Exploiting Sparsity and Structure in Parametric and Nonparametric Estimation
John Lafferty, Carnegie Mellon University
February 20, 2007
We present new results on sparse estimation in both the parametric setting for graphical models, and in the nonparametric setting for regression in high dimensions. For graphical models, we use l1 regularization to estimate the structure of the underlying graph in the high dimensional setting. In the case of nonparametric regression, we present a method that regularizes the derivatives of an estimator, resulting in a type of nonparametric lasso technique. In addition, we discuss the problem of semi-supervised learning, where unlabeled data is used in an attempt to improve estimation. We analyze some current regularization methods in terms of minimax theory, and develop new methods that lead to improved rates of convergence. Joint work with Han Liu, Pradeep Ravikumar, Martin Wainwright, and Larry Wasserman.
John Lafferty is a professor in the Computer Science Department and the Machine Learning Department within the School of Computer Science at Carnegie Mellon University. His research interests are in machine learning, statistical learning theory, computational statistics, natural language processing, information theory, and information retrieval. Prof. Lafferty received the Ph.D. in Mathematics from Princeton University, where he was a member of the Program in Applied and Computational Mathematics. Before joining the faculty of CMU, he was a Research Staff Member at the IBM Thomas J. Watson Research Center as a Research Staff Member, working in Frederick Jelinek's group on statistical natural language processing. Prof. Lafferty currently serves as co-Director, with Steve Fienberg, of CMU's Ph.D. Program in Computational and Statistical Learning, and as an associate editor of the Journal of Machine Learning Research. His first glimpse of the power and magic of combining statistics and computation--in the practice of what has come to be called machine learning--was seeing the first decodings emerge from the IBM statistical machine translation system in the late 1980s.