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B0541
Title: Optimal and safe estimation for high-dimensional semi-supervised learning Authors:  Yang Ning - Cornell University (United States) [presenting]
Abstract: The estimation problem in high-dimensional semi-supervised learning is considered. The goal is to investigate when and how the unlabeled data can be exploited to improve the estimation of the regression parameters of a linear model in light of the fact that such linear models may be misspecified in data analysis. We first establish the minimax lower bound for parameter estimation in the semi-supervised setting. We show that the supervised estimators using the labeled data only cannot attain this lower bound. When the conditional mean function is correctly specified, we propose an optimal semi-supervised estimator which attains the lower bound and therefore improves the rate of the supervised estimators. To alleviate the strong requirement for this optimal estimator, we further propose a safe semi-supervised estimator. We view it safe, because this estimator remains minimax optimal when the conditional mean function is correctly specified, and is always at least as good as the supervised estimators. Furthermore, we extend our idea to aggregate multiple semi-supervised estimators caused by different misspecifications of the conditional mean function. Extensive numerical simulations and a real data analysis are conducted to illustrate our theoretical results.