This survey highlights the recent advances in algorithms for numerical linear algebra that
have come from the technique of linear sketching, whereby given a matrix, one first …

We develop and analyze a method to reduce the size of a very large set of data points in a
high-dimensional Euclidean space R^d to a small set of weighted points such that the result …

We show how to approximate a data matrix A with a much smaller sketch~ A that can be
used to solve a general class of constrained k-rank approximation problems to within (1+ ε) …

This paper describes a suite of algorithms for constructing low-rank approximations of an
input matrix from a random linear image, or sketch, of the matrix. These methods can …

We present a theoretically founded approach for high-dimensional Bayesian optimization
based on low-dimensional subspace embeddings. We prove that the error in the Gaussian …

Consider an instance of Euclidean k-means or k-medians clustering. We show that the cost
of the optimal solution is preserved up to a factor of (1+ ε) under a projection onto a random …

Kernel methods are fundamental tools in machine learning that allow detection of non-linear
dependencies between data without explicitly constructing feature vectors in high …

The Tanimoto coefficient is commonly used to measure the similarity between molecules
represented as discrete fingerprints, either as a distance metric or a positive definite kernel …

Kernel ridge regression (KRR) is a standard method for performing nonparametric
regression over reproducing kernel Hilbert spaces. Given n samples, the time and space …

Kernel ridge regression is a simple yet powerful technique for nonparametric regression
whose computation amounts to solving a linear system. This system is usually dense and …