Convex Influences

  title={Convex Influences},
  author={Anindya De and Shivam Nadimpalli and Rocco A. Servedio},
We introduce a new notion of influence for symmetric convex sets over Gaussian space, which we term “convex influence”. We show that this new notion of influence shares many of the familiar properties of influences of variables for monotone Boolean functions f : {± 1 } n → {± 1 } . Our main results for convex influences give Gaussian space analogues of many important results on influences for monotone Boolean functions. These include (robust) characterizations of extremal functions, the Poincar… 



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On learning monotone Boolean functions

  • A. BlumC. BurchJ. Langford
  • Computer Science, Mathematics
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
A simple algorithm is described that achieves error at most 1/2-/spl Omega/(1//spl radic/n), improving on the previous best bound of O(log n), and it is proved that no algorithm, given a polynomial number of samples, can guarantee error.