Related papers: A New Convex Relaxation for Tensor Completion
In this paper, we develop a novel regularization method for deep neural networks by penalizing the trace of Hessian. This regularizer is motivated by a recent guarantee bound of the generalization error. We explain its benefits in finding…
We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
A new time relaxation model with iterative modified Lavrentiev regularization method is studied. The aim of the relaxation term is to drive the unresolved fluctuations in a computational simulation to zero exponentially faster by an…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…
Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the non-convex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization…
In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…
A tensor nuclear norm (TNN) based method for solving the tensor recovery problem was recently proposed, and it has achieved state-of-the-art performance. However, it may fail to produce a highly accurate solution since it tends to treats…
Pose Graph Optimization involves the estimation of a set of poses from pairwise measurements and provides a formalization for many problems arising in mobile robotics and geometric computer vision. In this paper, we consider the case in…
We propose a relax-and-round approach combined with a greedy search strategy for performing complex lattice basis reduction. Taking an optimization perspective, we introduce a relaxed version of the problem that, while still nonconvex, has…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Various forms of regularization in learning tasks strive for different notions of simplicity. This paper presents a spectral regularization technique, which attaches a unique inductive bias to sequence modeling based on an intuitive concept…
Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a…