Related papers: Scalable Robust Matrix Recovery: Frank-Wolfe Meets…

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

Structured constraints in Machine Learning have recently brought the Frank-Wolfe (FW) family of algorithms back in the spotlight. While the classical FW algorithm has poor local convergence properties, the Away-steps and Pairwise FW…

In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak)…

Reconstruction of signals from undersampled and noisy measurements is a topic of considerable interest. Sharpness conditions directly control the recovery performance of restart schemes for first-order methods without the need for…

Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…

Robust subspace recovery (RSR) is a fundamental problem in robust representation learning. Here we focus on a recently proposed RSR method termed Dual Principal Component Pursuit (DPCP) approach, which aims to recover a basis of the…

We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank…

Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…

We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…

Factorizing large matrices by QR with column pivoting (QRCP) is substantially more expensive than QR without pivoting, owing to communication costs required for pivoting decisions. In contrast, randomized QRCP (RQRCP) algorithms have proven…

The stochastic Frank-Wolfe method has recently attracted much general interest in the context of optimization for statistical and machine learning due to its ability to work with a more general feasible region. However, there has been a…

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and…

Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a…

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…

This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a…

We develop a novel variant of the classical Frank-Wolfe algorithm, which we call spectral Frank-Wolfe, for convex optimization over a spectrahedron. The spectral Frank-Wolfe algorithm has a novel ingredient: it computes a few eigenvectors…

We prove that the block-coordinate Frank-Wolfe (BCFW) algorithm converges with state-of-the-art rates in both convex and nonconvex settings under a very mild "block-iterative" assumption. This appears to be the first result on BCFW…