A1425
Title: Stochastic representation, efficient computation methods, and stochastic ordering in tree-structured Ising models
Authors: Etienne Marceau - Laval University (Canada) [presenting]
Abstract: High-dimensional multivariate Bernoulli distributions are essential in the modeling of binary data in actuarial contexts. Tree-structured Ising models, a class of undirected graphical models for binary data, have been proven to be useful in a variety of applications in machine learning. The advantages of expressing tree-based Ising models are assessed via their mean parameterization rather than their commonly chosen canonical parameterization. This includes fixed marginal distributions, often convenient for dependence modeling, and the dispelling of the intractable normalizing constant otherwise plaguing Ising models. An analytic expression for the joint probability-generating function of mean-parameterized tree-structured Ising models is derived. The latter is used to build efficient computation methods for the sum of its constituent random variables. Similarly, an analytic expression is derived from their ordinary generating function of expected allocations, providing means for exact computations in the context of risk allocations.
