相关论文: L_1-regularized Boltzmann machine learning using m…

Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose…

The couplings in a sparse asymmetric, asynchronous Ising network are reconstructed using an exact learning algorithm. L$_1$ regularization is used to remove the spurious weak connections that would otherwise be found by simply minimizing…

Factorization machines (FMs) are machine learning predictive models based on second-order feature interactions and FMs with sparse regularization are called sparse FMs. Such regularizations enable feature selection, which selects the most…

Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…

The inverse Potts problem to infer a Boltzmann distribution for homologous protein sequences from their single-site and pairwise amino acid frequencies recently attracts a great deal of attention in the studies of protein structure and…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this…

Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effective under strong regularity assumptions, but…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we…

We study a family of sparse estimators defined as minimizers of some empirical Lipschitz loss function -- which include the hinge loss, the logistic loss and the quantile regression loss -- with a convex, sparse or group-sparse…

Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular…

We study the robustness properties of $\ell_1$ norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the $\ell_1$…

Problems in signal processing and medical imaging often lead to calculating sparse solutions to under-determined linear systems. Methodologies for solving this problem are presented as background to the method used in this work where the…

The use of L1 regularisation for sparse learning has generated immense research interest, with successful application in such diverse areas as signal acquisition, image coding, genomics and collaborative filtering. While existing work…

$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many…

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…

State-of-the-art methods for solving smooth optimization problems are nonlinear conjugate gradient, low memory BFGS, and Majorize-Minimize (MM) subspace algorithms. The MM subspace algorithm which has been introduced more recently has shown…

Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…

Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…