Sarah Emerson, Assistant Professor, Department of Statistics, OSU

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.