Learning intersections and thresholds of halfspaces
نویسندگان
چکیده
منابع مشابه
Learning Intersections and Thresholds of Halfspaces
We give the first polynomial time algorithm to learn any function of a constant number of halfspaces under the uniform distribution on the Boolean hypercube to within any constant error parameter. We also give the first quasipolynomial time algorithm for learning any Boolean function of a polylog number of polynomial-weight halfspaces under any distribution on the Boolean hypercube. As special ...
متن کاملLearning Intersections of Halfspaces with a Margin
We give a new algorithm for learning intersections of halfspaces with a margin, i.e. under the assumption that no example lies too close to any separating hyperplane. Our algorithm combines random projection techniques for dimensionality reduction, polynomial threshold function constructions, and kernel methods. The algorithm is fast and simple. It learns a broader class of functions and achiev...
متن کاملImproved Lower Bounds for Learning Intersections of Halfspaces
We prove new lower bounds for learning intersections of halfspaces, one of the most important concept classes in computational learning theory. Our main result is that any statistical-query algorithm for learning the intersection of √ n halfspaces in n dimensions must make 2 √ n) queries. This is the first non-trivial lower bound on the statistical query dimension for this concept class (the pr...
متن کاملCryptographic Hardness Results for Learning Intersections of Halfspaces
We give the first representation-independent hardness results for PAC learning intersections of halfspaces, a central concept class in computational learning theory. Our hardness results are derived from two public-key cryptosystems due to Regev, which are based on the worstcase hardness of well-studied lattice problems. Specifically, we prove that a polynomial-time algorithm for PAC learning i...
متن کاملHardness of learning noisy halfspaces using polynomial thresholds
We prove the hardness of weakly learning halfspaces in the presence of adversarial noise using polynomial threshold functions (PTFs). In particular, we prove that for any constants d ∈ Z and ε > 0, it is NP-hard to decide: given a set of {−1, 1}-labeled points in Rn whether (YES Case) there exists a halfspace that classifies (1−ε)-fraction of the points correctly, or (NO Case) any degree-d PTF ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2004
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2003.11.002