Related papers: Parameter optimization for low-rank matrix recover…

We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common…

A zeroth-order Hessian estimator aims to recover the Hessian matrix of an objective function at any given point, using minimal finite-difference computations. This paper studies zeroth-order Hessian estimation for low-rank Hessians, from a…

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…

We study nonconvex optimization for phase retrieval and the more general problem of semidefinite low-rank matrix sensing; in particular, we focus on the global nonconvex landscape of overparametrized versions of the nonsmooth amplitude…

Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…

Face recognition remains a hot topic in computer vision, and it is challenging to tackle the problem that both the training and testing images are corrupted. In this paper, we propose a novel semi-supervised method based on the theory of…

Most machine learning algorithms are configured by one or several hyperparameters that must be carefully chosen and often considerably impact performance. To avoid a time consuming and unreproducible manual trial-and-error process to find…

Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…

We study a nonconvex optimization algorithmic approach to phase retrieval and the more general problem of semidefinite low-rank matrix sensing. Specifically, we analyze the nonconvex landscape of a quartic Burer-Monteiro factored…

We propose in this paper a novel, information-theoretic method, called MaxEnt, for efficient data acquisition for low-rank matrix recovery. This proposed method has important applications to a wide range of problems, including image…

A major challenge in designing neural network (NN) systems is to determine the best structure and parameters for the network given the data for the machine learning problem at hand. Examples of parameters are the number of layers and nodes,…

Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict…

In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

Machine learning algorithms have been used widely in various applications and areas. To fit a machine learning model into different problems, its hyper-parameters must be tuned. Selecting the best hyper-parameter configuration for machine…

This paper proposes a new method for solving the well-known rank aggregation problem from pairwise comparisons using the method of low-rank matrix completion. The partial and noisy data of pairwise comparisons is transformed into a matrix…

Tuning the regularization hyperparameter $\alpha$ in inverse problems has been a longstanding problem. This is particularly true in the case of fetal brain magnetic resonance imaging, where an isotropic high-resolution volume is…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however,…

We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier…