Title: Identical maximum likelihood estimates for Gaussian and Ising models defined by a chordless cycle
Authors: Giovanni Maria Marchetti - University of Florence (Italy) [presenting]
Abstract: Undirected graphical models defined by a chordless cycle require in general an iterative fitting procedures to get maximum likelihood estimates. For Gaussian models, the canonical parameters are the concentrations, that is the off-diagonal element in the inverse covariance matrix, while for Ising models, are the log-linear, two-factor interactions. However, we show conditions under which, if the canonical parameters are transformed to partial correlations, the two different likelihood functions, one for the continuous and the other for the binary variables, give the same maximum likelihood estimates provided the relevant starting correlation matrices coincide and have a closed form.