Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures
✍ Scribed by M. Vidyasagar; S. Balaji; B. Hammer
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 107 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0167-6911
No coin nor oath required. For personal study only.
✦ Synopsis
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 a rmative. 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.