Related papers: A unified error analysis for randomized low-rank a…
Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…
Low-rank matrix recovery problems involving high-dimensional and heterogeneous data appear in applications throughout statistics and machine learning. The contribution of this paper is to establish the fundamental limits of recovery for a…
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…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…
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…
Low-rank matrix approximation is extremely useful in the analysis of data that arises in scientific computing, engineering applications, and data science. However, as data sizes grow, traditional low-rank matrix approximation methods, such…
Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…
This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
In modern randomized experiments, large-scale data collection increasingly yields rich baseline covariates and auxiliary information from multiple sources. Such information offers opportunities for more precise treatment effect estimation,…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
The problem of low rank approximation is ubiquitous in science. Traditionally this problem is solved in unitary invariant norms such as Frobenius or spectral norm due to existence of efficient methods for building approximations. However,…
Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy…
We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…
This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…