Daniel A. Spielman
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View article: Statistical inference of a ranked community in a directed graph
Statistical inference of a ranked community in a directed graph Open
We study the problem of detecting or recovering a planted ranked subgraph from a directed graph, an analog for directed graphs of the well-studied planted dense subgraph model. We suppose that, among a set of $n$ items, there is a subset $…
View article: Inference of rankings planted in random tournaments
Inference of rankings planted in random tournaments Open
We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the computat…
View article: Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design
Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design Open
The design of experiments involves a compromise between covariate balance and robustness. This article provides a formalization of this tradeoff and describes an experimental design that allows experimenters to navigate it. The design is s…
View article: Robust and Practical Solution of Laplacian Equations by Approximate Elimination
Robust and Practical Solution of Laplacian Equations by Approximate Elimination Open
We introduce a new algorithm and software for solving linear equations in symmetric diagonally dominant matrices with non-positive off-diagonal entries (SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate gradien…
View article: Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design
Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design Open
The design of experiments involves a compromise between covariate balance and robustness. This article provides a formalization of this tradeoff and describes an experimental design that allows experimenters to navigate it. The design is s…
View article: Hardness Results for Weaver's Discrepancy Problem
Hardness Results for Weaver's Discrepancy Problem Open
Marcus, Spielman and Srivastava (Annals of Mathematics 2014) solved the Kadison--Singer Problem by proving a strong form of Weaver's conjecture: they showed that for all $α> 0$ and all lists of vectors of norm at most $\sqrtα$ whose outer …
View article: Balancing covariates in randomized experiments using the Gram-Schmidt walk.
Balancing covariates in randomized experiments using the Gram-Schmidt walk. Open
The design of experiments involves a compromise between covariate balance and robustness. This paper introduces an experimental design that admits precise control over this trade-off. The design is specified by a parameter that bounds the …
View article: Balancing Covariates in Randomized Experiments with the Gram-Schmidt Walk Design
Balancing Covariates in Randomized Experiments with the Gram-Schmidt Walk Design Open
The design of experiments involves a compromise between covariate balance and robustness. This paper provides a formalization of this trade-off and describes an experimental design that allows experimenters to navigate it. The design is sp…
View article: Interlacing Families III: Sharper Restricted Invertibility Estimates
Interlacing Families III: Sharper Restricted Invertibility Estimates Open
We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by th…
View article: Graphs, Vectors, and Matrices
Graphs, Vectors, and Matrices Open
This survey accompanies the Josiah Williard Gibbs Lecture that I gave at the 2016 Joint Mathematics Meetings. It provides an introduction to three topics: algebraic and spectral graph theory, the sparsification of graphs, and the recent re…
View article: Sparsified Cholesky and multigrid solvers for connection laplacians
Sparsified Cholesky and multigrid solvers for connection laplacians Open
We introduce the sparsified Cholesky and sparsified multigrid algorithms for solving systems of linear equations. These algorithms accelerate Gaussian elimination by sparsifying the nonzero matrix entries created by the elimination process…