Exploiting product distributions to identify relevant variables of correlation immune functions

Published

Journal Article

A Boolean function f is correlation immune if each input variable is independent of the output, under the uniform distribution on inputs. For example, the parity function is correlation immune. We consider the problem of identifying relevant variables of a correlation immune function, in the presence of irrelevant variables. We address this problem in two different contexts. First, we analyze Skewing, a heuristic method that was developed to improve the ability of greedy decision tree algorithms to identify relevant variables of correlation immune Boolean functions, given examples drawn from the uniform distribution (Page and Ray, 2003). We present theoretical results revealing both the capabilities and limitations of skewing. Second, we explore the problem of identifying relevant variables in the Product Distribution Choice (PDC) learning model, a model in which the learner can choose product distributions and obtain examples from them. We prove a lemma establishing a property of Boolean functions that may be of independent interest. Using this lemma, we give two new algorithms for finding relevant variables of correlation immune functions in the PDC model. © 2009 Lisa Hellerstein, Bernard Roseli, Eric Bach, Soumya Ray and David Page.

Duke Authors

Cited Authors

  • Hellerstein, L; Roseli, B; Bach, E; Ray, S; Page, D

Published Date

  • November 30, 2009

Published In

Volume / Issue

  • 10 /

Start / End Page

  • 2375 - 2411

Electronic International Standard Serial Number (EISSN)

  • 1533-7928

International Standard Serial Number (ISSN)

  • 1532-4435

Citation Source

  • Scopus