相关论文: Optimal Estimation of Schatten Norms of a rectangu…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…

It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…

In distributed optimization or Nash-equilibrium seeking over directed graphs, it is crucial to find a matrix norm under which the disagreement of individual agents' states contracts. In existing results, the matrix norm is usually defined…

We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate approximate mass matrix which is diagonal,…

Let $A$ be a positive semidefinite matrix, block partitioned as $$ A=\twomat{B}{C}{C^*}{D}, $$ where $B$ and $D$ are square blocks. We prove the following inequalities for the Schatten $q$-norm $||.||_q$, which are sharp when the blocks are…

Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample…

Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns. We consider the problem of estimating such a matrix based on…

We consider the problem of identifying the sparse principal component of a rank-deficient matrix. We introduce auxiliary spherical variables and prove that there exists a set of candidate index-sets (that is, sets of indices to the nonzero…

We consider the question of learning $Q$-function in a sample efficient manner for reinforcement learning with continuous state and action spaces under a generative model. If $Q$-function is Lipschitz continuous, then the minimal sample…

We study the problem of finding orthogonal low-rank approximations of symmetric tensors. In the case of matrices, the approximation is a truncated singular value decomposition which is then symmetric. Moreover, for rank-one approximations…

We investigate estimation of a normal mean matrix under the matrix quadratic loss. Improved estimation under the matrix quadratic loss implies improved estimation of any linear combination of the columns. First, an unbiased estimate of risk…

This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

Many economic parameters are identified by ``thin sets'' (submanifolds with Lebesgue measure zero) and hence difficult to recover from data in an ambient space. This paper provides a unified theory for estimation and inference of such…