相关论文: Random matrix over a DVR and LU factorization

We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…

We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…

Accurate ranking of important features is a fundamental challenge in interpretable machine learning with critical applications in scientific discovery and decision-making. Unlike feature selection and feature importance, the specific…

This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer.…

In fully cooperative multi-agent reinforcement learning (MARL) settings, environments are highly stochastic due to the partial observability of each agent and the continuously changing policies of other agents. To address the above issues,…

Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…

This paper demonstrates how to apply machine learning algorithms to distinguish good stocks from the bad stocks. To this end, we construct 244 technical and fundamental features to characterize each stock, and label stocks according to…

The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…

In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…

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…

We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values of the observed…

We prove a large deviation result for a random symmetric n x n matrix with independent identically distributed entries to have a few eigenvalues of size n. If the spectrum S survives when the matrix is rescaled by a factor of n, it can only…

RSVDPACK is a library of functions for computing low rank approximations of matrices. The library includes functions for computing standard (partial) factorizations such as the Singular Value Decomposition (SVD), and also so called…

Multiple rotation averaging plays a crucial role in computer vision and robotics domains. The conventional optimization-based methods optimize a nonlinear cost function based on certain noise assumptions, while most previous learning-based…

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

This paper revisits the problem of decomposing a positive semidefinite matrix as a sum of a matrix with a given rank plus a sparse matrix. An immediate application can be found in portfolio optimization, when the matrix to be decomposed is…

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…

We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…

Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is the best…

Linear Quadratic Regulators (LQR) achieve enormous successful real-world applications. Very recently, people have been focusing on efficient learning algorithms for LQRs when their dynamics are unknown. Existing results effectively learn to…