### "The Universal Glivenko-Cantelli Property" (Next Week at the Statistics Seminar)

For the first statistics seminar of 2011, we are very happy to
welcome —

- Ramon van Handel, "The Universal Glivenko-Cantelli Property"
*Abstract*: Uniform laws of large numbers are basic tools in many
problems in probability theory, statistics, and machine learning. On the other
hand, the law of large numbers is ultimately "just" a special case of two
fundamental probabilistic limit theorems: the reverse martingale convergence
theorem and the pointwise ergodic theorem. What can one say about uniform
convergence in the more general setting? Surprisingly, it turns out that for a
given class of functions, universal uniform convergence in the law of large
numbers, the reverse martingale convergence theorem, and the pointwise ergodic
theorem are all equivalent. Moreover, such classes of functions (which are
more general than the well-known Vapnik-Chervonenkis classes) can be
characterized by certain geometric and combinatorial properties. As an
application, I will discuss the pathwise optimality of sequential decisions
under partial information.
*Place and time*: Scaife Hall 125, on Monday, 24 January 2011, 4--5 pm

As always, the seminar is free and open to the public.

Enigmas of Chance

Posted at January 19, 2011 14:50 | permanent link