发表机构
University of Guelph（圭尔夫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对有限混合回归模型，提出分量加权稀疏组LASSO方法，同时实现组级和个体级变量选择，并通过MM算法优化，在模拟和真实数据中验证有效性。
AI 中文摘要
在分析具有潜在子群体的异质性数据时，有限混合回归（FMR）模型是有效的，因为它们允许回归系数在不同混合分量之间变化。变量选择在两个层面上至关重要：（1）在组层面，通过移除所有子群体中完全无关的协变量；（2）在个体层面，通过移除每个子群体内无关的协变量。然而，现有的FMR变量选择方法仅关注个体层面的回归系数选择，没有提供组层面变量消除的机制。我们提出了一种分量加权稀疏组LASSO正则化方法，该方法在属于指数族的有限混合回归模型中同时进行两个层面的高效变量选择。我们通过Majorization-Minimization算法开发了一种新颖的优化过程。在高斯和泊松混合回归设置下的模拟研究证明了在两个层面都能可靠地恢复真实稀疏结构。该方法通过分析两个真实数据集进行了说明。
英文摘要
When analyzing heterogeneous data with latent subpopulations, finite mixture regression (FMR) models are effective as they allow for variations in regression coefficients across mixture components. Variable selection is important at two levels: (1) at the group level by removing completely irrelevant covariates across all subpopulations and (2) at the individual level by removing irrelevant covariates within each subpopulation. However, existing variable selection methods for FMR focus solely on individual-level regression coefficient selection, providing no mechanism for group-level variable elimination. We introduce a component-weighted sparse group LASSO regularization method that performs efficient variable selection at both levels simultaneously in finite mixture regression models belonging to the exponential family. We develop a novel optimization procedure through a Majorization-Minimization algorithm. Simulation studies under Gaussian and Poisson mixture regression settings demonstrate reliable recovery of the true sparsity structure at both levels. The method is illustrated by analyzing two real datasets.
