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Retarded learning: rigorous results from statistical mechanics
1Laboratoire de Physique Statistique de L'E.N.S., Ecole Normale Supérieure, Paris, France.
Physical Review Letters
|April 6, 2001
Summary
This study introduces bounds for learning probability distributions with unknown symmetry. An optimal method is suggested for learning nonsmooth distributions based on these findings.
Area of Science:
- Statistical mechanics
- Machine learning theory
Background:
- Learning probability distributions is crucial in various scientific fields.
- Characterizing distributions with unknown symmetry presents unique challenges.
Purpose of the Study:
- To develop bounds on the critical number of examples for learning distribution symmetry.
- To propose an asymptotically optimal learning method for nonsmooth distributions.
Main Methods:
- Utilizing an entropic performance measure.
- Applying the variational method from statistical mechanics.
Main Results:
- Established exact upper and lower bounds for learning symmetry direction.
- Demonstrated asymptotic tightness of the derived bounds.
Conclusions:
- The derived bounds provide insights into the learnability of symmetric distributions.
- An efficient method for learning nonsmooth distributions is suggested.