This work looks at fitting probabilistic graphical models to data when the structure is not known. The main tool to do this is `1-regularization and the more general group `1-regularization. We describe limited-memory quasi-Newton methods to solve optimization problems with these types of regularizers, and we examine learning directed acyclic graphical models with `1-regularization, learning un...

We discuss adaptive strategies for choosing regularization parameters in TikhonovPhillips regularization of discretized linear operator equations. Two rules turn out to be entirely based on the underlying regularization scheme. Among them only the discrepancy principle allows to search for the optimal regularization parameter from the easiest problem. This possible advantage cannot be used with...

We present a normalized LMS (NLMS) algorithm with robust regularization. Unlike conventional NLMS with the fixed regularization parameter, the proposed approach dynamically updates the regularization parameter. By exploiting a gradient descent direction, we derive a computationally efficient and robust update scheme for the regularization parameter. In simulation, we demonstrate the proposed al...

We consider Tikhonov regularization of large linear discrete ill-posed problems with a regularization operator of general form and present an iterative scheme based on a generalized Krylov subspace method. This method simultaneously reduces both the matrix of the linear discrete ill-posed problem and the regularization operator. The reduced problem so obtained may be solved, e.g., with the aid ...

Regularization is commonly used in classifier design, to assure good generalization. Classical regularization enforces a cost on classifier complexity, by constraining parameters. This is usually combined with a margin loss, which favors large-margin decision rules. A novel and unified view of this architecture is proposed, by showing that margin losses act as regularizers of posterior class pr...

We introduce and study a mathematical framework for broad class of regularization functionals ill-posed inverse problems: Regularization Graphs. graphs allow to construct using as building blocks linear operators convex functionals, assembled by means that can be seen generalizations classical infimal convolution operators. This exhaustively covers existing approaches it is flexible enough craf...

Dropout is a simple but effective technique for learning in neural networks and other settings. A sound theoretical understanding of dropout is needed to determine when dropout should be applied and how to use it most effectively. In this paper we continue the exploration of dropout as a regularizer pioneered by Wager et al. We focus on linear classification where a convex proxy to the misclass...

Manifold regularization is an approach which exploits the geometry of the marginal distribution. The main goal of this paper is to analyze the convergence issues of such regularization algorithms in learning theory. We propose a more general multi-penalty framework and establish the optimal convergence rates under the general smoothness assumption. We study a theoretical analysis of the perform...

Regularization approaches based on spectral filtering can be highly effective in solving ill-posed inverse problems. These methods, however, require computing the singular value decomposition (SVD) and choosing appropriate regularization parameters. These tasks can be prohibitively expensive for large-scale problems. In this paper, we present a framework that uses operator approximations to eff...

We examine several zero-range potentials in non-relativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff schemes and show explicitly that in certain cases dimensional regularization fails to reproduce the results obtained using cutoff regularization. First we consid...