COMS 6253 : Advanced
نویسندگان
چکیده
Previously: • Administrative basics, introduction and high-level overview • Concept classes and the relationships among them: DNF formulas, decision trees, decision lists, linear and polynomial threshold functions. • The Probably Approximately Correct (PAC) learning model. • PAC learning linear threshold functions in poly(n, 1/ , log 1/δ) time • PAC learning polynomial threshold functions. Today: • PAC algorithm to learn degree-d PTFs in O(n) time • PTFs for decision trees and DTFs Relevant Readings: • Lisa Hellerstein and Rocco Servedio,“On PAC learning algorithms for rich Boolean function classes”, Theoretical Computer Science 384(1), pp. 66-76 (2007) (in particular Sections 2-3) (for material on PAC learning using PTFs) • Avrim Blum, “Rank-r decision lists are a subclass of r-decision lists”, Information Processing Letters, 42, pp. 183-185 (1992) (as the title implies, gives the relation between rank-r decision trees and r-decision lists) • Adam Klivans and Rocco Servedio, “Learning DNF in Time 2Õ(n1/3)”, Journal of Computer and System Sciences 68(2), pp. 303-318 (2004) (learning DNFs using PTFs)
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