Algorithms for PAC learning of functions with smoothness properties

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We present three computationally efficient algorithms for Probably and Approximately Correct (PAC) learning of an unknown function f: [0, 1]{sup d} {r_arrow} [0,1], based on finite samples. The function f is chosen from the family F {intersection} C([0,1]{sup d}) or F {intersection} L{sup {infinity}} ([0,1]{sup d}), where F has either bounded modulus of smoothness or bounded capacity or both. Three function estimators based on: local averaging; nearest neighbor rule; and Nadaraya-Watson estimator, all computed using the Haar system, are analyzed. With no preprocessing of the sample, estimated function value at a given point can be computed in O(n) time. With ... continued below

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6 p.

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Rao, N.S.V. & Protopopescu, V.A. February 1, 1996.

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Description

We present three computationally efficient algorithms for Probably and Approximately Correct (PAC) learning of an unknown function f: [0, 1]{sup d} {r_arrow} [0,1], based on finite samples. The function f is chosen from the family F {intersection} C([0,1]{sup d}) or F {intersection} L{sup {infinity}} ([0,1]{sup d}), where F has either bounded modulus of smoothness or bounded capacity or both. Three function estimators based on: local averaging; nearest neighbor rule; and Nadaraya-Watson estimator, all computed using the Haar system, are analyzed. With no preprocessing of the sample, estimated function value at a given point can be computed in O(n) time. With preprocessing, the first and third estimators can be computed in O((log n){sup d}) time using a range-tree precomputed in O(dn(log n){sup d}) time.

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6 p.

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OSTI as DE96005973

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  • 4. international symposium on artificial intelligence and mathematics, Fort Lauderdale, FL (United States), 3-5 Jan 1996

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  • Other: DE96005973
  • Report No.: CONF-960130--1
  • Grant Number: AC05-84OR21400
  • DOI: 10.2172/217721 | External Link
  • Office of Scientific & Technical Information Report Number: 206360
  • Archival Resource Key: ark:/67531/metadc664452

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  • February 1, 1996

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  • June 29, 2015, 9:42 p.m.

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  • Jan. 15, 2016, 12:41 p.m.

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Rao, N.S.V. & Protopopescu, V.A. Algorithms for PAC learning of functions with smoothness properties, article, February 1, 1996; Tennessee. (digital.library.unt.edu/ark:/67531/metadc664452/: accessed August 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.