Related papers: Topics in Matrix Sampling Algorithms
We discuss a randomized strong rank-revealing QR factorization that effectively reveals the spectrum of a matrix $\textbf{M}$. This factorization can be used to address problems such as selecting a subset of the columns of $\textbf{M}$,…
Low-rank approximation is a common tool used to accelerate kernel methods: the $n \times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\tilde K$ which can be stored in much less space and processed more quickly. In this work…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan…
In problems involving matrix computations, the concept of leverage has found a large number of applications. In particular, leverage scores, which relate the columns of a matrix to the subspaces spanned by its leading singular vectors, are…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…
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…
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…
We consider $m \times s$ matrices (with $m\geq s$) in a real affine subspace of dimension $n$. The problem of finding elements of low rank in such spaces finds many applications in information and systems theory, where low rank is…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
A Low-rank Spectral Optimization Problem (LSOP) minimizes a linear objective subject to multiple two-sided linear matrix inequalities intersected with a low-rank and spectral constrained domain set. Although solving LSOP is, in general,…
Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…