Autoregressive Models for Sequences of Graphs

Zambon, Daniele; Grattarola, Daniele; Livi, Lorenzo; Alippi, Cesare

doi:10.1109/ijcnn.2019.8852131

Cited by 7 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this sense, the stable convergence in distribution paves the way towards an extension to a random and/or time-dependent adjacency matrix (e.g. as an additional, potentially non-ergodic, process) [51,5].…”

Section: With An Unknown Adjacency Matrixmentioning

confidence: 97%

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Courgeau

Veraart

2022

Electron. J. Statist.

View full text Add to dashboard Cite

We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete timegrid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component of the graph. Under a high-frequency sampling scheme, we study the asymptotic behaviour of those estimators as the mesh size of the observation grid goes to zero. We prove two stable central limit theorems to the same distribution as in the continuously-observed case under both finite and infinite jump activity for the Lévy driving noise. In addition to providing the consistency of the estimators, the stable convergence allows us to consider probabilistic sparse inference procedures on the edges themselves when a graph structure is not explicitly available. It also preserves its asymptotic properties. In particular, we also show the asymptotic normality and consistency of an Adaptive Lasso scheme. We apply the new estimators to wind capacity factor measurements, i.e. the ratio between the wind power produced locally compared to its rated peak power, across fifty locations in Northern Spain and Portugal. We compare those estimators to the standard least squares estimator through a simulation study extending known univariate results across graph configurations, noise types and amplitudes.

show abstract

Section: With An Unknown Adjacency Matrixmentioning

confidence: 97%

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Courgeau

Veraart

2022

Electron. J. Statist.

View full text Add to dashboard Cite

show abstract

“…We start by assessing the performance of hybrid global-local spatiotemporal models in a controlled environment, considering a variation of GPVAR, a synthetic dataset based on a polynomial graph filter [45] introduced by Zambon and Alippi [46], that we modify to include local effects. In particular, data are generated from the spatiotemporal process…”

Section: Synthetic Datamentioning

confidence: 99%

Taming Local Effects in Graph-based Spatiotemporal Forecasting

Cini¹,

Marisca²,

Zambon³

et al. 2023

Preprint

View full text Add to dashboard Cite

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.

show abstract

“…Probabilistic models As per any machine learning problem, dealing with uncertainty associated with the data-generating process and the learned model can be the key to accurate and trustworthy DGN solutions. Despite the recent progress in integrating DGNs with probabilistic components [28,29,30], estimating the uncertainty associated with combinatorial objects like the adjacency matrix and estimating non-factorized probability distribution over graphs are two of the most challenging problems.…”

Section: Promising Directionsmentioning

confidence: 99%

Graph Representation Learning

Bacciu,

Errica,

Micheli

et al. 2023

ESANN 2023 Proceesdings

View full text Add to dashboard Cite

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.

show abstract

Autoregressive Models for Sequences of Graphs

Cited by 7 publications

References 21 publications

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Taming Local Effects in Graph-based Spatiotemporal Forecasting

Graph Representation Learning

Contact Info

Product

Resources

About