报告题目：Centre-augmented L2-type regularization for subgroup learning

报告人：林华珍（西南财经大学统计研究中心，教授）

报告时间：2022年4月15日 19：00-20：30

报告地点：腾讯会议ID：335-790-977

校内联系人：李天然

报告摘要：The existing methods for subgroup analysis can be roughly divided into two categories: finite mixture models (FMM) and regularization methods with an L1 -type penalty. In this paper, by introducing the group centres and L2 -type penalty in the loss function, we propose a novel centre-augmented regularization (CAR) method; this method can be regarded as a unification of the regularization method and FMM and hence exhibits higher efficiency and robustness and simpler computations than the existing methods. Particularly, its computational complexity is reduced from the $O(n^2)$ of the conventional pairwise-penalty method to only $O(nK)$, where n is the sample size and K is the number of subgroups. The asymptotic normality of CAR is established, and the convergence of the algorithm is proven. CAR is applied to a dataset from a multicenter clinical trial: Buprenorphine in the Treatment of Opiate Dependence; a larger $R^2$ is produced and three additional significant variables are identified compared to those of the existing methods.