Extending the use of machine learning algorithms to Sufficient Dimension Reduction

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The investigator develops new methodologies for sufficient dimension reduction both for linear and nonlinear dimension reduction problems. A method developed recently by the investigator and his collaborators utilizes classic two-class Support Vector Machine algorithms to develop a new class of algorithms for linear and nonlinear sufficient dimension reduction under a unified framework. In this work the investigator extends this methodology in several directions. First, different extensions of the classic Support Vector Machine algorithms are used to improve the performance and the asymptotic properties of the original method. Second, the method is extended to algorithms that allow for multi-class classification. Third, the investigator develops new method-specific and method-free variable selection methodologies for sufficient dimension techniques based on ideas in the machine learning literature. Finally, new algorithms for the order determination of the dimension reduction space based on the new methodology are developed.Recent advancements in computer science have increased computer power and, subsequently, the capability of storing large datasets efficiently. Thus, to analyze large datasets effectively in many sciences, like Biology, Meteorology, Genetics and Economics, new techniques are needed to reduce the dimensionality of the datasets. This work creates new algorithms to reduce the dimensionality of large datasets effectively, for both linear or nonlinear relationships between variables. These techniques transform a high-dimensional regression or classification problem to a lower-dimensional one, which helps to identify hidden relationships among variables. The methodology being developed will be an efficient tool for scientists working with large datasets, and it will open new research frontiers to statisticians to develop new ideas in the area of dimension reduction.