Related papers: Non-convex Regularizations for Feature Selection i…
This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear…
This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are motivated as a…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
Owing to their statistical properties, non-convex sparse regularizers have attracted much interest for estimating a sparse linear model from high dimensional data. Given that the solution is sparse, for accelerating convergence, a working…
Recent work in signal processing and statistics have focused on defining new regularization functions, which not only induce sparsity of the solution, but also take into account the structure of the problem. We present in this paper a class…
This paper considers the problem of signal denoising using a sparse tight-frame analysis prior. The L1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the…
Normalization methods improve both optimization and generalization of ConvNets. To further boost performance, the recently-proposed switchable normalization (SN) provides a new perspective for deep learning: it learns to select different…
We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In…
In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…
The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…
Current online learning methods suffer issues such as lower convergence rates and limited capability to select important features compared to their offline counterparts. In this paper, a novel framework for online learning based on running…
Subspace clustering and feature extraction are two of the most commonly used unsupervised learning techniques in computer vision and pattern recognition. State-of-the-art techniques for subspace clustering make use of recent advances in…
In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…
In this manuscript, we research on the behaviors of surrogates for the rank function on different image processing problems and their optimization algorithms. We first propose a novel nonconvex rank surrogate on the general rank…
Many real world practical problems can be formulated as $\ell_{0}$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative signals to underdetermined linear systems. They have been widely applied in signal…
This work studies the problem of sparse signal recovery with automatic grouping of variables. To this end, we investigate sorted nonsmooth penalties as a regularization approach for generalized linear models. We focus on a family of sorted…
This paper provides a theoretical analysis of a new learning problem for recommender systems where users provide feedback by comparing pairs of items instead of rating them individually. We assume that comparisons stem from latent user and…
Regularization methods are often employed in deep learning neural networks (DNNs) to prevent overfitting. For penalty based DNN regularization methods, convex penalties are typically considered because of their optimization guarantees.…
Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…
Sparse Bayesian learning is a state-of-the-art supervised learning algorithm that can choose a subset of relevant samples from the input data and make reliable probabilistic predictions. However, in the presence of high-dimensional data…