thurstone models. In this model, the pairwise probabilities are determined by a (approximately) low-dimensional skew-symmetric matrix. Likelihood-based estimation methods and computational algorithms are developed, which allow for sparse data with only a small proportion of observed pairs. Theoretical analysis shows that the proposed estimator achieves minimax-rate optimality, which adapts effectively to the sparsity level of the data. The spectral theory for skew-symmetric matrices plays a crucial role in the implementation and theoretical analysis. The proposed method's superiority against the BT model, along with its broad applicability across diverse scenarios, is further supported by simulations and real data analysis.

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arXiv2026

Model-free Rank Aggregation in the Presence of Rater Heterogeneity: A Maximum Score Approach

This paper investigates the rank aggregation problem through the lens of multi-way comparison data derived from rater scores. Departing from traditional parametric frameworks, such as the Bradley-Terry and Plackett-Luce models, we propose a model-free method that accommodates highly heterogeneous preference distributions across raters and encompasses weak stochastic transitivity in pairwise comparisons as a special case. We establish the theoretical foundations of the proposed estimator by proving its consistency, demonstrating that the proportion of discordant pairs (Kendall tau) converges to zero in probability as the number of raters diverges. Furthermore, we derive upper and lower bounds for a performance metric based on Kendall's tau. In certain asymptotic regimes, these bounds coincide up to logarithmic factors, so the estimator is nearly minimax optimal. These results are obtained by analyzing the convergence behavior of a U-empirical process; the novel technical results developed for this analysis may be of independent theoretical interest. The practical utility of our method is validated through extensive simulations and applications to sports player rankings and survey preference aggregation.

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arXiv2026

Learning Perturbations to Extrapolate Your LLM

Recent advancements in large language models demonstrate that injecting perturbations can substantially enhance extrapolation performance. However, current approaches often rely on discrete perturbations with fixed designs, which limits their flexibility. In this work, we propose a framework where token prefixes are perturbed by a learnable transformation of a continuous latent vector within an embedding space. To overcome the challenge of an intractable marginal likelihood, we derive unbiased estimating equations for model parameters and optimize them via stochastic gradient descent. We establish the statistical properties of the resulting estimator in over-parameterized regimes. Empirical evaluations on both synthetic and real-world datasets demonstrate that our proposal yields significant gains in out-of-domain settings over a range of state-of-the-art baseline methods.

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arXiv2026

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.

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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

A Generalized Additive Partial-Mastery Cognitive Diagnosis Model

Cognitive diagnosis models (CDMs) are restricted latent class models widely used to measure attributes of interest in diagnostic assessments across education, psychology, biomedical sciences, and related fields. Partial-mastery CDMs (PM-CDMs) are an important extension of CDMs. They model individuals' status for each attribute as continuous to measure partial mastery levels, thereby relaxing the restrictive discrete-attribute assumption of classical CDMs. As a result, PM-CDMs often yield better fits to real-world data and more refined measurements of the substantive attributes of interest. However, these models inherit strong parametric assumptions from traditional CDMs about item response functions and thus still face a significant risk of model misspecification. This paper proposes a generalized additive PM-CDM (GaPM-CDM) that substantially relaxes the parametric assumptions of PM-CDMs. This proposal leverages model parsimony and interpretability by modeling each item response function as a mixture of nonparametric monotone functions of attributes. A method for estimating GaPM-CDM is developed that combines the marginal maximum likelihood estimator with a sieve approximation of the nonparametric functions. The new model is applicable in both confirmatory and exploratory settings, depending on whether prior knowledge of the relationship between observed variables and attributes is available. The proposed method is evaluated and compared with PM-CDMs through extensive simulation studies and further applied to two measurement problems from educational testing and healthcare research, respectively.

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arXiv2026

Exploratory Hierarchical Factor Analysis with an Application to Psychological Measurement

Hierarchical factor models, which include the bifactor model as a special case, are useful in social and behavioural sciences for measuring hierarchically structured constructs. Specifying a hierarchical factor model involves imposing hierarchically structured zero constraints on a factor loading matrix, which is often challenging. Therefore, an exploratory analysis is needed to learn the hierarchical factor structure from data. Unfortunately, there does not exist an identifiability theory for the learnability of this hierarchical structure, nor a computationally efficient method with provable performance. The method of Schmid-Leiman transformation, which is often regarded as the default method for exploratory hierarchical factor analysis, is flawed and likely to fail. The contribution of this paper is three-fold. First, an identifiability result is established for general hierarchical factor models, which shows that the hierarchical factor structure is learnable under mild regularity conditions. Second, a computationally efficient divide-and-conquer approach is proposed for learning the hierarchical factor structure. Finally, asymptotic theory is established for the proposed method, showing that it can consistently recover the true hierarchical factor structure as the sample size grows to infinity. The power of the proposed method is shown via simulation studies and a real data application to a personality test. The computation code for the proposed method is publicly available at https://github.com/EmetSelch97/EHFA/.

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arXiv2025

A Latent Variable Approach to Learning High-dimensional Multivariate longitudinal Data

High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for drawing statistical inferences on covariate effects and predicting future outcomes based on high-dimensional multivariate longitudinal data. This model introduces unobserved factors to account for the between-variable and across-time dependence and assist the prediction. Statistical inference and prediction tools are developed under a general setting that allows outcome variables to be of mixed types and possibly unobserved for certain time points, for example, due to right censoring. A central limit theorem is established for drawing statistical inferences on regression coefficients. Additionally, an information criterion is introduced to choose the number of factors. The proposed model is applied to customer grocery shopping records to predict and understand shopping behavior.

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arXiv2025

Boosting Stochastic Optimisation for High-dimensional Latent Variable Models

Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have become more common. However, estimating such models via marginal maximum likelihood is computationally challenging because it requires evaluating a large number of high-dimensional integrals. Stochastic optimisation, which combines stochastic approximation and sampling techniques, has been shown to be effective. It iterates between sampling latent variables from their posterior distribution under current parameter estimates and updating the model parameters using an approximate stochastic gradient constructed from the latent variable samples. In this paper, we investigate strategies to improve the performance of stochastic optimisation for high-dimensional latent variable models. The improvement is achieved through two strategies: a Metropolis-adjusted Langevin sampler that uses the gradient of the negative complete-data log-likelihood to sample latent variables efficiently, and a minibatch gradient technique that uses only a subset of observations when sampling latent variables and constructing stochastic gradients. Our simulation studies show that combining these strategies yields the best overall performance among competitors. An application to a personality test with 30 latent dimensions further demonstrates that the proposed algorithm scales effectively to high-dimensional settings.

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arXiv2025

A Latent Variable Framework for Multiple Imputation with Non-ignorable Missingness: Analyzing Perceptions of Social Justice in Europe

This paper proposes a general multiple imputation approach for analyzing large-scale data with missing values. An imputation model is derived from a joint distribution induced by a latent variable model, which can flexibly capture associations among variables of mixed types. The model also allows for missingness which depends on the latent variables and is thus non-ignorable with respect to the observed data. We develop a frequentist multiple imputation method for this framework and provide asymptotic theory that establishes valid inference for a broad class of analysis models. Simulation studies confirm the method's theoretical properties and robust practical performance. The procedure is applied to a cross-national analysis of individuals' perceptions of justice and fairness of income distributions in their societies, using data from the European Social Survey which has substantial nonresponse. The analysis demonstrates that failing to account for non-ignorable missingness can yield biased conclusions; for instance, complete-case analysis is shown to exaggerate the correlation between personal income and perceived fairness of income distributions in society. Code implementing the proposed methodology is publicly available at https://anonymous.4open.science/r/non-ignorable-missing-data-imputation-E885.

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arXiv2025

A Latent Variable Model with Change-Points and Its Application to Time Pressure Effects in Educational Assessment

Educational assessments are valuable tools for measuring student knowledge and skills, but their validity can be compromised when test takers exhibit changes in response behavior due to factors such as time pressure. To address this issue, we introduce a novel latent factor model with change-points for item response data, designed to detect and account for individual-level shifts in response patterns during testing. This model extends traditional Item Response Theory (IRT) by incorporating person-specific change-points, which enables simultaneous estimation of item parameters, person latent traits, and the location of behavioral changes. We evaluate the proposed model through extensive simulation studies, which demonstrate its ability to accurately recover item parameters, change-point locations, and individual ability estimates under various conditions. Our findings show that accounting for change-points significantly reduces bias in ability estimates, particularly for respondents affected by time pressure. Application of the model to two real-world educational testing datasets reveals distinct patterns of change-point occurrence between high-stakes and lower-stakes tests, providing insights into how test-taking behavior evolves during the tests. This approach offers a more nuanced understanding of test-taking dynamics, with important implications for test design, scoring, and interpretation.

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arXiv2025

Exact Exploratory Bi-factor Analysis: A Constraint-based Optimisation Approach

Bi-factor analysis is a form of confirmatory factor analysis widely used in psychological and educational measurement. The use of a bi-factor model requires the specification of an explicit bi-factor structure on the relationship between the observed variables and the group factors. In practice, the bi-factor structure is sometimes unknown, in which case an exploratory form of bi-factor analysis is needed to find the bi-factor structure. Unfortunately, there are few methods for exploratory bi-factor analysis, with the exception of a rotation-based method proposed in Jennrich and Bentler (2011, 2012). However, this method only finds approximate bi-factor structures, as it does not yield an exact bi-factor loading structure, even after applying hard thresholding. In this paper, we propose a constraint-based optimisation method that learns an exact bi-factor loading structure from data, overcoming the issue with the rotation-based method. The key to the proposed method is a mathematical characterisation of the bi-factor loading structure as a set of equality constraints, which allows us to formulate the exploratory bi-factor analysis problem as a constrained optimisation problem in a continuous domain and solve the optimisation problem with an augmented Lagrangian method. The power of the proposed method is shown via simulation studies and a real data example. Extending the proposed method to exploratory hierarchical factor analysis is also discussed. The codes are available on ``https://anonymous.4open.science/r/Bifactor-ALM-method-757D".

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arXiv2025

Sequential Change Point Detection with FDR Control in Reconfigurable Sensor Networks

This paper investigates sequential change-point detection in reconfigurable sensor networks. In this problem, data from multiple sensors are observed sequentially. Each sensor can have a unique change point, and the data distribution differs before and after the change. We aim to detect these changes as quickly as possible once they have occurred while controlling the false discovery rate at all times. Our setting is more realistic than traditional settings in that (1) the set of active sensors - i.e., those from which data can be collected - can change over time through the deactivation of existing sensors and the addition of new sensors, and (2) dependencies can occur both between sensors and across time points. We propose powerful e-value-based detection procedures that control the false discovery rate uniformly over time. Numerical experiments demonstrate that, with the same false discovery rate target, our procedures achieve superior performance compared to existing methods, exhibiting lower false non-discovery rates and reduced detection delays.

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arXiv2025

Dynamic Factor Analysis of High-dimensional Recurrent Events

Recurrent event time data arise in many studies, including biomedicine, public health, marketing, and social media analysis. High-dimensional recurrent event data involving many event types and observations have become prevalent with advances in information technology. This paper proposes a semiparametric dynamic factor model for the dimension reduction of high-dimensional recurrent event data. The proposed model imposes a low-dimensional structure on the mean intensity functions of the event types while allowing for dependencies. A nearly rate-optimal smoothing-based estimator is proposed. An information criterion that consistently selects the number of factors is also developed. Simulation studies demonstrate the effectiveness of these inference tools. The proposed method is applied to grocery shopping data, for which an interpretable factor structure is obtained.

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arXiv2024

When Composite Likelihood Meets Stochastic Approximation

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally intractable. While composite likelihood has computational advantages, it can still be demanding when dealing with numerous likelihood components and a large sample size. This paper tackles this challenge by employing an approximation of the conventional composite likelihood estimator, which is derived from an optimization procedure relying on stochastic gradients. This novel estimator is shown to be asymptotically normally distributed around the true parameter. In particular, based on the relative divergent rate of the sample size and the number of iterations of the optimization, the variance of the limiting distribution is shown to compound for two sources of uncertainty: the sampling variability of the data and the optimization noise, with the latter depending on the sampling distribution used to construct the stochastic gradients. The advantages of the proposed framework are illustrated through simulation studies on two working examples: an Ising model for binary data and a gamma frailty model for count data. Finally, a real-data application is presented, showing its effectiveness in a large-scale mental health survey.

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arXiv2024

Unfolding the Network of Peer Grades: A Latent Variable Approach

Peer grading is an educational system in which students assess each other's work. It is commonly applied under Massive Open Online Course (MOOC) and offline classroom settings. With this system, instructors receive a reduced grading workload, and students enhance their understanding of course materials by grading others' work. Peer grading data have a complex dependence structure, for which all the peer grades may be dependent. This complex dependence structure is due to a network structure of peer grading, where each student can be viewed as a vertex of the network, and each peer grade serves as an edge connecting one student as a grader to another student as an examinee. This paper introduces a latent variable model framework for analyzing peer grading data and develops a fully Bayesian procedure for its statistical inference. This framework has several advantages. First, when aggregating multiple peer grades, the average score and other simple summary statistics fail to account for grader effects and, thus, can be biased. The proposed approach produces more accurate model parameter estimates and, therefore, more accurate aggregated grades, by modeling the heterogeneous grading behavior with latent variables. Second, the proposed method provides a way to assess each student's performance as a grader, which may be used to identify a pool of reliable graders or generate feedback to help students improve their grading. Third, our model may further provide insights into the peer grading system by answering questions such as whether a student who performs better in coursework also tends to be a more reliable grader. Finally, thanks to the Bayesian approach, uncertainty quantification is straightforward when inferring the student-specific latent variables as well as the structural parameters of the model. The proposed method is applied to two real-world datasets.

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