Concept

Concentration inequality

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Incidences Between Planes Over Finite Fields

In this note, we use methods from spectral graph theory to obtain bounds on the number of incidences between k-planes and h-planes in F-q(d), which generalizes a recent result given by Bennett, Iosevich, and Pakianathan (2014). More precisely, we prove tha ...

AMER MATHEMATICAL SOC2019

Chebyshev Inequalities for Products of Random Variables

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...

2018

Robust Maximization of Non-Submodular Objectives

Volkan Cevher, Ilija Bogunovic, Junyao Zhao

We study the problem of maximizing a monotone set function subject to a cardinality constraint k in the setting where some number of elements is deleted from the returned set. The focus of this work is on the worst-case adversarial setting. While there exi ...

2018

Decision Rule Bounds for Two-Stage Stochastic Bilevel Programs

Daniel Kuhn

We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version an ...

2018

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

Nicolas Henri Bernard Flammarion, Aymeric Daphnis Kévin Dieuleveut

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that a ...

2017

Generalized Gauss Inequalities via Semidefinite Programming

Daniel Kuhn

A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to ...

Springer Verlag2016

Partial Recovery Bounds for the Sparse Stochastic Block Model

Volkan Cevher, Jonathan Mark Scarlett

In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities

\frac{a}{n}

and

\frac{b}{n}

respectively. We consider the ...

Ieee2016

Crossing Probabilities in Topological Rectangles for the Critical Planar FK-Ising model

Clément Hongler

We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundary conditions, generalizing results of [DCHN11] and [CS12]. Our result relies ...

Institute of Mathematical Statistics2016

A Composition Theorem for Conical Juntas

Mika Tapani Göös

We describe a general method of proving degree lower bounds for conical juntas (nonnegative combinations of conjunctions) that compute recursively defined boolean functions. Such lower bounds are known to carry over to communication complexity. We give two ...

Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany2016

Upper bounds for the reach-avoid probability via robust optimization

Maryam Kamgarpour, John Lygeros, Tyler Summers

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by restricting attentio ...

2015

Partial Recovery Bounds for the Sparse Stochastic Block Model

Volkan Cevher, Jonathan Mark Scarlett

In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities

\frac{a}{n}

and

\frac{b}{n}

respectively. We consider the ...

Ieee2016