Abstract. We introduce a novel method for relational learning with neural networks. The contributions of this paper are threefold. First, we introduce the concept of relational neural networks: feedforward networks with some recurrent components, the structure of which is determined by the relational database schema. For classifying a single tuple, they take as inputs the attribute values of not only the tuple itself, but also of sets of related tuples. We discuss several possible architectures for such networks. Second, we relate the expressiveness of these networks to the 'aggregation vs. selection' dichotomy in current relational learners, and argue that relational neural networks can learn non-trivial combinations of aggregation and selection, a task beyond the capabilities of most current relational learners. Third, we present and motivate different possible training strategies for such networks. We present experimental results on synthetic and benchmark data sets that support our claims and yield insight in the behaviour of the proposed training strategies.

In the last decade, connectionist models have been proposed that can process structured information directly. These methods, which are based on the use of graphs for the representation of the data and the relationships within the data, are particularly suitable for handling relational learning tasks. In this paper, two recently proposed architectures of this kind, i.e. Graph Neural Networks (GNNs) and Relational Neural Networks (RelNNs), are compared and discussed, along with their corresponding learning schemes. The goal is to evaluate the performance of these methods on benchmarks that are commonly used by the relational learning community. Moreover, we also aim at reporting differences in the behavior of the two models, in order to gain insights on possible extensions of the approaches. Since RelNNs have been developed with the specific task of learning aggregate functions in mind, some experiments are run considering that particular task. In addition, we carry out more general experiments on the mutagenesis and the biodegradability datasets, on which several other relational learners have been evaluated. The experimental results are promising and suggest that RelNNs and GNNs can be a viable approach for learning on relational data.

In various application domains, data can be represented as bags of vectors. Learning functions over such bags is a challenging problem. In this paper, a neural network approach, based on cascade-correlation networks, is proposed to handle this kind of data. By defining special aggregation units that are integrated in the network, a general framework to learn functions over bags is obtained. Results on both artificially created and real-world data sets are reported.

In various application domains, data can be represented as bags of vectors instead of single vectors. Learning aggregate functions from such bags is a challenging problem. In this paper, a number of simple neural network approaches and a combined approach based on cascadecorrelation are examined in order to handle this kind of data. Adapted feedforward networks, recurrent networks and networks with special aggregation units integrated in the network can all be used to construct networks that are capable of learning aggregate function. A combination of these three approaches is possible by using cascade-correlation, creating a method that automatically chooses the best of these options. Results on artificial and multi-instance data sets are reported, allowing a comparison between the different approaches.

No abstract