no code implementations • 1 Nov 2023 • 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.

1 code implementation • 22 May 2023 • Katharina Ott, Michael Tiemann, Philipp Hennig, François-Xavier Briol

Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an integral.

1 code implementation • 8 Mar 2023 • Zhuo Sun, Chris J. Oates, François-Xavier Briol

Control variates can be a powerful tool to reduce the variance of Monte Carlo estimators, but constructing effective control variates can be challenging when the number of samples is small.

1 code implementation • 9 Feb 2023 • Matias Altamirano, François-Xavier Briol, Jeremias Knoblauch

This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection.

1 code implementation • 27 Jan 2023 • Ayush Bharti, Masha Naslidnyk, Oscar Key, Samuel Kaski, François-Xavier Briol

Likelihood-free inference methods typically make use of a distance between simulated and real data.

no code implementations • 15 Sep 2022 • Mingtian Zhang, Oscar Key, Peter Hayes, David Barber, Brooks Paige, François-Xavier Briol

Score-based divergences have been widely used in machine learning and statistics applications.

1 code implementation • 16 Jun 2022 • Takuo Matsubara, Jeremias Knoblauch, François-Xavier Briol, Chris. J. Oates

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical.

1 code implementation • 9 Feb 2022 • Charita Dellaporta, Jeremias Knoblauch, Theodoros Damoulas, François-Xavier Briol

Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible.

1 code implementation • 3 Dec 2021 • Jonathan Wenger, Nicholas Krämer, Marvin Pförtner, Jonathan Schmidt, Nathanael Bosch, Nina Effenberger, Johannes Zenn, Alexandra Gessner, Toni Karvonen, François-Xavier Briol, Maren Mahsereci, Philipp Hennig

Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference.

1 code implementation • 19 Nov 2021 • Oscar Key, Arthur Gretton, François-Xavier Briol, Tamara Fernandez

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue.

1 code implementation • 15 Apr 2021 • Takuo Matsubara, Jeremias Knoblauch, François-Xavier Briol, Chris. J. Oates

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood.

1 code implementation • 16 Oct 2020 • Takuo Matsubara, Chris J. Oates, François-Xavier Briol

Our approach constructs a prior distribution for the parameters of the network, called a ridgelet prior, that approximates the posited Gaussian process in the output space of the network.

no code implementations • 12 Jun 2020 • Shijing Si, Chris. J. Oates, Andrew B. Duncan, Lawrence Carin, François-Xavier Briol

Control variates are a well-established tool to reduce the variance of Monte Carlo estimators.

1 code implementation • NeurIPS 2020 • Harrison Zhu, Xing Liu, Ruya Kang, Zhichao Shen, Seth Flaxman, François-Xavier Briol

The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, and on a Bayesian survey design problem.

no code implementations • 29 Jan 2020 • George Wynne, François-Xavier Briol, Mark Girolami

In this setting, an important theoretical question of practial relevance is how accurate the Gaussian process approximations will be given the difficulty of the problem, our model and the extent of the misspecification.

1 code implementation • 9 May 2019 • Wilson Ye Chen, Alessandro Barp, François-Xavier Briol, Jackson Gorham, Mark Girolami, Lester Mackey, Chris. J. Oates

Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target and, hence, require the solution of a non-convex optimisation problem to obtain each new point.

1 code implementation • ICML 2018 • Wilson Ye Chen, Lester Mackey, Jackson Gorham, François-Xavier Briol, Chris. J. Oates

An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$.

no code implementations • ICML 2018 • Xiaoyue Xi, François-Xavier Briol, Mark Girolami

This allows users to represent uncertainty in a more faithful manner and, as a by-product, provide increased numerical efficiency.

no code implementations • 3 Dec 2015 • François-Xavier Briol, Chris. J. Oates, Mark Girolami, Michael A. Osborne, Dino Sejdinovic

A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled.

no code implementations • NeurIPS 2015 • François-Xavier Briol, Chris. J. Oates, Mark Girolami, Michael A. Osborne

There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation.

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