Related papers: Indian Buffet process for model selection in convo…
Modelling the behaviour of highly nonlinear dynamical systems with robust uncertainty quantification is a challenging task which typically requires approaches specifically designed to address the problem at hand. We introduce a…
Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we…
A Gaussian process is proposed as a model for the posterior distribution of the local predictive ability of a model or expert, conditional on a vector of covariates, from historical predictions in the form of log predictive scores. Assuming…
The integration of physical relationships into stochastic models is of major interest e.g. in data assimilation. Here, a multivariate Gaussian random field formulation is introduced, which represents the differential relations of the…
In this paper we extend existing Bayesian methods for variable selection in Gaussian process regression, to select both the regression terms and the active covariates in the spatial correlation structure. We then use the estimated posterior…
Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…
We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…
Distributions over exchangeable matrices with infinitely many columns, such as the Indian buffet process, are useful in constructing nonparametric latent variable models. However, the distribution implied by such models over the number of…
In this article we use a covariance function that arises from limit of fluctuations of the rescaled occupation time process of a branching particle system, to introduce a family of weighted long-range dependence Gaussian processes. In…
In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is…
We introduce the Poisson Hierarchical Indian Buffet Process (PHIBP), a new class of species sampling models designed to address the challenges of complex, sparse count data by facilitating information sharing across and within groups. Our…
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model…
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…
In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…