We consider the sparsification of sums F: ℝ n→ ℝ+ where F (x)= f 1 (⟨ a 1, x⟩)+⋯+ fm (⟨ am,
x⟩) for vectors a 1,…, am∈ ℝ n and functions f 1,…, fm: ℝ→ ℝ+. We show that (1+ ε) …

Given a matrix A∈ ℝ n× d, a partitioning of [n] into groups S 1,…, Sm, an outer norm p, and
inner norms such that either p≥ 1 and p 1,..., pm≥ 2 or p1=···= pm= p≥ 1/log d, we prove …

Graph sparsification has been an important topic with many structural and algorithmic
consequences. Recently hypergraph sparsification has come to the fore and has seen …

Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine
inequality, have been an important tool in both applied and pure mathematics. We study …

A (1±ϵ)-sparsifier of a hypergraph G(V,E) is a (weighted) subgraph that preserves the value
of every cut to within a (1±ϵ)-factor. It is known that every hypergraph with n vertices admits …

We introduce a notion of code sparsification that generalizes the notion of cut sparsification
in graphs. For a (linear) code C⊆ 𝔽 nq of dimension ka (1±ɛ)-sparsification of size s is …

Flow sparsification is a classic graph compression technique which, given a capacitated
graph $ G $ on $ k $ terminals, aims to construct another capacitated graph $ H $, called a …

Data subsampling is one of the most natural methods to approximate a massively large data
set by a small representative proxy. In particular, sensitivity sampling received a lot of …

The $\ell_p $ subspace approximation problem is an NP-hard low rank approximation
problem that generalizes the median hyperplane problem ($ p= 1$), principal component …

We study vertex sparsification for preserving cuts. Given a graph $ G $ with a subset $| T|= k
$ of its vertices called terminals, a\emph {quality-$ q $ cut sparsifier} is a graph $ G'$ that …