Total Variation (TV) is an effective method of removing noise in digital image processing while preserving edges [23]. The choice of scaling or regularization parameter in the TV process defines the amount of denoising, with value of zero giving a result equivalent to the input signal. Here we explore three algorithms for specifying this parameter based on the statistics of the signal in the to...

Sparsity-promoting L1-regularization has recently been succesfully used to learn the structure of undirected graphical models. In this paper, we apply this technique to learn the structure of directed graphical models. Specifically, we make three contributions. First, we show how the decomposability of the MDL score, plus the ability to quickly compute entire regularization paths, allows us to ...

We study group variable selection on multivariate regression model. Group variable selection is selecting the non-zero rows of coefficient matrix, since there are multiple response variables and thus if one predictor is irrelevant to estimation then the corresponding row must be zero. In a high dimensional setup, shrinkage estimation methods are applicable and guarantee smaller MSE than OLS acc...

The regularization of a convex program is exact if all solutions of the regularized problem are also solutions of the original problem for all values of the regularization parameter below some positive threshold. For a general convex program, we show that the regularization is exact if and only if a certain selection problem has a Lagrange multiplier. Moreover, the regularization parameter thre...