High Dimensional Statistical Theory for Sparse Regularization

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High Dimensional Statistical Theory for Sparse RegularizationThe investigator studies statistical machine learning with sparse regularization in the setting of high dimensional statistical estimation. A number of research directions will be explored, including improved performance bounds for sparse regularization, new sparse learning formulations, and the statistical theory for several important computational algorithms.In the information age, more and more data become available electronically, and these data need to be automatically analyzed by computers in order to filter out the most important information. Statistical machine learning is the main technical tool for analyzing electronic data. Many modern applications involve data in very high dimension that cannot be handled by traditional algorithms. Sparse regularization is an important new statistical machine learning technique that can deal with this issue by effectively identifying the most significant patterns from a vast amount of available information. This research develops new sparse regularization algorithms that will significantly enhance the capability for modern computer systems to find critical information from available electronic data.