Campuses:

Contraction

Monday, October 14, 2019 - 4:00pm - 4:45pm
Wotao Yin (University of California, Los Angeles)
Have you ever fallen asleep while reading a convergence proof? Most convergence proofs are written in algebraic equalities and inequalities. They are rigorous but are often not an intuitive way to illustrate the core proof ideas.

The good news is, for nonexpansive operators that constitute popular optimization methods such as forward-backward, alternative projection, Douglas-Rachford, ADMM, and so on, there exists a simple 2D graphing tool, Scaled Relative Graph, that not only captures their core ideas but also serves as rigorous convergence proofs.
Thursday, April 16, 2015 - 2:50pm - 3:40pm
Maxim Raginsky (University of Illinois at Urbana-Champaign)
This talk deals with quantifying the rate of contraction of the relative entropy with respect to a reference probability measure under the action of a Markov kernel. Sharp contraction estimates for Markov kernels are useful in a variety of settings, including distributed communication and simulation, exact and approximate stochastic filtering, analysis of MCMC algorithms, and statistical physics.
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