5 papers
Sparse Probabilistic Richardson Extrapolation
Chris. J. Oates, Richard Howey, Toni Karvonen
Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilist…
Safe learning-based control via function-based uncertainty quantification
Abdullah Tokmak, Toni Karvonen, Thomas B. Schön +1
Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that e…
Bayesian Quadrature: Gaussian Processes for Integration
Maren Mahsereci, Toni Karvonen
Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was po…
BayesSum: Bayesian Quadrature in Discrete Spaces
Sophia Seulkee Kang, François-Xavier Briol, Toni Karvonen +1
This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roul…
A Dictionary of Closed-Form Kernel Mean Embeddings
François-Xavier Briol, Alexandra Gessner, Toni Karvonen +1
Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tool…