Related papers: Dynamic Screening: Accelerating First-Order Algori…
It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
A recently introduced technique for a sparse optimization problem called "safe screening" allows us to identify irrelevant variables in the early stage of optimization. In this paper, we first propose a flexible framework for safe screening…
Sparse sampling schemes have the potential to dramatically reduce image acquisition time while simultaneously reducing radiation damage to samples. However, for a sparse sampling scheme to be useful it is important that we are able to…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods…
We give safe screening rules to eliminate variables from regression with $\ell_0$ regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening…
Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…
Least absolute shrinkage and selection operator (Lasso), a popular method for high-dimensional regression, is now used widely for estimating high-dimensional time series models such as the vector autoregression (VAR). Selecting its tuning…
This paper focusses on "safe" screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed "joint" screening test, allowing to screen a set of atoms by carrying out one…
We describe two techniques that significantly improve the running time of several standard machine-learning algorithms when data is sparse. The first technique is an algorithm that effeciently extracts one-way and two-way counts--either…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
The theory of compressive sensing (CS) suggests that under certain conditions, a sparse signal can be recovered from a small number of linear incoherent measurements. An effective class of reconstruction algorithms involve solving a convex…
Nature has evolved many molecular machines such as kinesin, myosin, and the rotary flagellar motor powered by an ion current from the mitochondria. Direct observation of the step-like motion of these machines with time series from novel…
Group Ordered Weighted $L_{1}$-Norm (Group OWL) regularized models have emerged as a useful procedure for high-dimensional sparse multi-task learning with correlated features. Proximal gradient methods are used as standard approaches to…
Over the last century, risk scores have been the most popular form of predictive model used in healthcare and criminal justice. Risk scores are sparse linear models with integer coefficients; often these models can be memorized or placed on…
Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…