no code implementations • 16 Nov 2022 • Mattes Mollenhauer, Nicole Mücke, T. J. Sullivan

However, we prove that, in terms of spectral properties and regularisation theory, this inverse problem is equivalent to the known compact inverse problem associated with scalar response regression.

no code implementations • 22 Apr 2021 • Junyang Wang, Jon Cockayne, Oksana Chkrebtii, T. J. Sullivan, Chris. J. Oates

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied.

no code implementations • 23 Dec 2020 • Jon Cockayne, Matthew M. Graham, Chris J. Oates, T. J. Sullivan

A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset.

Bayesian Inference Statistics Theory Statistics Theory

no code implementations • 27 Aug 2020 • Ilja Klebanov, Björn Sprungk, T. J. Sullivan

The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important r\^ole in approximate Bayesian inference, especially the Bayes linear approach.

no code implementations • 2 Dec 2019 • Ilja Klebanov, Ingmar Schuster, T. J. Sullivan

Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications.

no code implementations • 14 Jan 2019 • C. J. Oates, T. J. Sullivan

This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern formal treatment.

no code implementations • 25 Jul 2018 • Hans Kersting, T. J. Sullivan, Philipp Hennig

A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems.

1 code implementation • 7 Jun 2017 • Florian Schäfer, T. J. Sullivan, Houman Owhadi

This block-factorisation can provably be obtained in complexity $\mathcal{O} ( N \log( N ) \log^{d}( N /\epsilon) )$ in space and $\mathcal{O} ( N \log^{2}( N ) \log^{2d}( N /\epsilon) )$ in time.

Numerical Analysis Computational Complexity Data Structures and Algorithms Probability 65F30, 42C40, 65F50, 65N55, 65N75, 60G42, 68Q25, 68W40

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