相关论文: Nonparametric Estimation of Low Rank Matrix Valued…

The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have…

Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…

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…

We propose new Riemannian preconditioned algorithms for low-rank tensor completion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric on the product space of the factor matrices of the low-rank…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

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…

In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we…

Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…

We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive…

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…

We consider semiparametric location-scatter models for which the $p$-variate observation is obtained as $X=\Lambda Z+\mu$, where $\mu$ is a $p$-vector, $\Lambda$ is a full-rank $p\times p$ matrix and the (unobserved) random $p$-vector $Z$…

We propose a rate optimal estimator for the linear regression model on network data with interacted (unobservable) individual effects. The estimator achieves a faster rate of convergence $N$ compared to the standard estimators' $\sqrt{N}$…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…

In this paper we develop algorithms for approximating matrix multiplication with respect to the spectral norm. Let A\in{\RR^{n\times m}} and B\in\RR^{n \times p} be two matrices and \eps>0. We approximate the product A^\top B using two…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

In this paper, we consider the nonparametric random regression model $Y=f_1(X_1)+f_2(X_2)+\epsilon$ and address the problem of estimating the function $f_1$. The term $f_2(X_2)$ is regarded as a nuisance term which can be considerably more…

We propose a computational framework for computing low-rank approximations to the ensemble of solutions of a parametrized system of the form $A(\xi)x(\xi)+g(x(\xi))=b(\xi)$ for multiple parameter values. The central idea is to reinterpret…