arXiv subjects

Wenbo Jing

Publications and source records attributed to Wenbo Jing.

6 recordsLinked to original sources

arXiv2026

Tuning-Free Efficient Estimation for Multi-Source Data via Covariance-Aware Shrinkage

Modern statistical learning problems often involve multiple related data sets, where learning efficiency on a target set can be improved by utilizing related source sets, while heterogeneity among the source sets may introduce bias. Existing approaches are limited by suboptimal performance in multi-source settings, insufficient use of covariance information, or the computational burden of tuning procedures. We propose a tuning-free and covariance-aware shrinkage framework that constructs shrinkage directions using covariance information to improve efficiency. We establish finite-sample risk bounds that yield an explicit risk-improving interval for the shrinkage size, making the procedure fully data-driven and tuning-free. When multiple source sets are available, we further propose a novel sequential algorithm that shrinks the estimator toward the sources one at a time according to their estimated risk reduction. The proposed algorithm asymptotically attains the oracle risk under mild conditions and is guaranteed to improve over the single-step shrinkage method in the literature. The framework is further extended to general smooth $M$-estimation problems via a local quadratic approximation. Numerical studies show substantial gains over competing methods, especially when the source data sets are highly heterogeneous.

stat.ME↗

arXiv2026

Data-Driven Knowledge Transfer in Batch $Q^*$ Learning

In data-driven decision-making in marketing, healthcare, and education, it is desirable to utilize a large amount of data from existing ventures to navigate high-dimensional feature spaces and address data scarcity in new ventures. We explore knowledge transfer in dynamic decision-making by concentrating on batch stationary environments and formally defining task discrepancies through the lens of Markov decision processes (MDPs). We propose a framework of Transferred Fitted $Q$-Iteration algorithm with general function approximation, enabling the direct estimation of the optimal action-state function $Q^*$ using both target and source data. We establish the relationship between statistical performance and MDP task discrepancy under sieve approximation, shedding light on the impact of source and target sample sizes and task discrepancy on the effectiveness of knowledge transfer. We show that the final learning error of the $Q^*$ function is significantly improved from the single task rate both theoretically and empirically.

cs.LG↗

arXiv2025

High-Dimensional Linear Bandits under Stochastic Latent Heterogeneity

This paper addresses the critical challenge of stochastic latent heterogeneity in online decision-making, where individuals' responses to actions vary not only with observable contexts but also with unobserved, randomly realized subgroups. Existing data-driven approaches largely capture observable heterogeneity through contextual features but fail when the sources of variation are latent and stochastic. We propose a latent heterogeneous bandit framework that explicitly models probabilistic subgroup membership and group-specific reward functions, using promotion targeting as a motivating example. Our phased EM-greedy algorithm jointly learns latent group probabilities and reward parameters in high dimensions, achieving optimal estimation and classification guarantees. Our analysis reveals a new phenomenon unique to decision-making with stochastic latent subgroups: randomness in group realizations creates irreducible classification uncertainty, making sub-linear regret against a fully informed strong oracle fundamentally impossible. We establish matching upper and minimax lower bounds for both the strong and regular regrets, corresponding, respectively, to oracles with and without access to realized group memberships. The strong regret necessarily grows linearly, while the regular regret achieves a minimax-optimal sublinear rate. These findings uncover a fundamental stochastic barrier in online decision-making and point to potential remedies through simple strategic interventions and mechanism-design-based elicitation of latent information.

cs.LG↗

arXiv2025

Distributed Tensor Principal Component Analysis with Data Heterogeneity

As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where large-scale tensors are distributed across diverse geographic locations, this paper investigates tensor PCA within a distributed framework where direct data pooling is impractical. We offer a comprehensive analysis of three specific scenarios in distributed Tensor PCA: a homogeneous setting in which tensors at various locations are generated from a single noise-affected model; a heterogeneous setting where tensors at different locations come from distinct models but share some principal components, aiming to improve estimation across all locations; and a targeted heterogeneous setting, designed to boost estimation accuracy at a specific location with limited samples by utilizing transferred knowledge from other sites with ample data. We introduce novel estimation methods tailored to each scenario, establish statistical guarantees, and develop distributed inference techniques to construct confidence regions. Our theoretical findings demonstrate that these distributed methods achieve sharp rates of accuracy by efficiently aggregating shared information across different tensors, while maintaining reasonable communication costs. Empirical validation through simulations and real-world data applications highlights the advantages of our approaches, particularly in managing heterogeneous tensor data.

stat.ME↗

arXiv2024

Distributed Estimation and Inference for Semi-parametric Binary Response Models

The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric binary choice model under a distributed computing environment without pre-specifying the noise distribution. An intuitive divide-and-conquer estimator is computationally expensive and restricted by a non-regular constraint on the number of machines, due to the highly non-smooth nature of the objective function. We propose (1) a one-shot divide-and-conquer estimator after smoothing the objective to relax the constraint, and (2) a multi-round estimator to completely remove the constraint via iterative smoothing. We specify an adaptive choice of kernel smoother with a sequentially shrinking bandwidth to achieve the superlinear improvement of the optimization error over the multiple iterations. The improved statistical accuracy per iteration is derived, and a quadratic convergence up to the optimal statistical error rate is established. We further provide two generalizations to handle the heterogeneity of datasets and high-dimensional problems where the parameter of interest is sparse.

math.ST↗

arXiv2023

A Regression Tree Method for Longitudinal and Clustered Data with Multivariate Responses

RE-EM tree is a tree-based method that combines the regression tree and the linear mixed effects model for modeling univariate response longitudinal or clustered data. In this paper, we generalize the RE-EM tree method to multivariate response data, by adopting the Multivariate Regression Tree method proposed by De'Ath [2002]. The Multivariate RE-EM tree method estimates a population-level single tree structure that is driven by the multiple responses simultaneously and object-level random effects for each response variable, where correlation between the response variables and between the associated random effects are each allowed. Through simulation studies, we verify the advantage of the Multivariate RE-EM tree over the use of multiple univariate RE-EM trees and the Multivariate Regression Tree. We apply the Multivariate RE-EM tree to analyze a real data set that contains multidimensional nonfinancial characteristics of poverty of different countries as responses, and various potential causes of poverty as predictors.

stat.ME↗