Hongzhe Zhang

Hongzhe Zhang, Xiaohang Zhao, Xiao Fang et al.

Disaster response is critical to save lives and reduce damages in the aftermath of a disaster. Fundamental to disaster response operations is the management of disaster relief resources. To this end, a local agency (e.g., a local emergency resource distribution center) collects demands from local communities affected by a disaster, dispatches available resources to meet the demands, and requests more resources from a central emergency management agency (e.g., Federal Emergency Management Agency in the U.S.). Prior resource management research for disaster response overlooks the problem of deciding optimal quantities of resources requested by a local agency. In response to this research gap, we define a new resource management problem that proactively decides optimal quantities of requested resources by considering both currently unfulfilled demands and future demands. To solve the problem, we take salient characteristics of the problem into consideration and develop a novel deep learning method for future demand prediction. We then formulate the problem as a stochastic optimization model, analyze key properties of the model, and propose an effective solution method to the problem based on the analyzed properties. We demonstrate the superior performance of our method over prevalent existing methods using both real world and simulated data. We also show its superiority over prevalent existing methods in a multi-stakeholder and multi-objective setting through simulations.

Hongzhe Zhang, Hongzhe Li

Ridge regression with random coefficients provides an important alternative to fixed coefficients regression in high dimensional setting when the effects are expected to be small but not zeros. This paper considers estimation and prediction of random coefficient ridge regression in the setting of transfer learning, where in addition to observations from the target model, source samples from different but possibly related regression models are available. The informativeness of the source model to the target model can be quantified by the correlation between the regression coefficients. This paper proposes two estimators of regression coefficients of the target model as the weighted sum of the ridge estimates of both target and source models, where the weights can be determined by minimizing the empirical estimation risk or prediction risk. Using random matrix theory, the limiting values of the optimal weights are derived under the setting when $p/n \rightarrow γ$, where $p$ is the number of the predictors and $n$ is the sample size, which leads to an explicit expression of the estimation or prediction risks. Simulations show that these limiting risks agree very well with the empirical risks. An application to predicting the polygenic risk scores for lipid traits shows such transfer learning methods lead to smaller prediction errors than the single sample ridge regression or Lasso-based transfer learning.

Hongzhe Zhang, Arnab Auddy, Hongzhe Lee

Linear discriminant analysis is a widely used method for classification. However, the high dimensionality of predictors combined with small sample sizes often results in large classification errors. To address this challenge, it is crucial to leverage data from related source models to enhance the classification performance of a target model. We propose to address this problem in the framework of transfer learning. In this paper, we present novel transfer learning methods via regularized random-effects linear discriminant analysis, where the discriminant direction is estimated as a weighted combination of ridge estimates obtained from both the target and source models. Multiple strategies for determining these weights are introduced and evaluated, including one that minimizes the estimation risk of the discriminant vector and another that minimizes the classification error. Utilizing results from random matrix theory, we explicitly derive the asymptotic values of these weights and the associated classification error rates in the high-dimensional setting, where $p/n \rightarrow γ$, with $p$ representing the predictor dimension and $n$ the sample size. We also provide geometric interpretations of various weights and a guidance on which weights to choose. Extensive numerical studies, including simulations and analysis of proteomics-based 10-year cardiovascular disease risk classification, demonstrate the effectiveness of the proposed approach.

Hongzhe Zhang, Jiasheng Shi, Jing Huang

Matching methods are widely used to reduce confounding effects in observational studies, but conventional approaches often treat all covariates as equally important, which can result in poor performance when covariates differ in their relevance to the study. We propose the Priority-Aware one-to-one Matching Algorithm (PAMA), a novel semi-supervised framework that learns a covariate importance measure from a subset data of units that are paired by experts and uses it to match additional units. It optimizes a weighted quadratic score that reflects the relevance between each covariate and the study, and iteratively updates the covariate importance measure in the score function using unlabeled data. PAMA is model-free, but we have established that the covariate importance measure -- the learned weights -- is consistent when the oracle matching rule aligns with the design. In addition, we introduce extensions that address imbalanced data, accommodate temporal covariates, and improve robustness to mispaired observations. In simulations, PAMA outperforms standard methods, particularly in high-dimensional settings and under model misspecification. Applied to a real-world study of in-person schooling and COVID-19 transmission, PAMA recovers nearly twice as many expert-designated matches as competing methods using baseline covariates. A self-taught learning extension improves performance in simulations, though its benefit is context-dependent. To our knowledge, PAMA is the first framework to apply semi-supervised learning to observational matching with covariates of unequal relevance. It offers a scalable and interpretable tool for incorporating expert insight into policy-relevant observational research.