Related papers: Reduced rank regression via adaptive nuclear norm …

The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$. Although this problem can be solved efficiently, we study an…

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…

Recently, there has been an abundance of works on designing Deep Neural Networks (DNNs) that are robust to adversarial examples. In particular, a central question is which features of DNNs influence adversarial robustness and, therefore,…

The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least…

Deep Neural Networks (DNNs) have encountered an emerging deployment challenge due to large and expensive memory and computation requirements. In this paper, we present a new Adaptive-Rank Singular Value Decomposition (ARSVD) method that…

We study the generalized trace regression with a near low-rank regression coefficient matrix, which extends notion of sparsity for regression coefficient vectors. Specifically, given a matrix covariate $X$, the probability density function…

The paper deals with the problem of penalized empirical risk minimization over a convex set of linear functionals on the space of Hermitian matrices with convex loss and nuclear norm penalty. Such penalization is often used in low rank…

Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…

We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…

While Convolutional Neural Networks (CNNs) excel at learning complex latent-space representations, their over-parameterization can lead to overfitting and reduced performance, particularly with limited data. This, alongside their high…

Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…

We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…

We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…

Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

Matrix completion has attracted much interest in the past decade in machine learning and computer vision. For low-rank promotion in matrix completion, the nuclear norm penalty is convenient due to its convexity but has a bias problem.…

Finding the rank of a tensor is a problem that has many applications. Unfortunately it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of…

In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss,…