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Title: On generalization and computation of Tukey's depth Authors:  Yiyuan She - Florida State University (United States) [presenting]
Abstract: Data depth provides a useful tool for nonparametric statistical inference and estimation but also encounters computational difficulties and scope limitations in modern statistical data analysis. The aim is to focus on the generalization and computation of Tukey's depth for supervised learning in multi-dimensions. A general framework of statistic-driven halfspace depth is presented, and on the basis of its connection to classification and M-estimation, we introduce polished data depth as a subspace pursuit problem. By use of generalized gradients and slack variables, we are able to generalize the concept significantly to accommodate restricted parameter spaces and non-smooth objectives in possibly high dimensions. The new formulation of Tukey's depth enables us to utilize state-of-the-art optimization techniques to develop algorithms with implementation ease and guaranteed fast convergence. Simulations and real data examples demonstrate the efficacy of the proposed methodology in statistical inference and estimation.