Related papers: Optimal Shrinkage of Singular Values Under Random …
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
We make use of recent results from random matrix theory to identify a derived threshold, for isolating noise from image features. The procedure assumes the existence of a set of noisy images, where denoising can be carried out on individual…
This work analyzes singular-value spectra of weight matrices in pretrained transformer models to understand how information is stored at both ends of the spectrum. Using Random Matrix Theory (RMT) as a zero information hypothesis, we…
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data…
Computing the first few singular vectors of a large matrix is a problem that frequently comes up in statistics and numerical analysis. Given the presence of noise, exact calculation is hard to achieve, and the following problem is of…
We give a new algorithm for the estimation of the cross-covariance matrix $\mathbb{E} XY'$ of two large dimensional signals $X\in\mathbb{R}^n$, $Y\in \mathbb{R}^p$ in the context where the number $T$ of observations of the pair $(X,Y)$ is…
We perturb a real matrix $A$ of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our bounds, which extend existing lower-order expressions,…
In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…
This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a new nuclear norm penalized estimator of $A_0$ and…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
In data analysis, contamination caused by outliers is inevitable, and robust statistical methods are strongly demanded. In this paper, our concern is to develop a new approach for robust data analysis based on scoring rules. The scoring…
We apply basic statistical reasoning to signal reconstruction by machine learning -- learning to map corrupted observations to clean signals -- with a simple and powerful conclusion: it is possible to learn to restore images by only looking…
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…
Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods…
In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
We consider the problem of reconstructing a rank-one matrix from a revealed subset of its entries when some of the revealed entries are corrupted with perturbations that are unknown and can be arbitrarily large. It is not known which…
In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…