Learning relational dependency networks in hybrid domains

Abstract

Statistical relational learning (SRL) is concerned with developing formalisms for representing and learning from data that exhibit both uncertainty and complex, relational structure. Most of the work in SRL has focused on modeling and learning from data that only contain discrete variables. As many important problems are characterized by the presence of both continuous and discrete variables, there has been a growing interest in developing hybrid SRL formalisms. Most of these formalisms focus on reasoning and representational issues and, in some cases, parameter learning. What has received little attention is learning the structure of a hybrid SRL model from data. In this paper, we fill that gap and make the following contributions. First, we propose hybrid relational dependency networks (HRDNs), an extension to relational dependency networks that are able to model continuous variables. Second, we propose an algorithm for learning both the structure and parameters of an HRDN from data. Third, we provide an empirical evaluation that demonstrates that explicitly modeling continuous variables results in more accurate learned models than discretizing them prior to learning.

Fast learning of relational dependency networks

“…This is a common restriction for statistical-relational structure learning methods [e.g. , Domingos and Lowd (2009) and Ravkic et al (2015)], which trades off expressive power for faster learning. For Bayesian network parameter estimation, we used maximum likelihood estimates, computed with previous methods ).…”

“…For instance, both Friend(A, B) and Friend (anna, B) are valid PRVs. Another language extension is to allow parametrized random variables to be formed with aggregate functions, as described by Kersting and De Raedt (2007); ; see also Ravkic et al (2015). For example, it is possible to use a functor that returns the number of friends of a generic person A.…”

“…Without this standardization, features with more instantiations carry exponentially more weight. Ravkic et al (2015) also use proportions for learning RDNs.…”

“…Using proportions as feature functions has the desirable consequence that the range of all feature functions is standardized to [0, 1] (Ravkic et al 2015). It is well-known that the number of instantiation counts in relational data can differ for different families, depending on the population variables they contain.…”

“…Two major classes of graphical models are dependency networks (DNs) (Heckerman et al 2000) and Bayesian networks (BNs) (Pearl 1988). While dependency networks have many attractive properties for modelling relational data (Ravkic et al 2015;Neville and Jensen 2007), relatively few structure learning methods have been developed for relational data. We describe a new approach to learning dependency networks: first learn a Bayesian network, then convert that network to a dependency network.…”