Related papers: Fast randomized numerical rank estimation for nume…
This paper studies the inference about linear functionals of high-dimensional low-rank matrices. While most existing inference methods would require consistent estimation of the true rank, our procedure is robust to rank misspecification,…
We study random submatrices of a large matrix A. We show how to approximately compute A from its random submatrix of the smallest possible size O(r log r) with a small error in the spectral norm, where r = ||A||_F^2 / ||A||_2^2 is the…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…
The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank $r$ reliably from the fewest possible random…
Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items…
Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…
Many automated machine learning methods, such as those for hyperparameter and neural architecture optimization, are computationally expensive because they involve training many different model configurations. In this work, we present a new…
In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…
The minimum rank of a graph is the minimum possible rank of a real matrix whose zero-nonzero pattern is described by the graph. The current algorithms can compute efficiently the minimum rank of undirected trees. This paper provides an…
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…
Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
This paper describes practical randomized algorithms for low-rank matrix approximation that accommodate any budget for the number of views of the matrix. The presented algorithms, which are aimed at being as pass efficient as needed, expand…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…