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

Matrix rank and inertia optimization problems are a class of discontinuous optimization problems, in which the decision variables are matrices running over certain feasible matrix sets, while the ranks and inertias of the variable matrices…

We provide a semi-parametric analysis for the proportional likelihood ratio model, proposed by Luo & Tsai (2012). We study the tangent spaces for both the parameter of interest and the nuisance parameter, and obtain an explicit expression…

This paper studies the inferential theory for estimating low-rank matrices. It also provides an inference method for the average treatment effect as an application. We show that the least square estimation of eigenvectors following the…

In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…

We study the $\ell_1$-low rank approximation problem, where for a given $n \times d$ matrix $A$ and approximation factor $\alpha \geq 1$, the goal is to output a rank-$k$ matrix $\widehat{A}$ for which $$\|A-\widehat{A}\|_1 \leq \alpha…

Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…

In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…

In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…

In this paper, we derive entrywise error bounds for low-rank approximations of kernel matrices obtained using the truncated eigen-decomposition (or singular value decomposition). While this approximation is well-known to be optimal with…

Representation learning plays a crucial role in automated feature selection, particularly in the context of high-dimensional data, where non-parametric methods often struggle. In this study, we focus on supervised learning scenarios where…

The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$. Although this problem can be solved efficiently, we study an…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

Recht, Fazel, and Parrilo provided an analogy between rank minimization and $\ell_0$-norm minimization. Subject to the rank-restricted isometry property, nuclear norm minimization is a guaranteed algorithm for rank minimization. The…

We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…

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…

The estimation of the diffusion matrix $\Sigma$ of a high-dimensional, possibly time-changed L\'evy process is studied, based on discrete observations of the process with a fixed distance. A low-rank condition is imposed on $\Sigma$.…

We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…

Let (V, E) be a graph with vertex set V and edge set E. Let (X, X', Y) \in V \times V \times {-1, 1} be a random triple, where X, X' are independent uniformly distributed vertices and Y is a label indicating whether X, X' are "similar" (Y =…

In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated has the "single-index" structure where neither the link function nor the index vector…

We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…