820 research outputs found
Projectivity revisited
The behaviour of statistical relational representations across differently
sized domains has become a focal area of research from both a modelling and a
complexity viewpoint.Recently, projectivity of a family of distributions
emerged as a key property, ensuring that marginal probabilities are independent
of the domain size. However, the formalisation used currently assumes that the
domain is characterised only by its size. This contribution extends the notion
of projectivity from families of distributions indexed by domain size to
functors taking extensional data from a database. This makes projectivity
available for the large range of applications taking structured input. We
transfer key known results on projective families of distributions to the new
setting. This includes a characterisation of projective fragments in different
statistical relational formalisms as well as a general representation theorem
for projective families of distributions. Furthermore, we prove a
correspondence between projectivity and distributions on countably infinite
domains, which we use to unify and generalise earlier work on statistical
relational representations in infinite domains. Finally, we use the extended
notion of projectivity to define a further strengthening, which we call
-projectivity, and which allows the use of the same representation in
different modes while retaining projectivity.Comment: 30 page
Stacked structure learning for lifted relational neural networks
Lifted Relational Neural Networks (LRNNs) describe relational domains using weighted first-order rules which act as templates for constructing feed-forward neural networks. While previous work has shown that using LRNNs can lead to state-of-the-art results in various ILP tasks, these results depended on hand-crafted rules. In this paper, we extend the framework of LRNNs with structure learning, thus enabling a fully automated learning process. Similarly to many ILP methods, our structure learning algorithm proceeds in an iterative fashion by top-down searching through the hypothesis space of all possible Horn clauses, considering the predicates that occur in the training examples as well as invented soft concepts entailed by the best weighted rules found so far. In the experiments, we demonstrate the ability to automatically induce useful hierarchical soft concepts leading to deep LRNNs with a competitive predictive power
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
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