Go back to

• Abstracts of the Talks
• Program

Johannes Rauh  (Max Planck Institute for Mathematics in the Sciences, Germany)
Friday, August 06, 2010, room Hörsaal 2
Maximizing the Kullback-Leibler distance

Nihat Ay proposed the following problem [1], motivated from statistical learning theory: Let be an exponential family. Find the maximizer of the Kullback-Leibler distance from . A maximizing probability measure P has a lot of interesting properties. For example, the restriction of to the support of P will be equal to P, i.e. if (for the proof in the most general case see [2]). This simple property can be used to transform the problem into another form. The first observation is that probability measures having this ``projection property'' always come in pairs , such that and have the same sufficient statistics A and disjoint supports. Therefore we can solve the original problem by investigating the kernel of the sufficient statistics . If we find all local maximizers of

subject to , then we know all maximizers of the original problem. The talk will present the transformed problem and its relation to the original problem. In the end I will give some consequences for the solutions of the original problem.

[1] N. Ay: An Information-Geometric Approach to a Theory of Pragmatic Structuring. The Annals of Probability 30 (2002) 416-436.

[2] F. Matúš: Optimality conditions for maximizers of the information divergence from an exponential family. Kybernetika 43, 731-746.