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Title: On a 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 limitation in modern statistical data analysis. The focus is on the generalization and computation of Tukey's depth for supervised learning in multi-dimensions. Our framework of method-driven halfspace depth emphasizes the importance and properties of the underlying residual space and allows for various distance measures. Moreover, our extension can handle restricted parameter spaces and non-smooth objectives in possibly high dimensions by use of generalized gradients and slack variables. The new formulation of Tukey's depth enables us to utilize state-of-the-art optimization techniques to develop accelerated 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.