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Quantization of Models: Local Approach and Asymptotically Optimal Partitions

  • Klaus Pötzelberger
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In this paper we review algorithmic aspects related to maximum-supportplane partitions. These partitions have been defined in Bock (1992) and analyzed in Pötzelberger and Strasser (2001). The local approach to inference leads to a certain subclass of partitions. They are obtained from quantizing the distribution of the score function. We propose a numerical method to compute these partitions B approximately, in the sense that they are asymptotically optimal for increasing sizes |B|. These findings are based on recent results on the asymptotic distribution of sets of prototypes.

Keywords

Score Function Relative Efficiency Quantization Error Optimal Partition Local Alternative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. BOCK, H.H. (1992): A clustering technique for maximizing ø-divergence, noncentrality and discriminating power. In M. Schader (ed.): Analyzing and Modeling Data and Knowledge, Springer, Heidelberg, 19–36.CrossRefGoogle Scholar
  2. FLURY, B.A. (1990): Principal points. Biomrnetrika, 77, 33–41.MathSciNetzbMATHCrossRefGoogle Scholar
  3. GRAF, S. and LUSCHGY, H. (2000): Foundations of Quantization for Probability Distributions. Lecture Notes in Mathematics 1730, Springer, Berl in Heidelberg.zbMATHCrossRefGoogle Scholar
  4. POTZELBERGER, K. (2000): The general quantization problem for distributions with regular support. Math. Methods Statist., 2, 176–198.MathSciNetGoogle Scholar
  5. POTZELBERGER, K. (2002): Admissible unbiased quantizations: Distributions without linear components. To appear in: Math. Methods Statist.Google Scholar
  6. POTZELBERGER K. and STRASSER, H. (2001): Clustering and quantization by MSP-partitions. Statistics and Decisions, 19, 331–371.MathSciNetGoogle Scholar
  7. STEINER, G. (1999): Quantization and clustering with maximal information: Algorithms and numerical experiments, Ph.D. Thesis, Vienna University of Economics and Business Administration.Google Scholar
  8. STRASSER, H. (2000): Towards a statistical theory of optimal quantization. In W. Gaul, O. Opitz, M. Schader (eds.): Data Analysis: Scientific Modeling and Practical Application, Springer, Berlin Heidelberg, 369–383.Google Scholar
  9. ZADOR, P.L. (1964): Development and evaluation of procedures for quantizing Multivariate distributions, Ph.D. Thesis, Stanford University.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Klaus Pötzelberger
    • 1
  1. 1.Department of StatisticsVienna University of Economics and Business AdministrationViennaAustria

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