no code implementations • 26 Mar 2024 • Lawrence A. Bull, Chiho Jeon, Mark Girolami, Andrew Duncan, Jennifer Schooling, Miguel Bravo Haro
We formulate a combined model from simple units, representing strain envelopes (of each train passing) for two types of commuter train.
no code implementations • 29 Nov 2023 • Andrea Marinoni, Pietro Lio', Alessandro Barp, Christian Jutten, Mark Girolami
The reliability of graph embeddings directly depends on how much the geometry of the continuous space matches the graph structure.
1 code implementation • 5 Nov 2023 • Hanlin Yu, Marcelo Hartmann, Bernardo Williams, Mark Girolami, Arto Klami
Laplace's method approximates a target density with a Gaussian distribution at its mode.
no code implementations • 16 Aug 2023 • Marcelo Hartmann, Bernardo Williams, Hanlin Yu, Mark Girolami, Alessandro Barp, Arto Klami
We use Riemannian geometry notions to redefine the optimisation problem of a function on the Euclidean space to a Riemannian manifold with a warped metric, and then find the function's optimum along this manifold.
no code implementations • 15 May 2023 • Lawrence A. Bull, Matthew R. Jones, Elizabeth J. Cross, Andrew Duncan, Mark Girolami
Most interestingly, domain expertise and knowledge of the underlying physics can be encoded in the model at the system, subgroup, or population level.
1 code implementation • 30 Mar 2023 • Thomas Gaskin, Grigorios A. Pavliotis, Mark Girolami
Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media.
no code implementations • 23 Mar 2023 • Ö. Deniz Akyildiz, Francesca Romana Crucinio, Mark Girolami, Tim Johnston, Sotirios Sabanis
We achieve this by formulating a continuous-time interacting particle system which can be seen as a Langevin diffusion over an extended state space of parameters and latent variables.
no code implementations • 26 Jan 2023 • Arnaud Vadeboncoeur, Ieva Kazlauskaite, Yanni Papandreou, Fehmi Cirak, Mark Girolami, Ömer Deniz Akyildiz
We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes.
no code implementations • 16 Nov 2022 • Simon Hubbert, Emilio Porcu, Chris. J. Oates, Mark Girolami
This work provides theoretical foundations for kernel methods in the hyperspherical context.
no code implementations • 30 Sep 2022 • Alex Glyn-Davies, Connor Duffin, Ö. Deniz Akyildiz, Mark Girolami
To address these shortcomings, in this paper we develop a physics-informed dynamical variational autoencoder ($\Phi$-DVAE) to embed diverse data streams into time-evolving physical systems described by differential equations.
1 code implementation • 27 Sep 2022 • Thomas Gaskin, Grigorios A. Pavliotis, Mark Girolami
Computational models have become a powerful tool in the quantitative sciences to understand the behaviour of complex systems that evolve in time.
no code implementations • 26 Sep 2022 • Alessandro Barp, Carl-Johann Simon-Gabriel, Mark Girolami, Lester Mackey
Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference.
no code implementations • 9 Aug 2022 • Arnaud Vadeboncoeur, Ömer Deniz Akyildiz, Ieva Kazlauskaite, Mark Girolami, Fehmi Cirak
In the posited probabilistic model, both the forward and inverse maps are approximated as Gaussian distributions with a mean and covariance parameterized by deep neural networks.
no code implementations • 20 Mar 2022 • Alessandro Barp, Lancelot Da Costa, Guilherme França, Karl Friston, Mark Girolami, Michael I. Jordan, Grigorios A. Pavliotis
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making.
1 code implementation • 1 Feb 2022 • Marcelo Hartmann, Mark Girolami, Arto Klami
The efficiency of Markov Chain Monte Carlo (MCMC) depends on how the underlying geometry of the problem is taken into account.
no code implementations • 7 Dec 2021 • Andrea Marinoni, Christian Jutten, Mark Girolami
This system provides several constraints and assumptions on the data properties that might be not valid for multimodal data analysis, especially when large scale datasets collected from heterogeneous sources are considered, so that the accuracy and robustness of the outcomes might be severely jeopardized.
no code implementations • pproximateinference AABI Symposium 2022 • Francisco Vargas, Andrius Ovsianas, David Fernandes, Mark Girolami, Neil D. Lawrence, Nikolas Nüsken
In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i. e. Schr\"odinger bridges).
1 code implementation • 21 Oct 2021 • Ömer Deniz Akyildiz, Connor Duffin, Sotirios Sabanis, Mark Girolami
Through embedding uncertainty inside of the governing equations, finite element solutions are updated to give a posterior distribution which quantifies all sources of uncertainty associated with the model.
1 code implementation • 10 Sep 2021 • Connor Duffin, Edward Cripps, Thomas Stemler, Mark Girolami
Statistical learning additions to physically derived mathematical models are gaining traction in the literature.
no code implementations • 23 Jul 2021 • Guilherme França, Alessandro Barp, Mark Girolami, Michael I. Jordan
Optimization tasks are crucial in statistical machine learning.
no code implementations • 8 May 2021 • Andrea Marinoni, Saloua Chlaily, Eduard Khachatrian, Torbjørn Eltoft, Sivasakthy Selvakumaran, Mark Girolami, Christian Jutten
Nonetheless, when applied to multimodal datasets (i. e., datasets acquired by means of multiple sensing techniques or strategies), the state-of-theart methods for ensemble learning and transfer learning might show some limitations.
no code implementations • 6 May 2021 • Alessandro Barp, So Takao, Michael Betancourt, Alexis Arnaudon, Mark Girolami
A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework.
no code implementations • 7 Dec 2020 • James Walsh, Oluwafunmilola Kesa, Andrew Wang, Mihai Ilas, Patrick O'Hara, Oscar Giles, Neil Dhir, Mark Girolami, Theodoros Damoulas
During the COVID-19 pandemic, policy makers at the Greater London Authority, the regional governance body of London, UK, are reliant upon prompt and accurate data sources.
1 code implementation • 4 Mar 2020 • Ashley Scillitoe, Pranay Seshadri, Mark Girolami
The MF predictive uncertainty is also found to be better calibrated and less computationally costly than the uncertainty estimated from applying jackknifing to random forest predictions.
Fluid Dynamics Computational Physics
1 code implementation • 31 Jan 2020 • Leah F. South, Toni Karvonen, Chris Nemeth, Mark Girolami, Chris. J. Oates
The numerical approximation of posterior expected quantities of interest is considered.
Computation Methodology
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.
no code implementations • NeurIPS 2019 • Seppo Virtanen, Mark Girolami
Topic models are becoming increasingly relevant probabilistic models for dimensionality reduction of text data, inferring topics that capture meaningful themes of frequently co-occurring terms.
no code implementations • NeurIPS 2019 • Alessandro Barp, Francois-Xavier Briol, Andrew B. Duncan, Mark Girolami, Lester Mackey
We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kernel Stein discrepancy (DKSD) and diffusion score matching (DSM) estimators with complementary strengths.
1 code implementation • NeurIPS 2019 • Oliver Hamelijnck, Theodoros Damoulas, Kangrui Wang, Mark Girolami
We consider evidence integration from potentially dependent observation processes under varying spatio-temporal sampling resolutions and noise levels.
no code implementations • 13 Jun 2019 • Francois-Xavier Briol, Alessandro Barp, Andrew B. Duncan, Mark Girolami
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges.
1 code implementation • 15 May 2019 • Mark Girolami, Eky Febrianto, Ge Yin, Fehmi Cirak
From the outset, we postulate a data-generating model which additively decomposes data into a finite element, a model misspecification and a noise component.
Methodology Numerical Analysis Numerical Analysis
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.
no code implementations • 2 Dec 2018 • Richard Scalzo, David Kohn, Hugo Olierook, Gregory Houseman, Rohitash Chandra, Mark Girolami, Sally Cripps
We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty, using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study.
no code implementations • 26 Nov 2018 • Francois-Xavier Briol, Chris. J. Oates, Mark Girolami, Michael A. Osborne, Dino Sejdinovic
This article is the rejoinder for the paper "Probabilistic Integration: A Role in Statistical Computation?"
no code implementations • 4 Apr 2018 • Karla Monterrubio-Gómez, Lassi Roininen, Sara Wade, Theo Damoulas, Mark Girolami
Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed.
Computation
3 code implementations • 16 Jan 2018 • Jon Cockayne, Chris Oates, Ilse Ipsen, Mark Girolami
The estimates obtained in this case are of little value unless further information can be provided about the numerical error.
Methodology Numerical Analysis Numerical Analysis Statistics Theory Statistics Theory
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.
1 code implementation • 19 Jul 2017 • Chris. J. Oates, Jon Cockayne, Robert G. Aykroyd, Mark Girolami
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation.
Applications
no code implementations • ICML 2017 • Francois-Xavier Briol, Chris. J. Oates, Jon Cockayne, Wilson Ye Chen, Mark Girolami
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the smoothness and dimension of the integrand.
no code implementations • 8 May 2017 • Alessandro Barp, Francois-Xavier Briol, Anthony D. Kennedy, Mark Girolami
The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners and other users of the methodology with only a basic understanding of Monte Carlo methods.
no code implementations • 15 Jan 2017 • Jon Cockayne, Chris Oates, Tim Sullivan, Mark Girolami
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations.
Methodology Numerical Analysis Numerical Analysis Statistics Theory Statistics Theory
no code implementations • 9 Dec 2016 • Lassi Roininen, Mark Girolami, Sari Lasanen, Markku Markkanen
We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors.
Statistics Theory Statistics Theory
1 code implementation • 25 Apr 2016 • Matthew Moores, Kirsten Gracie, Jake Carson, Karen Faulds, Duncan Graham, Mark Girolami
Raman spectroscopy can be used to identify molecules such as DNA by the characteristic scattering of light from a laser.
Applications Computation 92E99, 65D10, 62F15, 62H12
no code implementations • 29 Jan 2016 • Samuel Livingstone, Michael Betancourt, Simon Byrne, Mark Girolami
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic.
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.
no code implementations • 3 Jun 2015 • Philipp Hennig, Michael A. Osborne, Mark Girolami
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations.
no code implementations • 14 Jan 2015 • Heiko Strathmann, Dino Sejdinovic, Mark Girolami
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution.
3 code implementations • 24 Nov 2014 • M. J. Betancourt, Simon Byrne, Mark Girolami
Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters.
Methodology Statistics Theory Statistics Theory
no code implementations • 2 Oct 2013 • Maurizio Filippone, Mark Girolami
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data.
no code implementations • 17 Jun 2013 • Anne-Marie Lyne, Mark Girolami, Yves Atchadé, Heiko Strathmann, Daniel Simpson
The methodology is reviewed on well-known examples such as the parameters in Ising models, the posterior for Fisher-Bingham distributions on the $d$-Sphere and a large-scale Gaussian Markov Random Field model describing the Ozone Column data.
no code implementations • NeurIPS 2009 • Yiming Ying, Colin Campbell, Mark Girolami
The recent introduction of indefinite SVM by Luss and dAspremont [15] has effectively demonstrated SVM classification with a non-positive semi-definite kernel (indefinite kernel).
no code implementations • NeurIPS 2008 • Ben Calderhead, Mark Girolami, Neil D. Lawrence
We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and delay differential equations, and provide a comprehensive comparison with current state of the art methods.