Francesca Chiaromonte

Riccardo Porcedda, Francesca Chiaromonte, Fabrizio Lillo et al.

Link prediction (inferring missing or future connections between nodes in a graph) is a fundamental problem in network science with widespread applications in, e.g., biological systems, recommender systems, finance and cybersecurity. The ability to accurately predict links has significant real-world applications, such as detecting fraudulent financial transactions or identifying drug-target interactions in biomedicine. Despite a rich literature, link prediction is still challenging, especially for graphs enriched with information on edges (direction) and nodes (attributes). In fact, research on link prediction, especially the one based on Graph Deep Learning (GDL), has mostly focused on undirected graphs, without fully leveraging node attributes. Here, we fill this gap by proposing Gravity-GraphSAGE (GG-SAGE), a modified version of GraphSAGE, a GDL model for node embeddings, composed of a gravity-inspired decoder. This implementation is the first example in the literature of a GraphSAGE backbone adopted for directed link prediction. Using the benchmark datasets Cora, Citeseer, PubMed and 16 real-world graphs from the online Netzschleuder repository, we show that our proposed model outperforms state-of-the-art GDL link prediction techniques. Using further experimental evidence, we relate the quality of the output of our model with various characteristics of the graph, suggesting that our framework scales well when applied to data of increasing complexity.

Riccardo Porcedda, Giuseppe Squillace, Bastian Epping et al.

While Graph Neural Networks (GNNs) have demonstrated significant efficacy in node classification tasks, where predictions rely on local neighborhood information, the performance of GNNs often drops when prediction tasks depend on long-range interactions. These limitations are attributed to phenomena such as oversquashing, where structural bottlenecks restrict signal propagation across the network topology. To address this challenge, we introduce RAwR, a computationally efficient rewiring framework that augments the input graph with a quotient graph derived from equitable partitions. This approach facilitates accelerated communication between nodes that share identical structural roles, as identified by the Weisfeiler-Leman graph coloring, and thereby reduces the total effective resistance of the system. Furthermore, by employing an approximate definition of the equitable partition, RAwR enables a controllable reduction of the quotient graph, which, in its most condensed state, recovers the conventional Master Node rewiring technique. Empirical evaluations across a diverse suite of benchmarks -- including homophilic, heterophilic, and synthetic long-range datasets -- demonstrate that RAwR achieves state-of-the-art results. Our contribution is further supported by an analytical investigation using a teacher-student model of linear GNNs, which elucidates the theoretical foundations of role-based rewiring. This analysis leads to the formulation of Spectral Role Lift (SRL), a metric designed to identify the optimal approximate equitable partition for maximizing predictive performance.

Corentin Lobet, Francesca Chiaromonte

Feature attribution is the dominant paradigm for explaining deep neural networks. However, most existing methods only loosely reflect the model's prediction-making process, thereby merely white-painting the black box. We argue that explanatory alignment is a key aspect of trustworthiness in prediction tasks: explanations must be directly linked to predictions, rather than serving as post-hoc rationalizations. We present model readability as a design principle enabling alignment, and PiNets as a modeling framework to pursue it in a deep learning context. PiNets are pseudo-linear networks that produce instance-wise linear predictions in an arbitrary feature space, making them linearly readable. We illustrate their use on image classification and segmentation tasks, demonstrating how PiNets produce explanations that are faithful across multiple criteria in addition to alignment.

Simone Tonini, Andrea Vandin, Francesca Chiaromonte et al.

We present a novel, simple and widely applicable semi-supervised procedure for anomaly detection in industrial and IoT environments, SAnD (Simple Anomaly Detection). SAnD comprises 5 steps, each leveraging well-known statistical tools, namely; smoothing filters, variance inflation factors, the Mahalanobis distance, threshold selection algorithms and feature importance techniques. To our knowledge, SAnD is the first procedure that integrates these tools to identify anomalies and help decipher their putative causes. We show how each step contributes to tackling technical challenges that practitioners face when detecting anomalies in industrial contexts, where signals can be highly multicollinear, have unknown distributions, and intertwine short-lived noise with the long(er)-lived actual anomalies. The development of SAnD was motivated by a concrete case study from our industrial partner, which we use here to show its effectiveness. We also evaluate the performance of SAnD by comparing it with a selection of semi-supervised methods on public datasets from the literature on anomaly detection. We conclude that SAnD is effective, broadly applicable, and outperforms existing approaches in both anomaly detection and runtime.

Vincent Pisztora, Yanglan Ou, Xiaolei Huang et al.

In this paper we propose $ε$-Consistent Mixup ($ε$mu). $ε$mu is a data-based structural regularization technique that combines Mixup's linear interpolation with consistency regularization in the Mixup direction, by compelling a simple adaptive tradeoff between the two. This learnable combination of consistency and interpolation induces a more flexible structure on the evolution of the response across the feature space and is shown to improve semi-supervised classification accuracy on the SVHN and CIFAR10 benchmark datasets, yielding the largest gains in the most challenging low label-availability scenarios. Empirical studies comparing $ε$mu and Mixup are presented and provide insight into the mechanisms behind $ε$mu's effectiveness. In particular, $ε$mu is found to produce more accurate synthetic labels and more confident predictions than Mixup.

Tobia Boschi, Matthew Reimherr, Francesca Chiaromonte

Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate additional known structure. In this article, we propose a new Semi-smooth Newton Augmented Lagrangian Method to efficiently solve the Elastic Net in ultra-high dimensional settings. Our new algorithm exploits both the sparsity induced by the Elastic Net penalty and the sparsity due to the second order information of the augmented Lagrangian. This greatly reduces the computational cost of the problem. Using simulations on both synthetic and real datasets, we demonstrate that our approach outperforms its best competitors by at least an order of magnitude in terms of CPU time. We also apply our approach to a Genome Wide Association Study on childhood obesity.

Jacopo Di Iorio, Francesca Chiaromonte, Marzia A. Cremona

In the last two decades several biclustering methods have been developed as new unsupervised learning techniques to simultaneously cluster rows and columns of a data matrix. These algorithms play a central role in contemporary machine learning and in many applications, e.g. to computational biology and bioinformatics. The H-score is the evaluation score underlying the seminal biclustering algorithm by Cheng and Church, as well as many other subsequent biclustering methods. In this paper, we characterize a potentially troublesome bias in this score, that can distort biclustering results. We prove, both analytically and by simulation, that the average H-score increases with the number of rows/columns in a bicluster. This makes the H-score, and hence all algorithms based on it, biased towards small clusters. Based on our analytical proof, we are able to provide a straightforward way to correct this bias, allowing users to accurately compare biclusters.

Bing Li, Hongyuan Zha, Francesca Chiaromonte

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of negligible variation for the response surface. These directions span the orthogonal complement of the minimal space relevant for the regression, and can be extracted according to a measure of the variation in the response, leading to General Contour Regression(GCR). In comparison to exiisting sufficient dimension reduction techniques, this sontour-based mothology guarantees exhaustive estimation of the central space under ellipticity of the predictoor distribution and very mild additional assumptions, while maintaining vn-consisytency and somputational ease. Moreover, it proves to be robust to departures from ellipticity. We also establish some useful population properties for GCR. Simulations to compare performance with that of standard techniques such as ordinary least squares, sliced inverse regression, principal hessian directions, and sliced average variance estimation confirm the advntages anticipated by theoretical analyses. We also demonstrate the use of contour-based methods on a data set concerning grades of students from Massachusetts colleges.