We are pleased to announce an upcoming talk by Dr. Ionas Erb from the Centre for Genomic Regulation (CRG), who will be presenting on April 23, 2025, at 15:00.

Abstract:

Contingency tables are data structures for discrete variables: each row stands for a value the row variable can take, and each column for a value the column variable can take (with higher dimensional tables for more than two variables). The table entries are event counts and are used to estimate the parameters of a cross-classified multinomial distribution, which allows to quantify interaction between the variables. The associated theory of log-linear models was established in the 1970ies already. In this context, marginal distributions are the distributions of subsets of variables obtained from coordinate projections. In this talk, I will scrutinize an alternative approach to the analysis of contingency tables that uses the logratio approach of compositional data analysis (CoDA). This latter approach leads to the so-called geometric marginals. These have an appealing geometric representation in terms of projections in Euclidean space, allowing for a Pythagorean theorem for probability distributions. The problem with this alternative form of marginalization is that the resulting distributions no longer have a clear probabilistic meaning. To obtain analogous geometric constructions for the classical (arithmetic) marginals, a generalization of Euclidean geometry known as Information Geometry must be applied. This approach is favored because it is based on the Fisher-Rao metric, the only metric on the simplex that is invariant under reparameterizations and sufficient statistics. A Pythagoras theorem for the Kullback-Leibler divergence of the distribution from its marginals makes use of the so-called information projections. These can be used to quantify the difference in mutual information that a distribution has from its arithmetic and geometric marginals, respectively. 

We are pleased to announce an upcoming talk by Dr. Ionas Erb from the Centre for Genomic Regulation (CRG), who will be presenting on April 23, 2025, at 15:00.

Abstract:

Contingency tables are data structures for discrete variables: each row stands for a value the row variable can take, and each column for a value the column variable can take (with higher dimensional tables for more than two variables). The table entries are event counts and are used to estimate the parameters of a cross-classified multinomial distribution, which allows to quantify interaction between the variables. The associated theory of log-linear models was established in the 1970ies already. In this context, marginal distributions are the distributions of subsets of variables obtained from coordinate projections. In this talk, I will scrutinize an alternative approach to the analysis of contingency tables that uses the logratio approach of compositional data analysis (CoDA). This latter approach leads to the so-called geometric marginals. These have an appealing geometric representation in terms of projections in Euclidean space, allowing for a Pythagorean theorem for probability distributions. The problem with this alternative form of marginalization is that the resulting distributions no longer have a clear probabilistic meaning. To obtain analogous geometric constructions for the classical (arithmetic) marginals, a generalization of Euclidean geometry known as Information Geometry must be applied. This approach is favored because it is based on the Fisher-Rao metric, the only metric on the simplex that is invariant under reparameterizations and sufficient statistics. A Pythagoras theorem for the Kullback-Leibler divergence of the distribution from its marginals makes use of the so-called information projections. These can be used to quantify the difference in mutual information that a distribution has from its arithmetic and geometric marginals, respectively.