Markov random fields and applications
A talk in the Bielefeld Stochastic Afternoon series by
Tetyana Pasurek
| Abstract: | This is the first of a series of lectures on Markov
random fields that will be continued in the cluster group "Stochastic
Analysis" (the announcement follows).
Markov fields appear as Gibbs equilibrium states in statistical
mechanics or as Markov networks or undirected graphical models in Big
Data analysis and machine learning. The goal is to develop a unified
theory that can then be applied to specific models (classical or
quantum; on lattices $Z^{d}$ and general graphs or in the continuum
$R^{d}$), covering a large amount of the results known so far. In
particular, we address the problems of existence and uniqueness of
Markov fields, their mixing properties and dimension-free estimates of
convergence rates. We also connect the two basic approaches --
Dobrushin's theory of weak dependence and Ruelle's superstability
estimates -- and extend them to unbounded interactions and irregular
underlying spaces. Within the CRC this talk is associated to the project(s): A5 |