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In this paper, we introduce a method for segmenting time series data using tools from Bayesian nonparametrics. We consider the task of temporal segmentation of a set of time series data into representative stationary segments. We use…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

Modelling real world systems involving humans such as biological processes for disease treatment or human behavior for robotic rehabilitation is a challenging problem because labeled training data is sparse and expensive, while high…

Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and…

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…

Accurate probabilistic prediction of wind power is crucial for maintaining grid stability and facilitating the efficient integration of renewable energy sources. Gaussian process (GP) models offer a principled framework for quantifying…

Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori…

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…

We introduce a performance-driven framework for constructing strictly causal forward-oriented observables in strongly non-stationary time series. The method combines a robustly normalized composite of heterogeneous indicators with a…

Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…

In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…

This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the…