相关论文: Guaranteed Rank Minimization via Singular Value Pr…
We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…
We consider the problem of high-dimensional channel estimation in fast time-varying millimeter-wave MIMO systems with a hybrid architecture. By exploiting the low-rank and sparsity properties of the channel matrix, we propose a two-phase…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in…
Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly,…
Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…
We introduce smallest valid partitioning (SVP), a segmentation method for multiple change-point detection in time-series. SVP relies on a local notion of segment validity: a candidate segment is retained only if it passes a user-chosen…
In this paper we study general Schatten-$p$ quasi-norm (SPQN) regularized matrix minimization problems. In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-$r$ positive semi-definite (PSD) matrices in $\mathbb{R}^{n \times…
Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…
Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often…
The restricted isometry property (RIP) is essential for the linear map to guarantee the successful recovery of low-rank matrices. The existing works show that the linear map generated by the measurement matrices with independent and…
Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum_{i=1}^r \sigma_i u_i v_i^\top,$ where $\sigma_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
This paper presents approaches to compute sparse solutions of Generalized Singular Value Problem (GSVP). The GSVP is regularized by $\ell_1$-norm and $\ell_q$-penalty for $0<q<1$, resulting in the $\ell_1$-GSVP and $\ell_q$-GSVP…
Low rank matrix recovery problems appear widely in statistics, combinatorics, and imaging. One celebrated method for solving these problems is to formulate and solve a semidefinite program (SDP). It is often known that the exact solution to…
In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one,…
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…
We study matrix estimation problems arising in reinforcement learning (RL) with low-rank structure. In low-rank bandits, the matrix to be recovered specifies the expected arm rewards, and for low-rank Markov Decision Processes (MDPs), it…