# Publications

This page contains all my publications; for more details, see my Google Scholar profile. If you would like a brief introduction to some of the fields I work in and have contributed to, you may want to have a look at the following project pages:

- Bayesian probabilistic numerical methods.
- Inference for intractable models.
- Stein’s method as a computational tool.
- Transfer learning for Monte Carlo.

## Preprints

- Key, O., Fernandez, T., Gretton, A. &
(2021).*Briol, F-X.**Composite goodness-of-fit tests with kernels*. arXiv.2111.10275. () (*Preprint*)*Code*- A preliminary version of the paper was accepted to the NeurIPS 2021 workshop “Your Model is Wrong: Robustness and misspecification in probabilistic modeling”.

## Published Papers

Chen, Z., Naslydnik, M., Gretton, A. &

(2024).*Briol, F-X.**Conditional Bayesian quadrature*. Uncertainty in Artificial Intelligence. () (*Conference*) (*Preprint*)*Code*Duran-Martin, G., Altamirano, M., Shestopaloff, A. Y., Sanchez-Betancourt, L., Knoblauch, J., Jones, M.,

& Murphy, K. (2024).*Briol, F-X.**Outlier-robust Kalman filtering through generalised Bayes*. arXiv:2405.05646. Accepted for publication at ICML 2024. () (*Preprint*)*Code*- Altamirano, M.,
& Knoblauch, J. (2024).*Briol, F-X.**Robust and conjugate Gaussian process regression*. arXiv:2311.00463. Accepted for publication at ICML 2024. () (*Preprint*)*Code*- This paper was accepted as a spotlight paper (top 3.5% of papers).

- Wenger, J., Krämer, N., Pförtner, M., Schmidt, J., Bosch, N., Effenberger, N., Zenn, J., Gessner, A., Karvonen, T.,
, Mahsereci, M. & Hennig, P. (2024).*Briol, F-X**ProbNum: Probabilistic numerics in Python*. arXiv:2112.02100. Accepted (subject to minor revisions) at the Journal of Machine Learning Research. ()*Preprint*- This paper is the reference for the open-source ProbNum software, which implements a range of probabilistic numerics methods in Python. Full details are available at http://www.probnum.org.

Matsubara, T., Knoblauch, J.,

& Oates, C. J. (2024).*Briol, F-X.**Generalised Bayesian inference for discrete intractable likelihood*. arXiv:2206.08420. Accepted (subject to minor revisions) at the Journal of the American Statistical Association. () (*Journal*) (*Preprint*)*Code*- Sun, Z., Oates, C. J. &
(2023).*Briol, F-X.**Meta-learning control variates: variance reduction with limited data*. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:2047-2057. () (*Conference*) (*Preprint*)*Code*- This paper was accepted for oral presentation at UAI.

Ott, K., Tiemann, M., Hennig, P., &

(2023).*Briol, F-X.**Bayesian numerical integration with neural networks*. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:1606-1617. () (*Conference*)*Preprint*Kirby, A.,

, Dunstan, T. & Nishino, T. (2023).*Briol, F-X.**Data-driven modelling of turbine wake interactions and flow resistance in large wind farms*. Wind Energy, 26, 9, 875-1011. () (*Journal*) (*Preprint*)*Code*Altamirano, M.,

& Knoblauch, J. (2023).*Briol, F-X.**Robust and scalable Bayesian online changepoint detection*. Proceedings of the 40th International Conference on Machine Learning, PMLR 202:642-663. () (*Conference*) (*Preprint*) (*Code*)*Video*Bharti, A., Naslidnyk, M., Key, O., Kaski, S., &

(2023).*Briol, F-X.**Optimally-weighted estimators of the maximum mean discrepancy for likelihood-free inference*. Proceedings of the 40th International Conference on Machine Learning, PMLR 202:2289-2312. () (*Conference*) (*Preprint*)*Code*- Sun, Z., Barp, A. &
(2023).*Briol, F-X.**Vector-valued control variates*. Proceedings of the 40th International Conference on Machine Learning, PMLR 202:32819-32846. () (*Conference*) (*Preprint*)*Code*- This paper received a
*Student Paper Award*from the section on Bayesian Statistical Science of the American Statistical Association in 2022. - Zhuo Sun was awarded a Silver Medal for his poster on this paper at the 2021 Fry conference at Bristol.

- This paper received a
- Li, K., Giles, D., Karvonen, T., Guillas, S. &
(2023).*Briol, F-X.**Multilevel Bayesian quadrature*. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:1845-1868. () (*Conference*) (*Preprint*)*Code*- This paper was accepted for an oral presentation (top 6% of accepted papers) at AISTATS.

Niu, Z., Meier, J. &

(2023).*Briol, F-X.**Discrepancy-based inference for intractable generative models using quasi-Monte Carlo*. Electronic Journal of Statistics, 17 (1), 1411-1456. () (*Journal*) (*Preprint*)*Code*Anastasiou, A., Barp, A.,

, Ebner, B., Gaunt, R. E., Ghaderinezhad, F., Gorham, J., Gretton, A., Ley, C., Liu, Q., Mackey, L., Oates, C. J., Reinert, G. & Swan, Y. (2023).*Briol, F-X.**Stein’s method meets Computational Statistics: A review of some recent developments*. Statistical Science, Vol. 38, No. 1, 120-139. () (*Journal*) (*Preprint 1*)*Preprint 2*- Matsubara, T., Knoblauch, J.,
& Oates, C. J. (2022).*Briol, F-X.**Robust generalised Bayesian inference for intractable likelihoods*. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 84:3, 997– 1022. () (*Journal*) (*Preprint*) (*Code*)*Video*- This paper received a
*Student Paper Award*from the section on Bayesian Statistical Science of the American Statistical Association in 2022. - This paper received a
*Best Student/Postdoc Contributed Paper Award*at ISBA 2021. - A preliminary version of the paper was accepted to the NeurIPS 2021 workshop “Your Model is Wrong: Robustness and misspecification in probabilistic modeling”.

- This paper received a
- Dellaporta, C., Knoblauch, J., Damoulas, T.
(2022).*Briol. F-X.**Robust Bayesian inference for simulator-based models via the MMD posterior bootstrap*. Proceedings of The 25th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 151:943-970. () (*Conference*) (*Preprint*) (*Code*)*Video*- This paper received the Best Paper Award at AISTATS 2022 (out of 1685 submissions and 492 accepted papers).
- A preliminary version of the paper was accepted to the NeurIPS 2021 workshop “Your Model is Wrong: Robustness and misspecification in probabilistic modeling”.
- This paper was discussed on the blog of Prof. Christian Robert

- Bharti, A.,
, Pedersen, T. (2022).*Briol, F-X.**A general method for calibrating stochastic radio channel models with kernels*. IEEE Transactions on Antennas and Propagation, vol. 70, no. 6, pp. 3986-4001, June 2022. () (*Journal*) (*Preprint*)*Code*- A preliminary version of this paper was accepted to the NeurIPS 2021 workshop on Machine Learning and the Physical Sciences.

Si, S., Oates, C. J., Duncan, A. B., Carin, L. &

(2021).*Briol. F-X.**Scalable control variates for Monte Carlo methods via stochastic optimization*. Accepted for publication in the proceedings of the 14th Monte Carlo and Quasi-Monte Carlo Methods (MCQMC) conference 2020. arXiv:2006.07487. () (*Conference*) (*Preprint*)*Video*Matsubara, T., Oates, C. J.,

(2021).*Briol, F-X.**The ridgelet prior: A covariance function approach to prior specification for Bayesian neural networks*. Journal of Machine Learning Research, 22 (157), 1-57. () (*Journal*) (*Preprint*) (*Video*)*Code*Wynne, G.,

, Girolami, M. (2021).*Briol, F-X.**Convergence guarantees for Gaussian process means with misspecified likelihoods and smoothness*. Journal of Machine Learning Research, 22 (123), 1-40. () (*Journal*)*Preprint*Bharti, A., Adeogun, R., Cai, X., Fan, W.,

, Clavier, L., Pedersen, T. (2021).*Briol, F-X.**Joint modeling of received power, mean delay and delay spread for wideband radio channels*. IEEE Transactions on Antennas and Propagation, vol. 69, no. 8, pp. 4871-4882, Aug. 2021. () (*Journal*)*Preprint*Zhu, H., Liu, X., Kang, R., Shen, Z., Flaxman, S.,

(2020).*Briol, F-X.**Bayesian probabilistic numerical integration with tree-based models*. Neural Information Processing Systems, 5837-5849. () (*Conference*) (*Preprint*)*Code*Barp, A.,

, Duncan, A. B., Girolami, M., Mackey, L. (2019).*Briol, F-X.**Minimum Stein discrepancy estimators*. Neural Information Processing Systems, 12964-12976. () (*Conference*) (*Preprint*)*Talk/Video*Chen, W. Y., Barp, A.,

, Gorham, J., Girolami, M., Mackey, L., Oates, C. J. (2019).*Briol, F-X.**Stein point Markov chain Monte Carlo*. International Conference on Machine Learning, PMLR 97:1011-1021. () (*Conference*) (*Preprint*)*Code*, Oates, C. J., Girolami, M., Osborne, M. A. & Sejdinovic, D. (2019).*Briol, F-X.**Probabilistic integration: a role in statistical computation?*Statistical Science, Vol 34, Number 1, 1-22. () (*Journal*) (*Preprint*)*Supplement*- This paper accepted with discussion and rejoinder. There are three discussion pieces by (i) Fred Hickernel and R. Jagadeeswaran (Journal) (Preprint), (ii) Art Owen (Journal) (Preprint), and (iii) Michael Stein and Ying Hung (Journal).
- This paper was awarded a Student Paper Award from the section on Bayesian Statistical Science of the American Statistical Association in 2016.
- This paper was discussed on several blogs, including by Prof. Andrew Gelman and Prof. Christian Robert.

Oates, C. J., Cockayne, J.,

& Girolami, M. (2019).*Briol, F-X.**Convergence rates for a class of estimators based on Stein’s identity*. Bernoulli, Vol. 25, No. 2, 1141-1159. () (*Journal*)*Preprint*- Xi, X.,
& Girolami, M. (2018).*Briol, F-X.**Bayesian quadrature for multiple related integrals*. International Conference on Machine Learning, PMLR 80:5369-5378. () (*Conference*)*Preprint*- This paper was accepted for a long talk (top 8% of submitted papers).

Chen, W. Y., Mackey, L., Gorham, J.

& Oates, C. J. (2018).*Briol, F-X.**Stein points*. International Conference on Machine Learning, PMLR 80:843-852. () (*Conference*) (*Preprint*)*Code*Barp, A.,

, Kennedy, A. D. & Girolami, M. (2018).*Briol, F-X.**Geometry and dynamics for Markov chain Monte Carlo*. Annual Review of Statistics and Its Applications, Vol. 5:451-471. () (*Journal*)*Preprint*Oates, C. J., Niederer, S., Lee, A.,

& Girolami, M. (2017).*Briol, F-X.**Probabilistic models for integration error in the assessment of functional cardiac models*. Advances in Neural Information Processing Systems (NeurIPS), 109-117. () (*Conference*)*Preprint*, Oates, C. J., Cockayne, J., Chen, W. Y. & Girolami, M. (2017).*Briol, F-X.**On the sampling problem for kernel quadrature*. Proceedings of the 34th International Conference on Machine Learning, PMLR 70:586-595. () (*Conference*)*Preprint*, Oates, C. J., Girolami, M. & Osborne, M. A. (2015).*Briol, F-X.**Frank-Wolfe Bayesian Quadrature: probabilistic integration with theoretical guarantees*. Advances In Neural Information Processing Systems (NIPS), 1162-1170. () (*Preprint*)*Conference*- This paper was accepted with a spotlight presentation (top 4.5% of submitted papers).
- This paper was discussed in the blog of Ingmar Schuster.

- Barp, A., Barp, E. G.,
& Ueltschi, D. (2015).*Briol, F-X.**A numerical study of the 3D random interchange and random loop models*. Journal of Physics A: Mathematical and Theoretical, 48(34). () (*Journal*)*Preprint*

## Technical Reports

, Barp, A., Duncan, A. B. & Girolami, M. (2019).*Briol, F-X.**Statistical inference for generative models with maximum mean discrepancy*. arXiv:1906.05944. () (*Preprint*)*Talk/Video*

## Workshop Papers

- Zhang, M., Key, O., Hayes, P., Barber, D., Paige, B. &
(2022).*Briol, F-X.**Towards healing the blindness of score matching*. NeurIPS 2022 workshop on score-based methods. arXiv:2209.07396. ()*Preprint*

## Technical Discussions and Opinion Pieces

Zhu, H., Liu, X., Caron, A., Manolopoulou, I. Flaxman, S.,

(2020).*Briol, F-X.**Contributed Discussion of “Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects”*. Bayesian Analysis, 15(3), 965-1056. () (*Journal (pp55-58)*)*Preprint*, Diaz De la O, F. A., Hristov, P. O. (2019).*Briol, F-X.**Contributed Discussion of “A Bayesian Conjugate Gradient Method”*. Bayesian Analysis, 14(3), 980-984. () (*Journal*)*Preprint*, Oates, C. J., Girolami, M., Osborne, M. A. & Sejdinovic, D. (2019).*Briol, F-X.**Rejoinder for “Probabilistic integration: a role in statistical computation?”*Statistical Science, Vol 34, Number 1, 38-42. () (*Journal*)*Preprint*& Girolami, M. (2018)*Briol, F-X.**Bayesian numerical methods as a case study for statistical data science*, Statistical Data Science (Chapter 6): 99-110. ()*Book*, Cockayne, J. & Teymur, O. (2016).*Briol, F-X.**Contributed discussion on article by Chkrebtii, Campbell, Calderhead, and Girolami*. Bayesian Analysis, 11(4), 1285-1293. () (*Journal*)*Preprint*

## Science Communication

Kirby, A.,

(2023).*Briol, F-X.**Using machine learning to design more efficient offshore wind farms*. ()*Turing Institute Blog Post*, Bharti, A. (2021).*Briol, F-X.**Using machine learning to improve the reliability of wireless communication systems*. ()*Turing Institute Blog Post*

## Dissertations

(2019).*Briol, F-X.**Statistical computation with kernels*. PhD thesis, Department of Statistics, University of Warwick. ()*PDF*- I was awarded an Honorable Mention for the Savage Award in the section “Theory and Methodology” for this thesis. This is awarded by the International Society on Bayesian Analysis (ISBA) for “a dissertation that makes important original contributions to the foundations, theoretical developments, and/or general methodology of Bayesian analysis”.

(2014).*Briol, F-X.**Inference for Hawkes Processes*. Masters thesis, Department of Statistics, University of Warwick.