Search Results for author: François-Xavier Briol

Found 20 papers, 13 papers with code

Robust and Conjugate Gaussian Process Regression

no code implementations1 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.

Bayesian Inference Bayesian Optimisation +3

Bayesian Numerical Integration with Neural Networks

1 code implementation22 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.

Numerical Integration

Meta-learning Control Variates: Variance Reduction with Limited Data

1 code implementation8 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.


Robust and Scalable Bayesian Online Changepoint Detection

1 code implementation9 Feb 2023 Matias Altamirano, François-Xavier Briol, Jeremias Knoblauch

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

Towards Healing the Blindness of Score Matching

no code implementations15 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.

Density Estimation

Generalised Bayesian Inference for Discrete Intractable Likelihood

1 code implementation16 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.

Bayesian Inference

Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap

1 code implementation9 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.

Bayesian Inference

Composite Goodness-of-fit Tests with Kernels

1 code implementation19 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.

Robust Generalised Bayesian Inference for Intractable Likelihoods

1 code implementation15 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.

Bayesian Inference

The Ridgelet Prior: A Covariance Function Approach to Prior Specification for Bayesian Neural Networks

1 code implementation16 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.

Gaussian Processes

Bayesian Probabilistic Numerical Integration with Tree-Based Models

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.

Numerical Integration

Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness

no code implementations29 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.

Experimental Design Gaussian Processes

Stein Point Markov Chain Monte Carlo

1 code implementation9 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.

Bayesian Inference

Stein Points

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 $\{x_i\}_{i=1}^n$.

Bayesian Quadrature for Multiple Related Integrals

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.

Probabilistic Integration: A Role in Statistical Computation?

no code implementations3 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.

Numerical Integration

Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees

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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