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Concept

Concentration inequality

Related publications (28)

Regularization via Mass Transportation

Daniel Kuhn, Peyman Mohajerin Esfahani, Soroosh Shafieezadeh Abadeh

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, ...

2019

Theoretical foundations of forward feature selection methods based on mutual information

Francisco Santos Paredes Quartin de Macedo

Feature selection problems arise in a variety of applications, such as microarray analysis, clinical prediction, text categorization, image classification and face recognition, multi-label learning, and classification of internet traffic. Among the various ...

ELSEVIER SCIENCE BV2019

Chebyshev Inequalities for Products of Random Variables

Daniel Kuhn, Wolfram Wiesemann, Napat Rujeerapaiboon

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

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

Lower Bounds on Active Learning for Graphical Model Selection

Volkan Cevher, Jonathan Mark Scarlett

We consider the problem of estimating the underlying graph associated with a Markov random field, with the added twist that the decoding algorithm can iteratively choose which subsets of nodes to sample based on the previous samples, resulting in an active ...

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

Dimensionality Reduction in Dynamic Optimization under Uncertainty

Napat Rujeerapaiboon

Dynamic optimization problems affected by uncertainty are ubiquitous in many application domains. Decision makers typically model the uncertainty through random variables governed by a probability distribution. If the distribution is precisely known, then ...

EPFL2016

Moment bounds and asymptotics for the stochastic wave equation

Robert Dalang, Le Chen

We consider the stochastic wave equation on the real line driven by space time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply we ...

Elsevier Science Bv2015