arXiv subjects

Anna Calissano

Publications and source records attributed to Anna Calissano.

7 recordsLinked to original sources

arXiv2026

A Metric Space of Spatial Graphs: Two-Sample Testing, Data Depth, and Application to Cardiac Fibrosis

Cardiac fibrosis reduces electrical conductivity and is a leading cause of arrhythmia. Arrhythmic waves typically rotate around non-conducting fibrotic patches, so the geometry and topology of these patches (spatially isolated regions of fibrotic tissue within the heart muscle) play an important role in arrhythmia dynamics. Despite their clinical relevance, these structures remain poorly understood. We address this open problem using histopathological images of human hearts affected by cardiac fibrosis. Each patch is represented as a spatial graph via skeletonization, where nodes are embedded as points in Euclidean space and edges encode geometric properties of the underlying tissue. The core methodological contribution of this work is the introduction of spatial graph space, a metric space equipped with a rotation-invariant Fused Gromov Wasserstein metric that enables comparison of spatial graphs with differing numbers of nodes and edges. Building on this, we perform a distribution-level statistical testing and depth measures for spatial graphs. To enable the interpretation of the spatial graph sample distribution, we introduce DepthPlot, a novel visualization tool for depth measures in metric spaces. Applying our methodology to compare patients and the spatial position of patches within the ventricles, we find that fibrotic textures exhibit strong patient-specific features, while some hearts display notable geometric similarities, potentially reflecting shared pathological mutations or other unknown factors. Through quantitative depth measures, we characterize test outcomes via central and peripheral spatial graphs, demonstrating that the proposed framework yields statistically and clinically meaningful insights into fibrotic texture characterization.

stat.AP↗

arXiv2026

Conformal Graph Prediction with Z-Gromov-Wasserstein Distances

Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal prediction framework for graph-valued outputs, providing distribution-free coverage guarantees in structured output spaces. Our method defines nonconformity via the Z-Gromov-Wasserstein distance, instantiated in practice through Fused Gromov-Wasserstein (FGW), enabling permutation invariant comparison between predicted and candidate graphs. To obtain adaptive prediction sets, we introduce Score Conformalized Quantile Regression (SCQR), an extension of Conformalized Quantile Regression (CQR) to handle complex output spaces such as graph-valued outputs. We evaluate the proposed approach on a synthetic task and a real problem of molecule identification.

stat.ML↗

arXiv2025

Topological Spatial Graph Coarsening

Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to find a smaller spatial graph (i.e., with less nodes) with the same overall structure as the initial one. In this context, performing the graph reduction while preserving the main topological features of the initial graph is particularly relevant, due to the additional spatial information. Thus, we propose a topological spatial graph coarsening approach based on a new framework that finds a trade-off between the graph reduction and the preservation of the topological characteristics. The coarsening is realized by collapsing short edges. In order to capture the topological information required to calibrate the reduction level, we adapt the construction of classical topological descriptors made for point clouds (the so-called persistent diagrams) to spatial graphs. This construction relies on the introduction of a new filtration called triangle-aware graph filtration. Our coarsening approach is parameter-free and we prove that it is equivariant under rotations, translations and scaling of the initial spatial graph. We evaluate the performances of our method on synthetic and real spatial graphs, and show that it significantly reduces the graph sizes while preserving the relevant topological information.

stat.ML↗

arXiv2025

Barycentric subspace analysis of network-valued data

Certain data are naturally modeled by networks or weighted graphs, be they arterial networks or mobility networks. When there is no canonical labeling of the nodes across the dataset, we talk about unlabeled networks. In this paper, we focus on the question of dimensionality reduction for this type of data. More specifically, we address the issue of interpreting the feature subspace constructed by dimensionality reduction methods. Most existing methods for network-valued data are derived from principal component analysis (PCA) and therefore rely on subspaces generated by a set of vectors, which we identify as a major limitation in terms of interpretability. Instead, we propose to implement the method called barycentric subspace analysis (BSA), which relies on subspaces generated by a set of points. In order to provide a computationally feasible framework for BSA, we introduce a novel embedding for unlabeled networks where we replace their usual representation by equivalence classes of isomorphic networks with that by equivalence classes of cospectral networks. We then illustrate BSA on simulated and real-world datasets, and compare it to tangent PCA.

math.DG↗

arXiv2025

Graph Counterfactual Explainable AI via Latent Space Traversal

Explaining the predictions of a deep neural network is a nontrivial task, yet high-quality explanations for predictions are often a prerequisite for practitioners to trust these models. Counterfactual explanations aim to explain predictions by finding the ''nearest'' in-distribution alternative input whose prediction changes in a pre-specified way. However, it remains an open question how to define this nearest alternative input, whose solution depends on both the domain (e.g. images, graphs, tabular data, etc.) and the specific application considered. For graphs, this problem is complicated i) by their discrete nature, as opposed to the continuous nature of state-of-the-art graph classifiers; and ii) by the node permutation group acting on the graphs. We propose a method to generate counterfactual explanations for any differentiable black-box graph classifier, utilizing a case-specific permutation equivariant graph variational autoencoder. We generate counterfactual explanations in a continuous fashion by traversing the latent space of the autoencoder across the classification boundary of the classifier, allowing for seamless integration of discrete graph structure and continuous graph attributes. We empirically validate the approach on three graph datasets, showing that our model is consistently high-performing and more robust than the baselines.

cs.LG↗

arXiv2024

Conformal Prediction Sets for Populations of Graphs

The analysis of data such as graphs has been gaining increasing attention in the past years. This is justified by the numerous applications in which they appear. Several methods are present to predict graphs, but much fewer to quantify the uncertainty of the prediction. The present work proposes an uncertainty quantification methodology for graphs, based on conformal prediction. The method works both for graphs with the same set of nodes (labelled graphs) and graphs with no clear correspondence between the set of nodes across the observed graphs (unlabelled graphs). The unlabelled case is dealt with the creation of prediction sets embedded in a quotient space. The proposed method does not rely on distributional assumptions, it achieves finite-sample validity, and it identifies interpretable prediction sets. To explore the features of this novel forecasting technique, we perform two simulation studies to show the methodology in both the labelled and the unlabelled case. We showcase the applicability of the method in analysing the performance of different teams during the FIFA 2018 football world championship via their player passing networks.

stat.ME↗

arXiv2024

Interpreting Equivariant Representations

Latent representations are used extensively for downstream tasks, such as visualization, interpolation or feature extraction of deep learning models. Invariant and equivariant neural networks are powerful and well-established models for enforcing inductive biases. In this paper, we demonstrate that the inductive bias imposed on the by an equivariant model must also be taken into account when using latent representations. We show how not accounting for the inductive biases leads to decreased performance on downstream tasks, and vice versa, how accounting for inductive biases can be done effectively by using an invariant projection of the latent representations. We propose principles for how to choose such a projection, and show the impact of using these principles in two common examples: First, we study a permutation equivariant variational auto-encoder trained for molecule graph generation; here we show that invariant projections can be designed that incur no loss of information in the resulting invariant representation. Next, we study a rotation-equivariant representation used for image classification. Here, we illustrate how random invariant projections can be used to obtain an invariant representation with a high degree of retained information. In both cases, the analysis of invariant latent representations proves superior to their equivariant counterparts. Finally, we illustrate that the phenomena documented here for equivariant neural networks have counterparts in standard neural networks where invariance is encouraged via augmentation. Thus, while these ambiguities may be known by experienced developers of equivariant models, we make both the knowledge as well as effective tools to handle the ambiguities available to the broader community.

cs.LG↗