Estimating Aggregate Properties In Relational Networks With Unobserved Data

Aggregate network properties such as cluster cohesion and the number of bridge nodes can be used to glean insights about a network's community structure, spread of influence and the resilience of the network to faults. Efficiently computing network properties when the network is fully observed has received significant attention (Wasserman and Faust 1994; Cook and Holder 2006), however the problem of computing aggregate network properties when there is missing data attributes has received little attention. Computing these properties for networks with missing attributes involves performing inference over the network. Statistical relational learning (SRL) and graph neural networks (GNNs) are two classes of machine learning approaches well suited for inferring missing attributes in a graph. In this paper, we study the effectiveness of these approaches in estimating aggregate properties on networks with missing attributes. We compare two SRL approaches and three GNNs. For these approaches we estimate these properties using point estimates such as MAP and mean. For SRL-based approaches that can infer a joint distribution over the missing attributes, we also estimate these properties as an expectation over the distribution. To compute the expectation tractably for probabilistic soft logic, one of the SRL approaches that we study, we introduce a novel sampling framework. In the experimental evaluation, using three benchmark datasets, we show that SRL-based approaches tend to outperform GNN-based approaches both in computing aggregate properties and predictive accuracy. Specifically, we show that estimating the aggregate properties as an expectation over the joint distribution outperforms point estimates.