Probabilistic ’generalization‘ of functions and dimension-based uniform convergence results

  • Authors:
  • Martin Anthony

  • Affiliations:
  • Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK email: m.anthony@lse.ac.uk

  • Venue:
  • Statistics and Computing
  • Year:
  • 1998

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Abstract

In this largely expository article, we highlight the significance of various types of ’dimension‘ for obtaining uniform convergence results in probability theory and we demonstrate how these results lead to certain notions of generalization for classes of binary-valued and real-valued functions. We also present new results on the generalization ability of certain types of artificial neural networks with real output.