We study the problem of learning structure an optimal Bayesian network when additional constraints are posed on or its moralized graph. More precisely, we consider constraint that graph close, in terms vertex edge deletions, to a sparse class Π. For example, show whose has deletion distance at most k from with maximum degree 1 can be computed polynomial time is constant. This extends previous w...

Functions preserving Loewner positivity when applied entrywise to positive semidefinite matrices have been widely studied in the literature. Following the work of Schoenberg [Duke Math. J. 9], Rudin [Duke Math. J. 26], and others, it is well-known that functions preserving positivity for matrices of all dimensions are absolutely monotonic (i.e., analytic with nonnegative Taylor coefficients). I...

A new approach is presented for inverse modeling to reconstruct continuous features in space, such as channels, that exhibit sparseness in a complementary basis (e.g. a Fourier basis) using observations in spatial domain. Continuity in space is used to constrain the solution to be sparse in the discrete cosine transform (DCT) domain. The DCT is used to effectively reduce the dimension of the se...

Inline digital holograms are classically reconstructed using linear operators to model diffraction. It has long been recognized that such reconstruction operators do not invert the hologram formation operator. Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin images. When objects located at different depths are reconstruct...

Devising efficient sparse decomposition algorithms in large redundant dictionaries has attracted much attention recently. However, choosing the right dictionary for a given data set remains an issue. An interesting approach is to learn the best dictionary from the data itself. The purpose of this contribution is to describe a new dictionary learning algorithm for multichannel data analysis purp...

We study the problem of online linear optimization with sparsity constraints in the 1 semi-bandit setting. It can be seen as a marriage between two well-known problems: 2 the online linear optimization problem and the combinatorial bandit problem. For 3 this problem, we provide two algorithms which are efficient and achieve sublinear 4 regret bounds. Moreover, we extend our results to two gener...

Tikhonov regularization with p-powers of the weighted `p norms as penalties, with p ∈ (1, 2), have been lately employed in reconstruction of sparse solutions of ill-posed inverse problems. This paper points out convergence rates for such a regularization with respect to the norm of the weighted spaces, by assuming that the solutions satisfy certain smoothness (source) condition. The meaning of ...

This paper is concerned with nonlinear inverse problems where data and solution are vector valued and, moreover, where the solution is assumed to have a sparse expansion with respect to a preassigned frame. We especially focus on such problems where the different components of the solution exhibit a common or so–called joint sparsity pattern. Joint sparsity means here that the measure (typicall...

Restricted BoltzmannMachine (RBM) has been applied to a wide variety of tasks due to its advantage in feature extraction. Implementing sparsity constraint in the activated hidden units is an important improvement on RBM. The sparsity constraints in the existing methods are usually specified by users and are independent of the input data. However, the input data could be heterogeneous in content...

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for analyzing the trade off between the sparsity and low rank constraints in these approaches which not only helps to provide guidelines to adjust the weights betwe...