PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On combinatorial testing problems
Louigi Addario-Berry, Nicolas Broutin, Luc Devroye and Gábor Lugosi
Annals of Statistics Volume 38, pp. 3063-3092, 2010.


We study a class of hypothesis testing problems in which, upon observ- ing the realization of an n-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alter- natively, whether there is a subset of the components belonging to a certain given class of sets whose elements have been “contaminated,” that is, have a mean different from zero. We establish some general conditions under which testing is possible and others under which testing is hopeless with a small risk. The combinatorial and geometric structure of the class of sets is shown to play a crucial role. The bounds are illustrated on various examples.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:7638
Deposited By:Gábor Lugosi
Deposited On:17 March 2011