@article{zhang_shen_kong_2022, title={Covariance Estimation for Matrix-valued Data}, ISSN={["1537-274X"]}, DOI={10.1080/01621459.2022.2068419}, abstractNote={Abstract Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class of distribution-free regularized covariance estimation methods for high-dimensional matrix data under a separability condition and a bandable covariance structure. Under these conditions, the original covariance matrix is decomposed into a Kronecker product of two bandable small covariance matrices representing the variability over row and column directions. We formulate a unified framework for estimating bandable covariance, and introduce an efficient algorithm based on rank one unconstrained Kronecker product approximation. The convergence rates of the proposed estimators are established, and the derived minimax lower bound shows our proposed estimator is rate-optimal under certain divergence regimes of matrix size. We further introduce a class of robust covariance estimators and provide theoretical guarantees to deal with heavy-tailed data. We demonstrate the superior finite-sample performance of our methods using simulations and real applications from a gridded temperature anomalies dataset and an S&P 500 stock data analysis. Supplementary materials for this article are available online.}, journal={JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION}, author={Zhang, Yichi and Shen, Weining and Kong, Dehan}, year={2022}, month={May} }
 @article{jiang_song_li_zeng_lu_he_xu_wang_qian_cheng_et al._2019, title={ENTROPY LEARNING FOR DYNAMIC TREATMENT REGIMES}, volume={29}, ISSN={["1996-8507"]}, DOI={10.5705/ss.202018.0076}, abstractNote={Estimating optimal individualized treatment rules (ITRs) in single or multi-stage clinical trials is one key solution to personalized medicine and has received more and more attention in statistical community. Recent development suggests that using machine learning approaches can significantly improve the estimation over model-based methods. However, proper inference for the estimated ITRs has not been well established in machine learning based approaches. In this paper, we propose a entropy learning approach to estimate the optimal individualized treatment rules (ITRs). We obtain the asymptotic distributions for the estimated rules so further provide valid inference. The proposed approach is demonstrated to perform well in finite sample through extensive simulation studies. Finally, we analyze data from a multi-stage clinical trial for depression patients. Our results offer novel findings that are otherwise not revealed with existing approaches.}, number={4}, journal={STATISTICA SINICA}, author={Jiang, Binyan and Song, Rui and Li, Jialiang and Zeng, Donglin and Lu, Wenbin and He, Xin and Xu, Shirong and Wang, Junhui and Qian, Min and Cheng, Bin and et al.}, year={2019}, month={Oct}, pages={1633–1710} }
 @article{zhang_laber_davidian_tsiatis_2018, title={Interpretable Dynamic Treatment Regimes}, volume={113}, ISSN={["1537-274X"]}, DOI={10.1080/01621459.2017.1345743}, abstractNote={ABSTRACT Precision medicine is currently a topic of great interest in clinical and intervention science.  A key component of precision medicine is that it is evidence-based, that is, data-driven, and consequently there has been tremendous interest in estimation of precision medicine strategies using observational or randomized study data. One way to formalize precision medicine is through a treatment regime, which is a sequence of decision rules, one per stage of clinical intervention, that map up-to-date patient information to a recommended treatment. An optimal treatment regime is defined as maximizing the mean of some cumulative clinical outcome if applied to a population of interest. It is well-known that even under simple generative models an optimal treatment regime can be a highly nonlinear function of patient information. Consequently, a focal point of recent methodological research has been the development of flexible models for estimating optimal treatment regimes. However, in many settings, estimation of an optimal treatment regime is an exploratory analysis intended to generate new hypotheses for subsequent research and not to directly dictate treatment to new patients. In such settings, an estimated treatment regime that is interpretable in a domain context may be of greater value than an unintelligible treatment regime built using “black-box” estimation methods. We propose an estimator of an optimal treatment regime composed of a sequence of decision rules, each expressible as a list of “if-then” statements that can be presented as either a paragraph or as a simple flowchart that is immediately interpretable to domain experts. The discreteness of these lists precludes smooth, that is, gradient-based, methods of estimation and leads to nonstandard asymptotics. Nevertheless, we provide a computationally efficient estimation algorithm, prove consistency of the proposed estimator, and derive rates of convergence. We illustrate the proposed methods using a series of simulation examples and application to data from a sequential clinical trial on bipolar disorder. Supplementary materials for this article are available online.}, number={524}, journal={JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION}, author={Zhang, Yichi and Laber, Eric B. and Davidian, Marie and Tsiatis, Anastasios A.}, year={2018}, pages={1541–1549} }
 @article{zhang_staicu_maity_2016, title={Testing for additivity in non-parametric regression}, volume={44}, ISSN={["1708-945X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84982980889&partnerID=MN8TOARS}, DOI={10.1002/cjs.11295}, abstractNote={Abstract}, number={4}, journal={CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE}, publisher={Wiley-Blackwell}, author={Zhang, Yichi and Staicu, Ana-Maria and Maity, Arnab}, year={2016}, month={Dec}, pages={445–462} }
 @article{zhang_laber_tsiatis_davidian_2015, title={Using Decision Lists to Construct Interpretable and Parsimonious Treatment Regimes}, volume={71}, ISSN={["1541-0420"]}, DOI={10.1111/biom.12354}, abstractNote={Summary}, number={4}, journal={BIOMETRICS}, author={Zhang, Yichi and Laber, Eric B. and Tsiatis, Anastasios and Davidian, Marie}, year={2015}, month={Dec}, pages={895–904} }