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Information technology has enabled collection of massive amounts of data in science, engineering, social science, finance and beyond. Extracting useful information from massive and high-dimensional data is the focus of today's statistical research and practice. After broad success of statistical machine learning on prediction through regularization, interpretability is gaining attention and sparsity is being used as its proxy.
With the virtues of both regularization and sparsity, sparse modeling methods (e.g. Lasso) has attracted much attention for theoretial research and for data modeling.
This talk discusses both theory and practice of sparse modeling. First we present some recent theoretical results on bounding L2-estimation error (when p>>n) for a class of M-estimation methods with decomposable penalties. As special cases, our results cover Lasso, L1-penalized GLMs, grouped Lasso, and low-rank sparse matrix estimation. Second we present on-going research on "subject-imaging" supported by an NSF-CDI grant.
This project employs sparse methods to derive lists of words
("subject-image") that associate with a particular word (e.g. "Microsoft") in, for example, New York Times articles. The lists generated by Lasso is found in a randomized human subject experiment to be the best overall method when compared with other sparse methods, regardless of pre-processing choices.
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