Vines inference

Abstract

Vines [19, 3] are reviewed. We prove that the product of 1 minus the square of partial correlations on a vine equals the determinant of the correlation matrix. This is used in learning vines. In model learning we are interested in models incorporating maximal (conditional) independence with minimal disturbance. This leads us to search for regular vines whose associated factorization of the determinant is dominant in the sense of majorization. We compare this with the method of independence graphs [21].