Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures
Vidyasagar M, Balaji S, Hammer B (2001)
Systems & Control Letters 42(2): 151-157.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Vidyasagar, M.;
Balaji, S.;
Hammer, BarbaraUniBi 
Einrichtung
Abstract / Bemerkung
Open Problem No. 12.2 of (Vidyasagar, A Theory of Learning and Generalization: with Application to Neural Networks and Control Systems, Springer, London, 1997) asks: “Are the properties of uniform convergence of empirical means, and learnability preserved when the family of probability measures is replaced by its closure?” In this note, the question is answered in the affirmative. Further, it is shown that these properties are not preserved in general if the family of probability measures is replaced by its convex closure. An open question is posed as to whether it is possible to replace the family of probability measures by its convex closure in case the family is compact.
Erscheinungsjahr
2001
Zeitschriftentitel
Systems & Control Letters
Band
42
Ausgabe
2
Seite(n)
151-157
ISSN
01676911
Page URI
https://pub.uni-bielefeld.de/record/2982127
Zitieren
Vidyasagar M, Balaji S, Hammer B. Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures. Systems & Control Letters. 2001;42(2):151-157.
Vidyasagar, M., Balaji, S., & Hammer, B. (2001). Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures. Systems & Control Letters, 42(2), 151-157. https://doi.org/10.1016/S0167-6911(00)00086-4
Vidyasagar, M., Balaji, S., and Hammer, Barbara. 2001. “Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures”. Systems & Control Letters 42 (2): 151-157.
Vidyasagar, M., Balaji, S., and Hammer, B. (2001). Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures. Systems & Control Letters 42, 151-157.
Vidyasagar, M., Balaji, S., & Hammer, B., 2001. Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures. Systems & Control Letters, 42(2), p 151-157.
M. Vidyasagar, S. Balaji, and B. Hammer, “Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures”, Systems & Control Letters, vol. 42, 2001, pp. 151-157.
Vidyasagar, M., Balaji, S., Hammer, B.: Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures. Systems & Control Letters. 42, 151-157 (2001).
Vidyasagar, M., Balaji, S., and Hammer, Barbara. “Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures”. Systems & Control Letters 42.2 (2001): 151-157.
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