arXiv subjects

Xiaoou Li

Publications and source records attributed to Xiaoou Li.

At least 19 recordsLinked to original sources

arXiv2026

On the Asymptotics of Item Selection in Multidimensional Computerized Adaptive Testing

We study Fisher-information-based item-selection rules for multidimensional computerized adaptive testing (MCAT) with intentional and nuisance abilities. Although such rules are widely used, rigorous asymptotic theory for the coupled dynamics of adaptive selection and latent-trait estimation remains limited. We consider a weighted A-optimality criterion that prioritizes intentional abilities while controlling accuracy in nuisance dimensions. For the multidimensional two-parameter logistic model, we first establish asymptotic optimality under an item-type reuse regime: paired with the maximum likelihood estimator, the weighted A-optimal rule attains the minimum asymptotic weighted mean squared error. We then prove consistency and asymptotic normality of the maximum likelihood estimator and express its asymptotic weighted mean squared error through a limiting Fisher information matrix. We also extend the analysis to the operational setting in which each item is administered at most once. These results justify normal approximations and information-based standard errors in MCAT. A simulation study examines finite-sample behavior at practical test lengths and shows favorable weighted mean squared error, with item-selection patterns consistent with the predicted limiting behavior.

math.ST↗

arXiv2026

Kairos: A Regret-Aware Native World-Action Model Stack for Physical AI

We introduce \textbf{Kairos}, a regret-aware native world-action model stack for Physical AI. Kairos is motivated by the view that a physical world model should not aim to fully simulate all future pixels, but should learn and maintain the information most relevant to embodiment control: object state, spatial relations, contact conditions, task progress, action consequences, failure boundaries, and deployment uncertainty. Kairos establishes three model-side prerequisites toward this goal. First, it \textbf{learns} control-relevant information through a \textbf{Cross-Embodiment Data Curriculum}, which organizes open-world videos, human behavioral data, and robot interactions into an intervention-strength progression from passive physical observation to intentional behavior and embodied action grounding. Second, it \textbf{maintains} control-sufficient states through a unified \textbf{understanding, generation, and prediction architecture} equipped with \textbf{Hybrid Linear Temporal Attention}, where local, mid-range, and global temporal pathways support multi-timescale state maintenance under efficient inference. Third, it \textbf{deploys} these states through a \textbf{Deployment-Aware System Co-Design}, treating latency, memory footprint, and hardware compatibility as first-order constraints for future observation, action, and feedback loops. Experiments on embodied world-model benchmarks, world-action benchmarks, long-horizon generation, and inference-efficiency evaluation show that Kairos achieves superior performance while offering a favorable efficiency to capability trade-off.

cs.AI↗

arXiv2026

Transfer Learning with Network Embeddings under Structured Missingness

Modern data-driven applications increasingly rely on large, heterogeneous datasets collected across multiple sites. Differences in data availability, feature representation, and underlying populations often induce structured missingness, complicating efforts to transfer information from data-rich settings to those with limited data. Many transfer learning methods overlook this structure, limiting their ability to capture meaningful relationships across sites. We propose TransNEST (Transfer learning with Network Embeddings under STructured missingness), a framework that integrates graphical data from source and target sites with prior group structure to construct and refine network embeddings. TransNEST accommodates site-specific features, captures within-group heterogeneity and between-site differences adaptively, and improves embedding estimation under partial feature overlap. We establish the convergence rate for the TransNEST estimator and demonstrate strong finite-sample performance in simulations. We apply TransNEST to a multi-site electronic health record study, transferring feature embeddings from a general hospital system to a pediatric hospital system. Using a hierarchical ontology structure, TransNEST improves pediatric embeddings and supports more accurate pediatric knowledge extraction, achieving the best accuracy for identifying pediatric-specific relational feature pairs compared with benchmark methods.

stat.ME↗

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.

stat.ME↗

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.

stat.ME↗

arXiv2024

Representation-Enhanced Neural Knowledge Integration with Application to Large-Scale Medical Ontology Learning

A large-scale knowledge graph enhances reproducibility in biomedical data discovery by providing a standardized, integrated framework that ensures consistent interpretation across diverse datasets. It improves generalizability by connecting data from various sources, enabling broader applicability of findings across different populations and conditions. Generating reliable knowledge graph, leveraging multi-source information from existing literature, however, is challenging especially with a large number of node sizes and heterogeneous relations. In this paper, we propose a general theoretically guaranteed statistical framework, called RENKI, to enable simultaneous learning of multiple relation types. RENKI generalizes various network models widely used in statistics and computer science. The proposed framework incorporates representation learning output into initial entity embedding of a neural network that approximates the score function for the knowledge graph and continuously trains the model to fit observed facts. We prove nonasymptotic bounds for in-sample and out-of-sample weighted MSEs in relation to the pseudo-dimension of the knowledge graph function class. Additionally, we provide pseudo-dimensions for score functions based on multilayer neural networks with ReLU activation function, in the scenarios when the embedding parameters either fixed or trainable. Finally, we complement our theoretical results with numerical studies and apply the method to learn a comprehensive medical knowledge graph combining a pretrained language model representation with knowledge graph links observed in several medical ontologies. The experiments justify our theoretical findings and demonstrate the effect of weighting in the presence of heterogeneous relations and the benefit of incorporating representation learning in nonparametric models.

stat.ME↗

arXiv2024

Globally-Optimal Greedy Experiment Selection for Active Sequential Estimation

Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequential estimation, which involves adaptively selecting experiments for sequentially collected data. The goal is to design experiment selection rules for more accurate model estimation. Greedy information-based experiment selection methods, optimizing the information gain for one-step ahead, have been employed in practice thanks to their computational convenience, flexibility to context or task changes, and broad applicability. However, statistical analysis is restricted to one-dimensional cases due to the problem's combinatorial nature and the seemingly limited capacity of greedy algorithms, leaving the multidimensional problem open. In this study, we close the gap for multidimensional problems. In particular, we propose adopting a class of greedy experiment selection methods and provide statistical analysis for the maximum likelihood estimator following these selection rules. This class encompasses both existing methods and introduces new methods with improved numerical efficiency. We prove that these methods produce consistent and asymptotically normal estimators. Additionally, within a decision theory framework, we establish that the proposed methods achieve asymptotic optimality when the risk measure aligns with the selection rule. We also conduct extensive numerical studies on both simulated and real data to illustrate the efficacy of the proposed methods. From a technical perspective, we devise new analytical tools to address theoretical challenges. These analytical tools are of independent theoretical interest and may be reused in related problems involving stochastic approximation and sequential designs.

math.ST↗

arXiv2022

A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistency

Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables (e.g., continuous, binary, ordinal). We formulate it as a low-rank matrix estimation problem under a general family of non-linear factor models and then propose entrywise consistent estimators for estimating the low-rank matrix. Tight probabilistic error bounds are derived for the proposed estimators. The proposed methods are evaluated by simulation studies and real-data applications for collaborative filtering and large-scale educational assessment.

stat.ML↗

arXiv2022

Optimal Parallel Sequential Change Detection under Generalized Performance Measures

This paper considers the detection of change points in parallel data streams, a problem widely encountered when analyzing large-scale real-time streaming data. Each stream may have its own change point, at which its data has a distributional change. With sequentially observed data, a decision maker needs to declare whether changes have already occurred to the streams at each time point.Once a stream is declared to have changed, it is deactivated permanently so that its future data will no longer be collected. This is a compound decision problem in the sense that the decision maker may want to optimize certain compound performance metrics that concern all the streams as a whole. Thus, the decisions are not independent for different streams. Our contribution is three-fold. First, we propose a general framework for compound performance metrics that includes the ones considered in the existing works as special cases and introduces new ones that connect closely with the performance metrics for single-stream sequential change detection and large-scale hypothesis testing. Second, data-driven decision procedures are developed under this framework. Finally, optimality results are established for the proposed decision procedures. The proposed methods and theory are evaluated by simulation studies and a case study.

stat.ME↗

arXiv2021

Item Quality Control in Educational Testing: Change Point Model, Compound Risk, and Sequential Detection

In standardized educational testing, test items are reused in multiple test administrations. To ensure the validity of test scores, the psychometric properties of items should remain unchanged over time. In this paper, we consider the sequential monitoring of test items, in particular, the detection of abrupt changes to their psychometric properties, where a change can be caused by, for example, leakage of the item or change of the corresponding curriculum. We propose a statistical framework for the detection of abrupt changes in individual items. This framework consists of (1) a multi-stream Bayesian change point model describing sequential changes in items, (2) a compound risk function quantifying the risk in sequential decisions, and (3) sequential decision rules that control the compound risk. Throughout the sequential decision process, the proposed decision rule balances the trade-off between two sources of errors, the false detection of pre-change items and the non-detection of post-change items. An item-specific monitoring statistic is proposed based on an item response theory model that eliminates the confounding from the examinee population which changes over time. Sequential decision rules and their theoretical properties are developed under two settings: the oracle setting where the Bayesian change point model is completely known and a more realistic setting where some parameters of the model are unknown. Simulation studies are conducted under settings that mimic real operational tests.

stat.AP↗

arXiv2021

Item Response Theory -- A Statistical Framework for Educational and Psychological Measurement

Item response theory (IRT) has become one of the most popular statistical models for psychometrics, a field of study concerned with the theory and techniques of psychological measurement. The IRT models are latent factor models tailored to the analysis, interpretation, and prediction of individuals' behaviors in answering a set of measurement items that typically involve categorical response data. Many important questions of measurement are directly or indirectly answered through the use of IRT models, including scoring individuals' test performances, validating a test scale, linking two tests, among others. This paper provides a review of item response theory, including its statistical framework and psychometric applications. We establish connections between item response theory and related topics in statistics, including empirical Bayes, nonparametric methods, matrix completion, regularized estimation, and sequential analysis. Possible future directions of IRT are discussed from the perspective of statistical learning.

stat.ME↗

arXiv2021

Determining the Number of Factors in High-dimensional Generalized Latent Factor Models

As a generalization of the classical linear factor model, generalized latent factor models are useful for analyzing multivariate data of different types, including binary choices and counts. This paper proposes an information criterion to determine the number of factors in generalized latent factor models. The consistency of the proposed information criterion is established under a high-dimensional setting where both the sample size and the number of manifest variables grow to infinity, and data may have many missing values. An error bound is established for the parameter estimates, which plays an important role in establishing the consistency of the proposed information criterion. This error bound improves several existing results and may be of independent theoretical interest. We evaluate the proposed method by a simulation study and an application to Eysenck's personality questionnaire.

stat.ME↗

arXiv2021

Compound Sequential Change-point Detection in Parallel Data Streams

We consider sequential change-point detection in parallel data streams, where each stream has its own change point. Once a change is detected in a data stream, this stream is deactivated permanently. The goal is to maximize the normal operation of the pre-change streams, while controlling the proportion of post-change streams among the active streams at all time points. Taking a Bayesian formulation, we develop a compound decision framework for this problem. A procedure is proposed that is uniformly optimal among all sequential procedures which control the expected proportion of postchange streams at all time points. We also investigate the asymptotic behavior of the proposed method when the number of data streams grows large. Numerical examples are provided to illustrate the use and performance of the proposed method.

math.ST↗

arXiv2020

A Note on Exploratory Item Factor Analysis by Singular Value Decomposition

We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (2019b) for exploratory Item Factor Analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for joint maximum likelihood estimation in Chen et al. (2019b). Thanks to the analytic and computational properties of SVD, this algorithm guarantees a unique solution and has computational advantage over other exploratory IFA methods. Its computational advantage becomes significant when the numbers of respondents, items, and factors are all large. This algorithm can be viewed as a generalization of principal component analysis (PCA) to binary data. In this note, we provide the statistical underpinning of the algorithm. In particular, we show its statistical consistency under the same double asymptotic setting as in Chen et al. (2019b). We also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory. Further extensions of the algorithm are discussed. Finally, simulation studies suggest that the algorithm has good finite sample performance.

stat.ME↗

arXiv2019

Spherical Regression under Mismatch Corruption with Application to Automated Knowledge Translation

Motivated by a series of applications in data integration, language translation, bioinformatics, and computer vision, we consider spherical regression with two sets of unit-length vectors when the data are corrupted by a small fraction of mismatch in the response-predictor pairs. We propose a three-step algorithm in which we initialize the parameters by solving an orthogonal Procrustes problem to estimate a translation matrix $\mathbb{W}$ ignoring the mismatch. We then estimate a mapping matrix aiming to correct the mismatch using hard-thresholding to induce sparsity, while incorporating potential group information. We eventually obtain a refined estimate for $\mathbb{W}$ by removing the estimated mismatched pairs. We derive the error bound for the initial estimate of $\mathbb{W}$ in both fixed and high-dimensional setting. We demonstrate that the refined estimate of $\mathbb{W}$ achieves an error rate that is as good as if no mismatch is present. We show that our mapping recovery method not only correctly distinguishes one-to-one and one-to-many correspondences, but also consistently identifies the matched pairs and estimates the weight vector for combined correspondence. We examine the finite sample performance of the proposed method via extensive simulation studies, and with application to the unsupervised translation of medical codes using electronic health records data.

stat.ME↗

arXiv2019

Joint Maximum Likelihood Estimation for High-dimensional Exploratory Item Response Analysis

Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them simultaneously by solving an optimization problem. However, the JML estimator is known to be asymptotically inconsistent for many IRT models, when the sample size goes to infinity and the number of items keeps fixed. Consequently, in the psychometrics literature, this estimator is less preferred to the marginal maximum likelihood (MML) estimator. In this paper, we re-investigate the JML estimator for high-dimensional exploratory item factor analysis, from both statistical and computational perspectives. In particular, we establish a notion of statistical consistency for a constrained JML estimator, under an asymptotic setting that both the numbers of items and people grow to infinity and that many responses may be missing. A parallel computing algorithm is proposed for this estimator that can scale to very large datasets. Via simulation studies, we show that when the dimensionality is high, the proposed estimator yields similar or even better results than those from the MML estimator, but can be obtained computationally much more efficiently. An illustrative real data example is provided based on the revised version of Eysenck's Personality Questionaire (EPQ-R).

stat.ME↗

arXiv2019

Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications

Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. When used in a confirmatory manner, design information is incorporated, yielding structured (confirmatory) latent factor models. Motivated by the applications of latent factor models to large-scale measurements which consist of many manifest variables (e.g. test items) and a large sample size, we study the properties of structured latent factor models under an asymptotic setting where both the number of manifest variables and the sample size grow to infinity. Specifically, under such an asymptotic regime, we provide a definition of the structural identifiability of the latent factors and establish necessary and sufficient conditions on the measurement design that ensure the structural identifiability under a general family of structured latent factor models. In addition, we propose an estimator that can consistently recover the latent factors under mild conditions. This estimator can be efficiently computed through parallel computing. Our results shed lights on the design of large-scale measurement and have important implications on measurement validity. The properties of the proposed estimator are verified through simulation studies.

stat.ME↗

arXiv2019

Asymptotic Analysis for Extreme Eigenvalues of Principal Minors of Random Matrices

Consider a standard white Wishart matrix with parameters $n$ and $p$. Motivated by applications in high-dimensional statistics and signal processing, we perform asymptotic analysis on the maxima and minima of the eigenvalues of all the $m \times m$ principal minors, under the asymptotic regime that $n,p,m$ go to infinity. Asymptotic results concerning extreme eigenvalues of principal minors of real Wigner matrices are also obtained. In addition, we discuss an application of the theoretical results to the construction of compressed sensing matrices, which provides insights to compressed sensing in signal processing and high dimensional linear regression in statistics.

math.ST↗