Exploiting product distributions to identify relevant variables of correlation immune functions

Lisa Hellerstein, Bernard Roseli, Eric Bach, Soumya Ray, David Page

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)2375-2411
    Number of pages37
    JournalJournal of Machine Learning Research
    Volume10
    StatePublished - 2009

    Keywords

    • Boolean functions
    • Correlation immune functions
    • Product distributions
    • Relevant variables
    • Skewing

    ASJC Scopus subject areas

    • Software
    • Control and Systems Engineering
    • Statistics and Probability
    • Artificial Intelligence

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