Related papers: Graphical models for nonstationary time series

In recent years, there has been an increasing interest in the use of graph neural networks (GNNs) for analyzing dynamic graphs, which are graphs that evolve over time. However, there is still a lack of understanding of how different…

The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…

We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…

This paper challenges the dominance of stochastic trend models by introducing the Seasonal-Trend-Stationary ARMA (STSA) framework, which represents univariate nonstationary time series as stationary fluctuations around deterministic trend…

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…

For the problem of inferring a Gaussian graphical model (GGM), this work explores the application of a recent approach from the multiple testing literature for graph inference. The main idea of the method by Rebafka et al. (2022) is to…

State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance to name a few. Inference and prediction in SSMs are…

Traffic forecasting is one of the most fundamental problems in transportation science and artificial intelligence. The key challenge is to effectively model complex spatial-temporal dependencies and correlations in modern traffic data.…

With the growing amount of available temporal real-world network data, an important question is how to efficiently study these data. One can simply model a temporal network as either a single aggregate static network, or as a series of…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

Well-designed open-source software drives progress in Machine Learning (ML) research. While static graph ML enjoys mature frameworks like PyTorch Geometric and DGL, ML for temporal graphs (TG), networks that evolve over time, lacks…

The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the…

This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a…

Irregularly sampling a spatially stationary random field does not yield a graph stationary signal in general. Based on this observation, we build a definition of graph stationarity based on intrinsic stationarity, a less restrictive…

We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a…

The rich information underlying graphs has inspired further investigation of unsupervised graph representation. Existing studies mainly depend on node features and topological properties within static graphs to create self-supervised…

We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a…

Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…

Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the…

In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…