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Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…

A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…

This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

Existing models to extract temporal relations between events lack a principled method to incorporate external knowledge. In this study, we introduce Bayesian-Trans, a Bayesian learning-based method that models the temporal relation…

We introduce a scalable Bayesian preference learning method for identifying convincing arguments in the absence of gold-standard rat- ings or rankings. In contrast to previous work, we avoid the need for separate methods to perform quality…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when…

Rapid developments in streaming data technologies have enabled real-time monitoring of human activity that can deliver high-resolution data on health variables over trajectories or paths carved out by subjects as they conduct their daily…

This paper proposes a model learning Semi-parametric relationships in an Expert Bayesian Network (SEBN) with linear parameter and structure constraints. We use Gaussian Processes and a Horseshoe prior to introduce minimal nonlinear…

We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…

A classical method for risk-sensitive nonlinear control is the iterative linear exponential quadratic Gaussian algorithm. We present its convergence analysis from a first-order optimization viewpoint. We identify the objective that the…