Title: Coordinate-free analysis of multivariate categorical data
Authors: Tamas Rudas - Hungarian Academy of Sciences Centre for Social Sciences (Hungary) [presenting]
Anna Klimova - IST Austria (Austria)
Abstract: Graphical models generalize the notion of conditional independence among variables which, most often, is equivalent to a factorization of the joint distribution. Relational models consider more general factorizations, and generalize conditional independence to situations when the sample space is not a Cartesian product of ranges of variables, and the effects entering the factorization are not related to cylinder sets of the sample space, i.e., to groups of variables. Basic concepts of statistical modeling are introduced, which can be applied in this situation. First, motivating examples are presented, then coordinate free exponential families of probability distributions are introduced, which postulate simple multiplicative structures. Some of the properties of these families are similar to that of log-linear or graphical models, but the maximum likelihood estimates under relational models have a few very surprising characteristics.