Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no longer apply. These difficulties are particularly pronounced for spatio-temporal data, which exhibit dependencies across both space and time and are often characterized by nonlinear dynamics, time variance, and missing observations, hence calling for new accuracy assessment methodologies. This paper introduces a residual correlation analysis framework for assessing the optimality of spatio-temporal relational-enabled neural predictive models, notably in settings with incomplete and heterogeneous data. By leveraging the principle that residual correlation indicates information not captured by the model, enabling the identification and localization of regions in space and time where predictive performance can be improved. A strength of the proposed approach is that it operates under minimal assumptions, allowing also for robust evaluation of deep learning models applied to multivariate time series, even in the presence of missing and heterogeneous data. In detail, the methodology constructs tailored spatio-temporal graphs to encode sparse spatial and temporal dependencies and employs asymptotically distribution-free summary statistics to detect time intervals and spatial regions where the model underperforms. The effectiveness of what proposed is demonstrated through experiments on both synthetic and real-world datasets using state-of-the-art predictive models. • Proposes a novel residual correlation analysis to assess the quality of deep spatio-temporal models and identify regions where the predictions can be improved. • Complements traditional accuracy-based evaluations by offering an independent, metric-agnostic assessment of model quality. • Operates under minimal assumptions and remains effective even with missing or heterogeneous data, making it broadly applicable to real-world scenarios and deep learning models.

The rapidly evolving field of machine learning for graphstructured data gathered significant attention due to its ability to preserve critical information inherent in complex data structures.As a result, significant efforts have been dedicated to designing advanced architectures and foundational models optimized for graph-based operations.Research in this area explores methodologies for graph representation learning and graph generation, incorporating probabilistic models such as variational autoencoders and normalizing flows.Despite increasing interest from researchers as well as their efforts in solving graph-related problems, several issues and areas remain to be addressed to improve model generalization and reliability.This tutorial reviews foundational concepts and challenges in graph representation, structure learning, and graph generation, while also summarizing the contributions accepted for publication in the special session on this topic at the 33th European

Graph neural networks use relational information as an inductive bias to enhance prediction performance. Not rarely, task-relevant relations are unknown and graph structure learning approaches have been proposed to learn them from data. Given their latent nature, no graph observations are available to provide a direct training signal to the learnable relations. Therefore, graph topologies are typically learned on the prediction task alongside the other graph neural network parameters. In this paper, we demonstrate that minimizing point-prediction losses does not guarantee proper learning of the latent relational information and its associated uncertainty. Conversely, we prove that suitable loss functions on the stochastic model outputs simultaneously grant solving two tasks: (i) learning the unknown distribution of the latent graph and (ii) achieving optimal predictions of the target variable. Finally, we propose a sampling-based method that solves this joint learning task. Empirical results validate our theoretical claims and demonstrate the effectiveness of the proposed approach.

The Temporal Graph Learning (TGL) workshop, now in its third edition at KDD 2025, offers an interdisciplinary platform for researchers to explore the evolving applications of temporal networks in various domains, including recommender systems, social network analysis, traffic analytics, and epidemiological data analysis.The workshop aims to facilitate the exchange of ideas across disciplines, highlight successes and challenges in TGL, and outline future research directions.The workshop welcomes diverse contributions, offers keynote talks from academic and industry experts, and is complemented by a panel discussion on emerging aspects of TGL.

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

Many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. In this article, we present an operational framework to unify this vast and diverse literature by describing pooling operators as the combination of three functions: selection, reduction, and connection (SRC). We then introduce a taxonomy of pooling operators, based on some of their key characteristics and implementation differences under the SRC framework. Finally, we propose three criteria to evaluate the performance of pooling operators and use them to investigate the behavior of different operators on a variety of tasks.

In a broad range of real-world machine learning applications, representing examples as graphs is crucial to avoid a loss of information.For this reason, in the last few years, the definition of machine learning methods, particularly neural networks, for graph-structured inputs has been gaining increasing attention.In particular, Deep Graph Networks (DGNs) are nowadays the most commonly adopted models to learn a representation that can be used to address different tasks related to nodes, edges, or even entire graphs.This tutorial paper reviews fundamental concepts and open challenges of graph representation learning and summarizes the contributions that have been accepted for publication to the ESANN 2023 special session on the topic.

Spatiotemporal graph neural networks have shown to be effective in time series forecasting applications, achieving better performance than standard univariate predictors in several settings. These architectures take advantage of a graph structure and relational inductive biases to learn a single (global) inductive model to predict any number of the input time series, each associated with a graph node. Despite the gain achieved in computational and data efficiency w.r.t. fitting a set of local models, relying on a single global model can be a limitation whenever some of the time series are generated by a different spatiotemporal stochastic process. The main objective of this paper is to understand the interplay between globality and locality in graph-based spatiotemporal forecasting, while contextually proposing a methodological framework to rationalize the practice of including trainable node embeddings in such architectures. We ascribe to trainable node embeddings the role of amortizing the learning of specialized components. Moreover, embeddings allow for 1) effectively combining the advantages of shared message-passing layers with node-specific parameters and 2) efficiently transferring the learned model to new node sets. Supported by strong empirical evidence, we provide insights and guidelines for specializing graph-based models to the dynamics of each time series and show how this aspect plays a crucial role in obtaining accurate predictions.

Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational information characterizing the underlying data-generating process is unavailable and the practitioner is left with the problem of inferring from data which relational graph to use in the subsequent processing stages. We propose novel, principled - yet practical - probabilistic score-based methods that learn the relational dependencies as distributions over graphs while maximizing end-to-end the performance at task. The proposed graph learning framework is based on consolidated variance reduction techniques for Monte Carlo score-based gradient estimation, is theoretically grounded, and, as we show, effective in practice. In this paper, we focus on the time series forecasting problem and show that, by tailoring the gradient estimators to the graph learning problem, we are able to achieve state-of-the-art performance while controlling the sparsity of the learned graph and the computational scalability. We empirically assess the effectiveness of the proposed method on synthetic and real-world benchmarks, showing that the proposed solution can be used as a stand-alone graph identification procedure as well as a graph learning component of an end-to-end forecasting architecture.

The flourishing field of deep learning for graphs relies on the layered computation of representations from graph-structured input data.Message passing is the most common strategy for such processing of graphs, based on an efficient information exchange among the connected nodes via a local and iterative procedure.Representations learned in this way can be used to address different tasks related to nodes, edges, or even entire graphs.This tutorial paper reviews fundamental concepts and open challenges of deep learning for graphs and summarizes the contributions that have been accepted for publication to the ESANN 2022 special session on the topic.

In this paper, we consider the recently proposed family of continual learning models, called Gated Linear Networks (GLNs), and study two crucial aspects impacting on the amount of catastrophic forgetting affecting gated linear networks, namely, data standardization and gating mechanism. Data standardization is particularly challenging in the online/continual learning setting because data from future tasks is not available beforehand. The results obtained using an online standardization method show a considerably higher amount of forgetting compared to an offline -static- standardization. Interestingly, with the latter standardization, we observe that GLNs show almost no forgetting on the considered benchmark datasets. Secondly, for an effective GLNs, it is essential to tailor the hyperparameters of the gating mechanism to the data distribution. In this paper, we propose a gating strategy based on a set of prototypes and the resulting Voronoi tessellation. The experimental assessment shows that the proposed approach is more robust to different data standardizations compared to the original one, based on a halfspace gating mechanism, and shows improved predictive performance.

We present an anomaly and outlier detection method for graph data. The method relies on the consideration that anomalies and outliers are more easily isolated by certain incremental partitionings of the data space. Specifically, we build upon the isolation forest method and introduce a new incremental partitioning of the space of graphs that makes the isolation forest method applicable to generic attributed graphs, i.e., graphs where both nodes and edges can be associated with attributes. Within the considered general setup, the topology and the number of nodes can change from graph to graph, and a node correspondence between different graphs can be absent or unknown. Examples of applications of what proposed include the identification of frauds and fake news in communication networks, and breakage of systems monitored by sensor networks. The main novel contribution of the paper is a graph space partitioning which we prove to be expressive enough to identify anomalies and outlier graphs in a given dataset. An empirical analysis on synthetic and real-world graphs validates the effectiveness of the proposed method.

We present the first whiteness hypothesis test for graphs, i.e., a whiteness test for multivariate time series associated with the nodes of a dynamic graph; as such, the test represents an important model assessment tool for graph deep learning, e.g., in forecasting setups. The statistical test aims at detecting existing serial dependencies among close-in-time observations, as well as spatial dependencies among neighboring observations given the underlying graph. The proposed AZ-test can be intended as a spatio-temporal extension of traditional tests designed for system identification to graph signals. The AZ-test is versatile, allowing the underlying graph to be dynamic, changing in topology and set of nodes over time, and weighted, thus accounting for connections of different strength, as it is the case in many application scenarios like sensor and transportation networks. The asymptotic distribution of the designed test can be derived under the null hypothesis without assuming identically distributed data. We show the effectiveness of the test on both synthetic and real-world problems, and illustrate how it can be employed to assess the quality of spatio-temporal forecasting models by analyzing the prediction residuals appended to the graph stream.

We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves the metric structure of the graph domain, in probability. In addition to being an explicit embedding method, it also allows us to efficiently and effectively approximate graph metric distances (as well as complete kernel functions); a criterion to select the embedding dimension trading off the approximation accuracy with the computational cost is also provided. GRNF can be used within traditional processing methods or as a training-free input layer of a graph neural network. The theoretical guarantees that accompany GRNF ensure that the considered graph distance is metric, hence allowing to distinguish any pair of non-isomorphic graphs.

The space of graphs is often characterized by a nontrivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional Euclidean space, but non-Euclidean spaces have often been shown to be better suited for embedding graphs. Among these, constant-curvature Riemannian manifolds (CCMs) offer embedding spaces suitable for studying the statistical properties of a graph distribution, as they provide ways to easily compute metric geodesic distances. In this paper, we focus on the problem of detecting changes in stationarity in a stream of attributed graphs. To this end, we introduce a novel change detection framework based on neural networks and CCMs, which takes into account the non-Euclidean nature of graphs. Our contribution in this paper is twofold. First, via a novel approach based on adversarial learning, we compute graph embeddings by training an autoencoder to represent graphs on CCMs. Second, we introduce two novel change detection tests operating on CCMs. We perform experiments on synthetic data, as well as two real-world application scenarios: the detection of epileptic seizures using functional connectivity brain networks and the detection of hostility between two subjects, using human skeletal graphs. Results show that the proposed methods are able to detect even small changes in a graph-generating process, consistently outperforming approaches based on Euclidean embeddings.

This paper proposes an autoregressive (AR) model for sequences of graphs, which generalises traditional AR models. A first novelty consists in formalising the AR model for a very general family of graphs, characterised by a variable topology, and attributes associated with nodes and edges. A graph neural network (GNN) is also proposed to learn the AR function associated with the graph-generating process (GGP), and subsequently predict the next graph in a sequence. The proposed method is compared with four baselines on synthetic GGPs, denoting a significantly better performance on all considered problems.

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data representation possibly characterised by convenient geometric properties. Euclidean spaces are by far the most widely used embedding spaces, thanks to their well-understood structure and large availability of consolidated inference methods. However, recent research demonstrated that many types of complex data (e.g., those represented as graphs) are actually better described by non-Euclidean geometries. Here, we investigate how embedding graphs on constant-curvature manifolds (hyper-spherical and hyperbolic manifolds) impacts on the ability to detect changes in sequences of attributed graphs. The proposed methodology consists in embedding graphs into a geometric space and perform change detection there by means of conventional methods for numerical streams. The curvature of the space is a parameter that we learn to reproduce the geometry of the original application-dependent graph space. Preliminary experimental results show the potential capability of representing graphs by means of curved manifold, in particular for change and anomaly detection problems.

Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such processes. The methodology is general and considers a process generating attributed graphs with a variable number of vertices/edges, without the need to assume a one-to-one correspondence between vertices at different time steps. The methodology acts by embedding every graph of the stream into a vector domain, where a conventional multivariate change detection procedure can be easily applied. We ground the soundness of our proposal by proving several theoretical results. In addition, we provide a specific implementation of the methodology and evaluate its effectiveness on several detection problems involving attributed graphs representing biological molecules and drawings. Experimental results are contrasted with respect to suitable baseline methods, demonstrating the effectiveness of our approach.