Search Results for author: T. J. Sullivan

Found 8 papers, 1 papers with code

Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem

no code implementations16 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.


Bayesian Numerical Methods for Nonlinear Partial Differential Equations

no code implementations22 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.

Bayesian Inference Uncertainty Quantification

Testing whether a Learning Procedure is Calibrated

no code implementations23 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

The linear conditional expectation in Hilbert space

no code implementations27 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.

Bayesian Inference BIG-bench Machine Learning

A Rigorous Theory of Conditional Mean Embeddings

no code implementations2 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.

A Modern Retrospective on Probabilistic Numerics

no code implementations14 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.

Convergence Rates of Gaussian ODE Filters

no code implementations25 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.

Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity

1 code implementation7 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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