Talagrand’s Inequality and Locality in Distributed Computing

Dubhashi, Devdatt

doi:10.7146/brics.v5i24.19430

BRICS

1998

DOI: 10.7146/brics.v5i24.19430

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Talagrand’s Inequality and Locality in Distributed Computing

Devdatt Dubhashi¹

Abstract: We illustrate the use of Talagrand's inequality and an extension of it to dependent random variables due to Marton for the analysis of distributed randomised algorithms, specifically, for edge colouring graphs.

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Cited by 2 publications

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Distances and Diameters in Concentration Inequalities: From Geometry to Optimal Assignment of Sampling Resources

Sullivan

Owhadi

2012

Int J Uncertainty Quantification

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Abstract. This note reviews, compares and contrasts three notions of "distance" or "size" that arise often in concentration-of-measure inequalities. We review Talagrand's convex distance and McDiarmid's diameter, and consider in particular the normal distance on a topological vector space X , which corresponds to the method of Chernoff bounds, and is in some sense "natural" with respect to the duality structure on X . We show that, notably, with respect to this distance, concentration inequalities on the tails of linear, convex, quasiconvex and measurable functions on X are mutually equivalent. We calculate the normal distances that correspond to families of Gaussian and of bounded random variables in R N , and to functions of N empirical means. As an application, we consider the problem of estimating the confidence that one can have in a quantity of interest that depends upon many empirical -as opposed to exact -means and show how the normal distance leads to a formula for the optimal assignment of sampling resources.

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Distances and Diameters in Concentration Inequalities: From Geometry to Optimal Assignment of Sampling Resources

Sullivan

Owhadi

2012

Int J Uncertainty Quantification

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Talagrand’s Inequality in Hereditary Settings

Dubhashi¹

1998

BRICS

Self Cite

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Talagrand’s Inequality and Locality in Distributed Computing

Abstract: We illustrate the use of Talagrand's inequality and an extension of it to dependent random variables due to Marton for the analysis of distributed randomised algorithms, specifically, for edge colouring graphs.

Cited by 2 publications

References 8 publications

Distances and Diameters in Concentration Inequalities: From Geometry to Optimal Assignment of Sampling Resources

Distances and Diameters in Concentration Inequalities: From Geometry to Optimal Assignment of Sampling Resources

Talagrand’s Inequality in Hereditary Settings

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