The Maseeh Mathematics and Statistics Colloquium Series*
Sarah Emerson, Ph.D.
Oregon State University
Alternatives to penalization for sparse models
Abstract: Penalized methods, such as the lasso, adaptive lasso, and L2 shrinkage, are employed in a wide variety of high-dimensional problems including regression modeling, covariance matrix estimation and decomposition, and variable selection and clustering. These methods are frequently applied in analysis of genomic data, or more generally in any setting where a large number of predictors are available, with the goal of identifying or discriminating between phenotypes or sub-populations. In some of these settings, particularly where sparsity is desired, it is not clear that the penalization approach or the chosen penalties are an efficient or optimal solution to the problem. While minimizing the sum of absolute values of a collection of parameters, as is done by the lasso (L1) penalty, does produce a sparse solution for most problems, it does not necessarily produce the best sparse solution, and involves the inconvenient choice of tuning parameter value required to obtain a desired level of sparsity. We explore computationally simpler, faster, and more direct approaches to obtaining sparse matrix decompositions and variable selection for clustering, and demonstrate that the resulting solutions are generally superior to the lasso (L1) penalty approach in the sense that for a given degree of sparsity, our solutions retain/recover a higher proportion of the signal present. Furthermore, the proposed approach makes it easier to obtain a solution with a desired sparsity.
Friday, November 9th, 2012 at 3:15pm
Neuberger Hall room 454
(Refreshments served at 3:00 in the presentation room)
* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.