Motivated by a sampling problem basic to computational statistical inference, we develop a
toolset based on spectral sparsification for a family of fundamental problems involving …

We consider the problem of learning a sparse graph underlying an undirected Gaussian
graphical model, a key problem in statistical machine learning. Given $ n $ samples from a …

Given a statistical estimation problem where regularization is performed according to the
structure of a large, dense graph G, we consider fitting the statistical estimate using a\it …

We consider a fundamental algorithmic question in spectral graph theory: Compute a
spectral sparsifier of random-walk matrix-polynomial $$ L_\alpha (G)= D-\sum_ {r= 1} …

Abstract How might one``reduce''a graph? That is, generate a smaller graph that preserves
the global structure at the expense of discarding local details? There has been extensive …

The present thesis focuses on the design and analysis of randomized algorithms for
accelerating several linear algebraic tasks. In particular, we develop simple, efficient …

Many real-world data sets are sparse or almost sparse. One method to measure this for a
matrix $ A\in\mathbb {R}^{n\times n} $ is the\emph {numerical sparsity}, denoted $\mathsf …

The representation and learning benefits of methods based on graph Laplacians, such as
Laplacian smoothing or harmonic function solution for semi-supervised learning (SSL), are …

We give a row sampling algorithm for the quantile loss function with sample complexity
nearly linear in the dimensionality of the data, improving upon the previous best algorithm …

Undirected probabilistic graphical models represent the conditional dependencies, or
Markov properties, of a collection of random variables. Knowing the sparsity of such a …