Cesare Miglioli

Maciej Besta, Raphael Grob, Cesare Miglioli et al.

Link prediction is one of the central problems in graph mining. However, recent studies highlight the importance of higher-order network analysis, where complex structures called motifs are the first-class citizens. We first show that existing link prediction schemes fail to effectively predict motifs. To alleviate this, we establish a general motif prediction problem and we propose several heuristics that assess the chances for a specified motif to appear. To make the scores realistic, our heuristics consider - among others - correlations between links, i.e., the potential impact of some arriving links on the appearance of other links in a given motif. Finally, for highest accuracy, we develop a graph neural network (GNN) architecture for motif prediction. Our architecture offers vertex features and sampling schemes that capture the rich structural properties of motifs. While our heuristics are fast and do not need any training, GNNs ensure highest accuracy of predicting motifs, both for dense (e.g., k-cliques) and for sparse ones (e.g., k-stars). We consistently outperform the best available competitor by more than 10% on average and up to 32% in area under the curve. Importantly, the advantages of our approach over schemes based on uncorrelated link prediction increase with the increasing motif size and complexity. We also successfully apply our architecture for predicting more arbitrary clusters and communities, illustrating its potential for graph mining beyond motif analysis.

Roberto Molinari, Gaetan Bakalli, Stéphane Guerrier et al.

The majority of machine learning methods and algorithms give high priority to prediction performance which may not always correspond to the priority of the users. In many cases, practitioners and researchers in different fields, going from engineering to genetics, require interpretability and replicability of the results especially in settings where, for example, not all attributes may be available to them. As a consequence, there is the need to make the outputs of machine learning algorithms more interpretable and to deliver a library of "equivalent" learners (in terms of prediction performance) that users can select based on attribute availability in order to test and/or make use of these learners for predictive/diagnostic purposes. To address these needs, we propose to study a procedure that combines screening and wrapper approaches which, based on a user-specified learning method, greedily explores the attribute space to find a library of sparse learners with consequent low data collection and storage costs. This new method (i) delivers a low-dimensional network of attributes that can be easily interpreted and (ii) increases the potential replicability of results based on the diversity of attribute combinations defining strong learners with equivalent predictive power. We call this algorithm "Sparse Wrapper AlGorithm" (SWAG).