Related papers: Nonlinear Hawkes Process with Gaussian Process Sel…

Given a collection of entities (or nodes) in a network and our intermittent observations of activities from each entity, an important problem is to learn the hidden edges depicting directional relationships among these entities. Here, we…

The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…

We introduce a point process regression model that is applicable to price models and limit order book models. Hawkes type autoregression in the intensity process is generalized to a stochastic regression to covariate processes. We establish…

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few…

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…

Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…

Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstrate the…

We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter…

This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions,…

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…

The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification.…

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.…

Nonlinear mixed effects models have become a standard platform for analysis when data is in the form of continuous and repeated measurements of subjects from a population of interest, while temporal profiles of subjects commonly follow a…

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with…

Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing…