Related papers: On Deterministic Sampling Patterns for Robust Low-…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising…
We study the problem of robust matrix completion (RMC), where the partially observed entries of an underlying low-rank matrix is corrupted by sparse noise. Existing analysis of the non-convex methods for this problem either requires the…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…
In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted…
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…
This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion…
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…
In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the…
We investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries, for finite completability of a low-rank tensor given some components of its Tucker rank. In order to find the deterministic necessary…
This paper studies the stability of low-rank implicit regularization in perturbed deep matrix factorization, where the target matrix is corrupted by a noise matrix. We first derive sufficient spectral conditions under which gradient descent…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…
The problem of low-rank matrix completion with heterogeneous and sub-exponential (as opposed to homogeneous and Gaussian) noise is particularly relevant to a number of applications in modern commerce. Examples include panel sales data and…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…