59 citations · 173 across the 29 of their papers we have counts for
13 papers · 1 filter
On the Optimisation Landscape of Overparameterised Weighted MMD
Tharrshann Jayan Logarajah, Jeremias Knoblauch, Louis Sharrock
We study the optimisation landscape of the maximum mean discrepancy (MMD) over weighted atomic measures. For the one-dimensional Gaussian kernel, we show that, for any compactly su…
Predictively Oriented Gaussian Process Posteriors
Callum Lau, Jeremias Knoblauch, Louis Sharrock
Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitioners to make a number of design d…
Robust Bayesian Optimisation with Unbounded Corruptions
Abdelhamid Ezzerg, Ilija Bogunovic, Jeremias Knoblauch
Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defen…
Multi-Output Robust and Conjugate Gaussian Processes
Joshua Rooijakkers, Leiv Rønneberg, François-Xavier Briol +2
Multi-output Gaussian process (MOGP) regression allows modelling dependencies among multiple correlated response variables. Similarly to standard Gaussian processes, MOGPs are sens…
Near-Optimal Approximations for Bayesian Inference in Function Space
Veit Wild, James Wu, Dino Sejdinovic +1
We propose a scalable inference algorithm for Bayes posteriors defined on a reproducing kernel Hilbert space (RKHS). Given a likelihood function and a Gaussian random element repre…
Outlier-robust Kalman Filtering through Generalised Bayes
Gerardo Duran-Martin, Matias Altamirano, Alexander Y. Shestopaloff +5
We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models.…
Robust and Conjugate Gaussian Process Regression
Matias Altamirano, François-Xavier Briol, Jeremias Knoblauch
To enable closed form conditioning, a common assumption in Gaussian process (GP) regression is independent and identically distributed Gaussian observation noise. This strong and s…
A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methods
Veit David Wild, Sahra Ghalebikesabi, Dino Sejdinovic +1
We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisat…
Robust and Scalable Bayesian Online Changepoint Detection
Matias Altamirano, François-Xavier Briol, Jeremias Knoblauch
This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection. The resulting algorithm has key advantages over previous work: it provides…
Robust Deep Gaussian Processes
Jeremias Knoblauch
This report provides an in-depth overview over the implications and novelty Generalized Variational Inference (GVI) (Knoblauch et al., 2019) brings to Deep Gaussian Processes (DGPs…
Generalized Variational Inference: Three arguments for deriving new Posteriors
Jeremias Knoblauch, Jack Jewson, Theodoros Damoulas
We advocate an optimization-centric view on and introduce a novel generalization of Bayesian inference. Our inspiration is the representation of Bayes' rule as infinite-dimensional…
Spatio-temporal Bayesian On-line Changepoint Detection with Model Selection
Jeremias Knoblauch, Theodoros Damoulas
Bayesian On-line Changepoint Detection is extended to on-line model selection and non-stationary spatio-temporal processes. We propose spatially structured Vector Autoregressions (…
Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with -Divergences
Jeremias Knoblauch, Jack Jewson, Theodoros Damoulas
We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with -divergences. The resulting inference procedure is…