3 citations · 3 across the 9 of their papers we have counts for
9 papers
Why not to use the Gaussian kernel
Toni Karvonen, Chris J. Oates
Kernels measure similarity or correlation in tasks such as regression and classification. The Gaussian kernel, other names of which include squared exponential and radial basis fun…
Hierarchical Bayesian Quadrature
Tim Weiland, Toni Karvonen, Philipp Hennig
Numerical integration is a cornerstone of various scientific computing applications, such as engineering simulations and model evidence computations in probabilistic machine learni…
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
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…
Stationary MMD Points
Zonghao Chen, Toni Karvonen, Heishiro Kanagawa +2
Approximation of a target probability distribution using a finite set of points is a problem of fundamental importance in numerical integration. Several authors have proposed to se…
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…
Comparing Scale Parameter Estimators for Gaussian Process Interpolation with the Brownian Motion Prior: Leave-One-Out Cross Validation and Maximum Likelihood
Masha Naslidnyk, Motonobu Kanagawa, Toni Karvonen +1
Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation, offering a principled way of quantifying the uncertainties of predicted functi…