We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our approach, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known a priori and can be applied on top of any pre-trained predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and achieves state-of-the-art uncertainty quantification in relevant benchmarks.

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.

Relationships among time series can be exploited as inductive biases in learning effective forecasting models. In hierarchical time series, relationships among subsets of sequences induce hard constraints (hierarchical inductive biases) on the predicted values. In this paper, we propose a graph-based methodology to unify relational and hierarchical inductive biases in the context of deep learning for time series forecasting. In particular, we model both types of relationships as dependencies in a pyramidal graph structure, with each pyramidal layer corresponding to a level of the hierarchy. By exploiting modern - trainable - graph pooling operators we show that the hierarchical structure, if not available as a prior, can be learned directly from data, thus obtaining cluster assignments aligned with the forecasting objective. A differentiable reconciliation stage is incorporated into the processing architecture, allowing hierarchical constraints to act both as an architectural bias as well as a regularization element for predictions. Simulation results on representative datasets show that the proposed method compares favorably against the state of the art.

Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in most spatiotemporal GNNs, the computational complexity scales up to a quadratic factor with the length of the sequence times the number of links in the graph, hence hindering the application of these models to large graphs and long temporal sequences. While methods to improve scalability have been proposed in the context of static graphs, few research efforts have been devoted to the spatiotemporal case. To fill this gap, we propose a scalable architecture that exploits an efficient encoding of both temporal and spatial dynamics. In particular, we use a randomized recurrent neural network to embed the history of the input time series into high-dimensional state representations encompassing multi-scale temporal dynamics. Such representations are then propagated along the spatial dimension using different powers of the graph adjacency matrix to generate node embeddings characterized by a rich pool of spatiotemporal features. The resulting node embeddings can be efficiently pre-computed in an unsupervised manner, before being fed to a feed-forward decoder that learns to map the multi-scale spatiotemporal representations to predictions. The training procedure can then be parallelized node-wise by sampling the node embeddings without breaking any dependency, thus enabling scalability to large networks. Empirical results on relevant datasets show that our approach achieves results competitive with the state of the art, while dramatically reducing the computational burden.

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.

High-level Synthesis (HLS) Design-Space Exploration (DSE) aims at identifying Pareto-optimal synthesis configurations whose exhaustive search is unfeasible due to the design-space dimensionality and the prohibitive computational cost of the synthesis process. Within this framework, we address the design automation problem by proposing graph neural networks that jointly predict acceleration performance and hardware costs of a synthesized behavioral specification given optimization directives. Learned models can be used to rapidly approach the Pareto curve by guiding the DSE, taking into account performance and cost estimates. The proposed method outperforms traditional HLS-driven DSE approaches, by accounting for the arbitrary length of computer programs and the invariant properties of the input. We propose a novel hybrid control and dataflow graph representation that enables training the graph neural network on specifications of different hardware accelerators. Our approach achieves prediction accuracy comparable with that of state-of-the-art simulators without having access to analytical models of the HLS compiler. Finally, the learned representation can be exploited for DSE in unexplored configuration spaces by fine-tuning on a small number of samples from the new target domain. The outcome of the empirical evaluation of this transfer learning shows strong results against state-of-the-art baselines in relevant benchmarks.

Accurate forecasting of electricity demand is a core component of the modern electricity infrastructure. Several approaches exist that tackle this problem by exploiting modern deep learning tools. However, most previous works focus on predicting the total load as a univariate time series forecasting task, ignoring all fine-grained information captured by the smart meters distributed across the power grid. We introduce a methodology to account for this information in the graph neural network framework. In particular, we consider spatio-temporal graphs where each node is associated with the aggregate load of a cluster of smart meters, and a global graph-level attribute indicates the total load on the grid. We propose two novel spatio-temporal graph neural network models to process this representation and take advantage of both the finer-grained information and the relationships existing between the different clusters of meters. We compare these models on a widely used, openly available, benchmark against a competitive baseline which only accounts for the total load profile. Within these settings, we show that the proposed methodology improves forecasting accuracy.

Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be processed by autoregressive graph neural networks to recursively learn representations at each discrete point in time and space. Spatiotemporal graphs are often highly sparse, with time series characterized by multiple, concurrent, and long sequences of missing data, e.g., due to the unreliable underlying sensor network. In this context, autoregressive models can be brittle and exhibit unstable learning dynamics. The objective of this paper is, then, to tackle the problem of learning effective models to reconstruct, i.e., impute, missing data points by conditioning the reconstruction only on the available observations. In particular, we propose a novel class of attention-based architectures that, given a set of highly sparse discrete observations, learn a representation for points in time and space by exploiting a spatiotemporal propagation architecture aligned with the imputation task. Representations are trained end-to-end to reconstruct observations w.r.t. the corresponding sensor and its neighboring nodes. Compared to the state of the art, our model handles sparse data without propagating prediction errors or requiring a bidirectional model to encode forward and backward time dependencies. Empirical results on representative benchmarks show the effectiveness of the proposed method.

Temporal-Difference off-policy algorithms are among the building blocks of reinforcement learning (RL). Within this family, Q-Learning is arguably the most famous one, which has been widely studied and extended. The update rule of Q-learning involves the use of the maximum operator to estimate the maximum expected value of the return. However, this estimate is positively biased, and may hinder the learning process, especially in stochastic environments and when function approximation is used. We introduce the Weighted Estimator as an effective solution to mitigate the negative effects of overestimation in Q-Learning. The Weighted Estimator estimates the maximum expected value as a weighted sum of the action values, with the weights being the probabilities that each action value is the maximum. In this work, we study the problem from the statistical perspective of estimating the maximum expected value of a set of random variables and provide bounds to the bias and the variance of the Weighted Estimator, showing its advantages over other estimators present in literature. Then, we derive algorithms to enable the use of the Weighted Estimator, in place of the Maximum Estimator, in online and batch RL, and we introduce a novel algorithm for deep RL. Finally, we empirically evaluate our algorithms in a large set of heterogeneous problems, encompassing discrete and continuous, low and high dimensional, deterministic and stochastic environments. Experimental results show the effectiveness of the Weighted Estimator in controlling the bias of the estimate, resulting in better performance than representative baselines and robust learning w.r.t. a large set of diverse environments.

Highly accurate power demand forecasting represents one of key challenges of Smart Grid applications. In this setting, a large number of Smart Meters produces huge amounts of data that need to be processed to predict the load requested by the grid. Due to the high dimensionality of the problem, this often results in the adoption of simple aggregation strategies for the power that fail in capturing the relational information existing among the different types of user. A possible alternative, known as Cluster-based Aggregate Forecasting, consists in clustering the load profiles and, on top of that, building predictors of the aggregate at the cluster-level. In this work we explore the technique in the context of predictors based on deep recurrent neural networks and address the scalability issues presenting neural architectures adequate to process cluster-level aggregates. The proposed methods are finally evaluated both on a publicly available benchmark and a heterogenous dataset of Smart Meter data from an entire, medium-sized, Swiss town.

Most of the research in Reinforcement Learning (RL) focuses on balancing exploration and exploitation. Indeed, the reasons for the success or failure of an RL algorithm often deal with the choice between the execution of exploratory actions and the exploitation of actions that are known to be good. In the context of Multi-Armed Bandits (MABs), many algorithms have addressed this dilemma. In particular, Thompson Sampling (TS) is a solution that, besides having good theoretical properties, usually works very well in practice. Unfortunately, the success of TS in MAB problems has not been replicated in RL, where it has shown to scale very poorly w.r.t. the dimensionality of the problem. Nevertheless, the application of TS in RL, instead of more myopic strategies such as ε-greedy, remains a promising solution. This paper addresses such issue proposing several algorithms to use TS in RL and deep RL in a feasible way. We present these algorithms explaining the intuitions and theoretical considerations behind them and discussing their advantages and drawbacks. Furthermore, we provide an empirical evaluation on an increasingly complex set of RL problems, showing the benefit of TS w.r.t. other sampling strategies available in classical and more recent RL literature.