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 design a new distribution over m× n matrices S so that, for any fixed n× d matrix A of rank
r, with probability at least 9/10,∥ SAx∥ 2=(1±ε)∥ Ax∥ 2 simultaneously for all x∈ R d …

An oblivious subspace embedding (OSE) given some parameters ε, d is a distribution D over
matrices Π∈ R m× n such that for any linear subspace W⊆ R n with dim (W)= d, P Π~ D (∀ …

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 …

We give two different and simple constructions for dimensionality reduction in ℓ 2 via linear
mappings that are sparse: only an O (ε)-fraction of entries in each column of our embedding …

We consider the problem of training a multi-layer over-parametrized neural network to
minimize the empirical risk induced by a loss function. In the typical setting of over …

We show that for n points in d-dimensional Euclidean space, a data oblivious random
projection of the columns onto m∈ O ((log k+ loglog n) ε− 6log1/ε) dimensions is sufficient to …

The massive volume of data generated in modern applications can overwhelm our ability to
conveniently transmit, store, and index it. For many scenarios, building a compact summary …

We present a technical survey on the state of the art approaches in data reduction and the
coreset framework. These include geometric decompositions, gradient methods, random …

Let Φ∈ Rm xn be a sparse Johnson-Lindenstrauss transform [52] with column sparsity s.
For a subset T of the unit sphere and ε∈(0, 1/2), we study settings for m, s to ensure EΦ …