Related papers: Learning Temporal Evolution of Spatial Dependence …

Spatial-temporal network traffic forecasting is a challenging task due to the complex spatial relationships and dynamic temporal patterns present in each node. Traditional regression methods are not directly applicable to such graph data.…

This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is…

Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…

Most practical engineering design problems involve nonlinear spatio-temporal dynamical systems. Multi-physics simulations are often performed to capture the fine spatio-temporal scales which govern the evolution of these systems. However,…

In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…

This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…

To study the impact of climate variables on morbidity of some diseases in Mexico, we propose a spatio-temporal varying coefficients regression model. For that we introduce a new spatio-temporal dependent process prior, in a Bayesian…

Dimensionality reduction represents a crucial step in extracting meaningful insights from Molecular Dynamics (MD) simulations. Conventional approaches, including linear methods such as principal component analysis as well as various…

Spatio-temporal graphs such as traffic networks or gene regulatory systems present challenges for the existing deep learning methods due to the complexity of structural changes over time. To address these issues, we introduce…

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…

In this publication, we combine two Bayesian non-parametric models: the Gaussian Process (GP) and the Dirichlet Process (DP). Our innovation in the GP model is to introduce a variation on the GP prior which enables us to model structured…

Spatial boundaries, such as ecological transitions or climatic regime interfaces, capture steep environmental gradients, and shifts in their structure can signal emerging environmental changes. Quantifying uncertainty in spatial boundary…

Gaussian Process State Space Models (GP-SSMs) are a non-parametric model class suitable to represent nonlinear dynamics. They become increasingly popular in data-driven modeling approaches, i.e. when no first-order physics-based models are…

Spatiotemporal modeling has evolved beyond simple time series analysis to become fundamental in structural time series analysis. While current research extensively employs graph neural networks (GNNs) for spatial feature extraction with…

Motivated by the needs of selecting important features for massive neuroimaging data, we propose a spatially varying coefficient model (SVCMs) with sparsity and piecewise smoothness imposed on the coefficient functions. A new class of…

We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…

We study the problem of traffic forecasting, aiming to predict the inflow and outflow of a region in the subsequent time slot. The problem is complex due to the intricate spatial and temporal interdependence among regions. Prior works study…

This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

Diffusion models have emerged as a powerful tool for generating high-quality images, videos, and 3D content. While sampling guidance techniques like CFG improve quality, they reduce diversity and motion. Autoguidance mitigates these issues…