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Risk prediction, as a typical time series modeling problem, is usually achieved by learning trends in markers or historical behavior from sequence data, and has been widely applied in healthcare and finance. In recent years, deep learning…

Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications,…

Multi-task Gaussian process (MTGP) is a well-known non-parametric Bayesian model for learning correlated tasks effectively by transferring knowledge across tasks. But current MTGPs are usually limited to the multi-task scenario defined in…

A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional…

It is an important task to model realized volatilities for high-frequency data in finance and economics and, as arguably the most popular model, the heterogeneous autoregressive (HAR) model has dominated the applications in this area.…

Accurate forecasting of multivariate time series is an extensively studied subject in finance, transportation, and computer science. Fully mining the correlation and causation between the variables in a multivariate time series exhibits…

Generative models of graphs are well-known, but many existing models are limited in scalability and expressivity. We present a novel sequential graphical variational autoencoder operating directly on graphical representations of data. In…

Due to the complex and changing interactions in dynamic scenarios, motion forecasting is a challenging problem in autonomous driving. Most existing works exploit static road graphs to characterize scenarios and are limited in modeling…

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…

Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…

Hidden Markov Models (HMMs) comprise a powerful generative approach for modeling sequential data and time-series in general. However, the commonly employed assumption of the dependence of the current time frame to a single or multiple…

The graph-based variational autoencoder represents an architecture that can handle the uncertainty of different geological scenarios, such as depositional or structural, through the concept of a lowerdimensional latent space. The main…

The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First,…

Models with random effects, such as generalised linear mixed models (GLMMs), are often used for analysing clustered data. Parameter inference with these models is difficult because of the presence of cluster-specific random effects, which…

Volatility forecasting is essential for risk management and decision-making in financial markets. Traditional models like Generalized Autoregressive Conditional Heteroskedasticity (GARCH) effectively capture volatility clustering but often…

The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not…

Irregular Medical Time Series play a critical role in the clinical domain to better understand the patient's condition. However, inherent irregularity arising from heterogeneous sampling rates, asynchronous observations, and variable gaps…

A novel spatial autoregressive model for panel data is introduced, which incorporates multilayer networks and accounts for time-varying relationships. Moreover, the proposed approach allows the structural variance to evolve smoothly over…

Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…