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Found 8 papers, 1 papers with code
Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem
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
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied.
Testing whether a Learning Procedure is Calibrated
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
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.
A Rigorous Theory of Conditional Mean Embeddings
Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications.
A Modern Retrospective on Probabilistic Numerics
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
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
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
