# Luc Rey-Bellet: Variational representation and concentration inequalities for uncertainty quantification

**Time: **
Mon 2020-10-26 15.15 - 16.15

**Location: **
Zoom, meeting ID: 621 4469 8204

**Lecturer: **
Luc Rey-Bellet, UMass Amherst

### Abstract

We use variational representation for information-theoretic divergences (such as the KL-divergences) and concentration

inequalities to derive, in a systematic way, tight information inequalities. A central question in uncertainty quantification and statistical learning is how to choose the right divergences for the right quantity of interest. We concentrate on KL-divergence, f-divergences, and Renyi divergences and discuss several examples: expected values, variance and other functionals, rare events, and steady state expectation for MCMC dynamics (for example Hamiltonian Monte-Carlo).

**Zoom notes:** The passcode for this meeting is 321777. This meeting ID —
621 4469 8204
— will be the recurring meeting for the Statistics and Probability Seminar.