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A0182
Title: An efficient greedy search algorithm for high-dimensional linear discriminant analysis Authors:  Quefeng Li - University of North Carolina - Chapel Hill (United States) [presenting]
Abstract: High-dimensional classification is an important statistical problem that has applications in many areas. One widely used classifier is the Linear Discriminant Analysis (LDA). In recent years, many regularized LDA classifiers have been proposed to solve the problem of high-dimensional classification. However, these methods rely on inverting a large matrix or solving large-scale optimization problems to render classification rules: methods that are computationally prohibitive when the dimension is ultra-high. With the emergence of big data, it is increasingly important to develop more efficient algorithms to solve the high-dimensional LDA problem. We propose an efficient greedy search algorithm that depends solely on closed-form formulae to learn a high-dimensional LDA rule. We establish a theoretical guarantee of its statistical properties in terms of variable selection and error rate consistency; in addition, we provide an explicit interpretation of the extra information brought by an additional feature in an LDA problem under some mild distributional assumptions. We demonstrate that this new algorithm drastically improves the computational speed compared with other high-dimensional LDA methods, while maintaining comparable or even better classification performance.