Generic properties of learning systems

Tomasz Szarek

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 2, page 93-103
  • ISSN: 0066-2216

Abstract

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It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.

How to cite

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Szarek, Tomasz. "Generic properties of learning systems." Annales Polonici Mathematici 73.2 (2000): 93-103. <http://eudml.org/doc/262803>.

@article{Szarek2000,
abstract = {It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.},
author = {Szarek, Tomasz},
journal = {Annales Polonici Mathematici},
keywords = {iterated function systems; Markov operators; average contractivity condition},
language = {eng},
number = {2},
pages = {93-103},
title = {Generic properties of learning systems},
url = {http://eudml.org/doc/262803},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Szarek, Tomasz
TI - Generic properties of learning systems
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 2
SP - 93
EP - 103
AB - It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.
LA - eng
KW - iterated function systems; Markov operators; average contractivity condition
UR - http://eudml.org/doc/262803
ER -

References

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  1. [1] W. Bartoszek, Norm residuality of ergodic operators, Bull. Polish Acad. Sci. Math. 29 (1981), 165-167. Zbl0472.47006
  2. [2] R. M. Dudley, Probabilities and Metrics, Aarhus Universitet, 1976. 
  3. [3] R. Fortet et B. Mourier, Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. École Norm. Sup. 70 267-285 (1953). Zbl0053.09601
  4. [4] A. Iwanik, Approximation theorem for stochastic operators, Indiana Univ. Math. J. 29 (1980), 415-425. Zbl0474.47003
  5. [5] A. Iwanik and R. Rębowski, Structure of mixing and category of complete mixing for stochastic operators, Ann. Polon. Math. 56 (1992), 233-242. Zbl0786.47004
  6. [6] A. Lasota and J. Myjak, Generic properties of fractal measures, Bull. Polish Acad. Sci. Math. 42 (1994), 283-296. Zbl0851.28004
  7. [7] A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41-77. Zbl0804.47033
  8. [8] T. Szarek, Generic properties of continuous iterated function systems, Bull. Polish Acad. Sci. Math. 47 (1997), 77-89. Zbl0926.60057
  9. [9] T. Szarek, Iterated function systems depending on a previous transformation, Univ. Iagel. Acta Math. 33 (1996), 161-172. Zbl0888.47016
  10. [10] T. Szarek, Markov operators acting on Polish spaces, Ann. Polon. Math. 67 (1997), 247-257. Zbl0903.60052

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