Toni Karvonen

I am Academy of Finland Postdoctoral Researcher in the Department of Mathematics and Statistics at the University of Helsinki, Finland. My research is currently funded by the Academy project Scalable, adaptive and reliable probabilistic integration. Previously I have been

• (2020–2021) Research Fellow on the Programme for Data-Centric Engineering at the Alan Turing Institute, London, UK, where I worked with Chris Oates and Mark Girolami.
• (2016–2020) Doctoral Student and Postdoctoral Researcher supervised by Simo Särkkä in the Department of Electrical Engineering and Automation at Aalto University, Espoo, Finland. I completed my doctoral degree in 2019.
• (2010–2015) Student in the Department of Mathematics and Statistics at the University of Helsinki, Finland. I obtained my Bachelor's (in mathematics) and Master's degrees (in applied mathematics) in 2015.

Research interests

I am interested in approximation theory, numerical analysis and probabilistic modelling. Most of my research focusses on theory and methodology for methods based on positive-definite kernels, such as Gaussian process regression and radial basis function interpolation, and approximation in reproducing kernel Hilbert spaces. I am particularly interested in using Hilbert space methods to analyse Gaussian process regression in interpolatory settings where the data are assumed noiseless. Bayesian cubature (an example of a probabilistic numerical method) for numerical integration is the method I have the most experience in. Topics that I am actively working on include

• Parameter estimation in Gaussian process regression. How do statistical parameter estimation methods, such as maximum likelihood estimation or cross-validation, behave in interpolatory settings? The problem has connections to sample path properties. [Kar21, KWTOS20 & KTS19]
• Reliability of Gaussian process regression. In which settings and to what extent can we trust the uncertainty quantification that Gaussian process models provide? [KWTOS20]
• Scalable and high-dimensional of Bayesian cubature. Kernel-based methods typically suffer from cubic computational complexity. How can Bayesian cubature, which uses Gaussian process modelling, be sped up and used in high-dimensional settings? [KSO19 & KS18]
• Integration in reproducing kernel Hilbert spaces. How fast do numerical integration methods converge in reproducing kernel Hilbert spaces? Which nodes should one use? How to approximate the worst-case optimal weights? I have been particularly interested in the Gaussian kernel. [KOM21 & SKH21]

During my doctoral studies I worked on filtering methods for non-linear systems. [KBMS20] See also my full list of publications and Google Scholar profile.

Contact information