Dependencydependent Bounds for Sums of Dependent Random Variables
Abstract
We consider the problem of bounding large deviations for noni.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent components. Bounds that depend on the degree of dependence between the observations have only been studied in the theory of mixing processes, where variables are timeordered. Here, we introduce a new way of measuring dependences within an unordered set of variables. We prove concentration inequalities, that apply to any set of random variables, but benefit from the presence of weak dependencies. We also discuss applications and extensions of our results to related problems of machine learning and large deviations.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.01404
 Bibcode:
 2018arXiv181101404L
 Keywords:

 Mathematics  Probability