Related papers: Low-rank matrix denoising for count data using unb…
In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density…
In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
Count data are collected in many scientific and engineering tasks including image processing, single-cell RNA sequencing and ecological studies. Such data sets often contain missing values, for example because some ecological sites cannot…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…
This paper is concerned with non-parametric estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied. The proposed estimator is compared with the rival estimator in simple random…
A common data analysis task is the reduced-rank regression problem: $$\min_{\textrm{rank-}k \ X} \|AX-B\|,$$ where $A \in \mathbb{R}^{n \times c}$ and $B \in \mathbb{R}^{n \times d}$ are given large matrices and $\|\cdot\|$ is some norm.…
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…
We introduce a new method to reconstruct the density matrix $\rho$ of a system of $n$-qubits and estimate its rank $d$ from data obtained by quantum state tomography measurements repeated $m$ times. The procedure consists in minimizing the…
This paper considers a nuclear norm penalized estimator for panel data models with interactive effects. The low-rank interactive effects can be an approximate model and the rank of the best approximation unknown and grow with sample size.…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
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…
The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However,…
In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…
To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…