Related papers: Computational Efficient and Minimax Optimal Nonign…

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we…

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…

We propose a general method for optimally approximating an arbitrary matrix $\mathbf{M}$ by a structured matrix $\mathbf{T}$ (circulant, Toeplitz/Hankel, etc.) and examine its use for estimating the spectra of genomic linkage disequilibrium…

This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…

We study the robust matrix completion (RMC) problem subject to both sparse outliers and stochastic noise. A non-convex method termed Accelerated Robust Matrix Completion (ARMC) is proposed, which accelerates a prior non-convex approach by…

Missing data are inevitable in clinical trials, and trials that produce categorical ordinal responses are not exempted from this. Typically, missing values in the data occur due to different missing mechanisms, such as missing completely at…

This paper investigates the asymmetric low-rank matrix completion problem, which can be formulated as an unconstrained non-convex optimization problem with a nonlinear least-squares objective function, and is solved via gradient descent…

Ranked data appear in many different applications, including voting and consumer surveys. There often exhibits a situation in which data are partially ranked. Partially ranked data is thought of as missing data. This paper addresses…

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…

The recently introduced algorithm randUTV provides a highly efficient technique for computing accurate approximations to all the singular values of a given matrix $A$. The original version of randUTV was designed to compute a full…

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. We propose a proximally…

In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…

Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…

With the rising penetration of distributed energy resources, distribution system control and enabling techniques such as state estimation have become essential to distribution system operation. However, traditional state estimation…

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

Missing data are frequently encountered in high-dimensional problems, but they are usually difficult to deal with using standard algorithms, such as the expectation-maximization (EM) algorithm and its variants. To tackle this difficulty,…