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We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…
We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…
Past research on pedestrian trajectory forecasting mainly focused on deterministic predictions which provide only point estimates of future states. These future estimates can help an autonomous vehicle plan its trajectory and avoid…
Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…
In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…
Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…
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…
In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…
We consider the problem of estimating states and parameters in a model based on a system of coupled stochastic differential equations, based on noisy discrete-time data. Special attention is given to nonlinear dynamics and state-dependent…
In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term,…
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…
This paper proposes consistent and asymptotically Gaussian estimators for the drift, the diffusion coefficient and the Hurst exponent of the discretely observed fractional Ornstein-Uhlenbeck process. For the estimation of the drift, the…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…