Learning and Sampling with Markov Random Fields

Markov Random Fields (MRFs) are a powerful tool for describing high-dimensional probability distributions. MRFs are related to general concepts known under the names of Boltzmann distribution in physics, Gibbs measure in mathematics, exponential family distributions in statistics, undirected graphical models in computer science, or energy-based models in machine learning. A recurrent interest for MRFs in many different branches of science is explained by the fact that they serve as a natural and interpretable modeling foundation for many scientific applications: MRFs have been used for modeling of natural systems at equilibrium since the creation of statistical physics! Yet, unknown training algorithms, as well as the lack of tools for generating predictions from these models present the main barriers to the widespread use of MRFs in scientific machine learning.

This workshop will discuss the progress at eliminating these known barriers by advancing the mathematics behind the statistical learning methods for MRFs. This includes addressing the challenges of designing a suite of efficient learning algorithms that incorporate physical symmetries, dealing with heterogeneous and noisy data sets, constructing MRFs in a form which allows for generation of predictions and sampling, at the same time having a robust implementation. The workshop will also demonstrate a wide applicability of the developed methods on open problems in several distinct scientific areas that require rigorous learning of interpretable and physics-informed probabilistic network models from distributed data.

Technical/Scientific Organizer:

Andrey Lokhov

Organizing Committee:

Anna Trujillo

Carissa Meierdierks Wall