Learning Gaussian Networks

We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. Previ­ ous work has concentrated on metrics for do­ mains containing only discrete variables, un­ der the assumption that data represents a multinomial sample. In this paper, we ex­ tend this work, developing scoring metrics for domains containing only continuous variables under the assumption that continuous data is sampled from a multivariate normal distribu­ tion. Our work extends traditional statistical approaches for identifying vanishing regres­ sion coefficients in that we identify two im­ portant assumptions, called event equivalence and parameter modularity, that when com­ bined allow the construction of prior distri­ butions for multivariate normal parameters from a single prior Bayesian network speci­ fied by a user.