Related papers: Variational Inference for Gaussian Process Modulat…

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…

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

Sparse Gaussian Processes are a key component of high-throughput Bayesian Optimisation (BO) loops; however, we show that existing methods for allocating their inducing points severely hamper optimisation performance. By exploiting the…

We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the…

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…

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…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…

Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive…

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…

Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel…

We implement gradient-based variational inference routines for Wishart and inverse Wishart processes, which we apply as Bayesian models for the dynamic, heteroskedastic covariance matrix of a multivariate time series. The Wishart and…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally…

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…

Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases…

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance…