Pursuing Sources of Heterogeneity in Modeling Clustered Population
University of Connecticut（康涅狄格大学）；Jiangxi University of Finance and Economics（江西财经大学）；Yale School of Public Health（耶鲁公共卫生学院）；University of California, Riverside（加州大学河滨分校）；University of Connecticut Health Center（康涅狄格大学健康中心）
Yan Li, Chun Yu, Yize Zhao, Robert H. Aseltine, Weixin Yao, Kun Chen
Researchers often have to deal with heterogeneous population with mixed regression relationships, increasingly so in the era of data explosion. In such problems, when there are many candidate predictors, it is not only of interest to identify the predictors that are associated with the outcome, but also to distinguish the true sources of heterogeneity, i.e., to identify the predictors that have different effects among the clusters and thus are the true contributors to the formation of the clusters. We clarify the concepts of the source of heterogeneity that account for potential scale differences of the clusters and propose a regularized finite mixture effects regression to achieve heterogeneity pursuit and feature selection simultaneously. As the name suggests, the problem is formulated under an effects-model parameterization, in which the cluster labels are missing and the effect of each predictor on the outcome is decomposed to a common effect term and a set of cluster-specific terms. A constrained sparse estimation of these effects leads to the identification of both the variables with common effects and those with heterogeneous effects. We propose an efficient algorithm and show that our approach can achieve both estimation and selection consistency. Simulation studies further demonstrate the effectiveness of our method under various practical scenarios. Three applications are presented, namely, an imaging genetics study for linking genetic factors and brain neuroimaging traits in Alzheimer's disease, a public health study for exploring the association between suicide risk among adolescents and their school district characteristics, and a sport analytics study for understanding how the salary levels of baseball players are associated with their performance and contractual status.
Cluster-induced target shift and synthetic approximation for high-dimensional clustered data
Florida International University（佛罗里达国际大学）；University of Nottingham Ningbo China（诺丁汉大学宁波校区）；University of Pennsylvania（宾夕法尼亚大学）；Dartmouth College（达特茅斯学院）；Oklahoma State University（俄克拉荷马州立大学）
A new method for clustered survival data]{A new method for clustered survival data: Estimation of treatment effect heterogeneity and variable selection
Structural grouping of extreme value models via graph fused lasso
Graduate School of Science and Engineering, Kagoshima University（鹿儿岛大学理工学研究科）；Data Science and AI Innovation Research Promotion Center, Shiga University（滋贺大学数据科学与AI创新研究促进中心）；Faculty of Mathematics, Kyushu University（九州大学数学系）
In diverse fields ranging from finance to omics, it is increasingly common that data is distributed and with multiple individual sources (referred to as ``clients'' in some studies). Integrating raw data, although powerful, is often not feasible, for example, when there are considerations on privacy protection. Distributed learning techniques have been developed to integrate summary statistics as opposed to raw data. In many of the existing distributed learning studies, it is stringently assumed that all the clients have the same model. To accommodate data heterogeneity, some federated learnin…
Rare populations, such as endangered species, drug users and individuals infected by rare diseases, tend to cluster in regions. Adaptive cluster designs are generally applied to obtain information from clustered and sparse populations. The aim of this work is to propose a unit-level mixture model for clustered and sparse populations when the data are obtained from an adaptive cluster sample. Our approach considers heterogeneity among units belonging to different clusters. The proposed model is evaluated using simulated data and a real experiment in which adaptive samples were drawn from an enu…
Tsinghua University（清华大学）；University of Connecticut（康涅狄格大学）；University of Michigan（密歇根大学）；Cornell University（康奈尔大学）
Finite Mixture Regression (FMR) refers to the mixture modeling scheme which learns multiple regression models from the training data set. Each of them is in charge of a subset. FMR is an effective scheme for handling sample heterogeneity, where a single regression model is not enough for capturing the complexities of the conditional distribution of the observed samples given the features. In this paper, we propose an FMR model that 1) finds sample clusters and jointly models multiple incomplete mixed-type targets simultaneously, 2) achieves shared feature selection among tasks and cluster comp…
New York University（纽约大学）；North Carolina State University（北卡罗来纳州立大学）；University of California, Berkeley（加利福尼亚大学伯克利分校）
Reinforcement Learning (RL) has the promise of providing data-driven support for decision-making in a wide range of problems in healthcare, education, business, and other domains. Classical RL methods focus on the mean of the total return and, thus, may provide misleading results in the setting of the heterogeneous populations that commonly underlie large-scale datasets. We introduce the K-Heterogeneous Markov Decision Process (K-Hetero MDP) to address sequential decision problems with population heterogeneity. We propose the Auto-Clustered Policy Evaluation (ACPE) for estimating the value of …
Two-stage Least Squares with Clustered Data under the Local Average Treatment Effect Framework
Fuqua School of Business, Duke University（杜克大学福库商学院）；Department of Statistics, University of California, Berkeley（加州大学伯克利分校统计学系）；Department of Statistical Sciences, Duke University（杜克大学统计科学系）
A recent literature in econometrics models unobserved cross-sectional heterogeneity in panel data by assigning each cross-sectional unit a one-dimensional, discrete latent type. Such models have been shown to allow estimation and inference by regression clustering methods. This paper is motivated by the finding that the clustered heterogeneity models studied in this literature can be badly misspecified, even when the panel has significant discrete cross-sectional structure. To address this issue, we generalize previous approaches to discrete unobserved heterogeneity by allowing each unit to ha…
With the advent of ubiquitous monitoring and measurement protocols, studies have started to focus more and more on complex, multivariate and heterogeneous datasets. In such studies, multivariate response variables are drawn from a heterogeneous population often in the presence of additional covariate information. In order to deal with this intrinsic heterogeneity, regression analyses have to be clustered for different groups of units. Up until now, mixture model approaches assigned units to distinct and non-overlapping groups. However, not rarely these units exhibit more complex organization a…
Healthcare cost prediction is a challenging task due to the high-dimensionality and high correlation among covariates. Additionally, the skewed, heavy-tailed, and often multi-modal nature of cost data can complicate matters further due to unobserved heterogeneity. In this study, we propose a novel framework for finite mixture regression models that incorporates covariate clustering methods to better account for the effects of clustered covariates on subgroups of the outcome, which enables a more accurate characterization of the complex distribution of the data. The proposed framework can be fo…
