A Boolean function f is correlationimmune if each input variable is independent of the output, under the uniform distribution on inputs. For example, the parity function is correlationimmune. We consider the problem...
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A Boolean function f is correlationimmune if each input variable is independent of the output, under the uniform distribution on inputs. For example, the parity function is correlationimmune. We consider the problem of identifying relevant variables of a correlationimmune 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 correlationimmune 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.
In this correspondence, we present a number of methods for constructing new resilient functions from old ones, These methods are significant generalizations of some previously known methods. The nonlinearity of some n...
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In this correspondence, we present a number of methods for constructing new resilient functions from old ones, These methods are significant generalizations of some previously known methods. The nonlinearity of some new constructed resilient functions is also discussed.
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