Toni Karvonen
Research Fellow at the Alan Turing Institute
Contact Information
email: tkarvonen@turing.ac.ukI am a Research Fellow on the Programme for Data-Centric Engineering at the Alan Turing Institute, London, UK, where I work with Mark Girolami and Chris Oates.
I completed my doctoral degree, supervised by Simo Särkkä, in the Department of Electrical Engineering and Automation at Aalto University, Finland, in 2016–2019. Prior to this, I did my Bachelor's and Master's degrees in mathematics in the Department of Mathematics and Statistics at the University of Helsinki in 2010–2015.
My main research interests are
- Probabilistic numerics and uncertainty quantification. My focus is on developing computationally efficient probabilistic numerical methods, understanding how the methods are related to classical methods of numerical analysis, and analysing properties of the uncertainty quantification these methods provide. In particular, I am interested in numerical integration using Bayesian cubature rules.
- Kernel-based approximation. I develop and analyse kernel-based algorithms that are optimal in reproducing kernel Hilbert spaces.
Publications (Google Scholar)
Preprints
- Onur Teymur, Christopher N. Foley, Philip G. Green, Toni Karvonen and Chris J. Oates (2021). Black box probabilistic numerics. arXiv:2106.13718.
- Toni Karvonen (2021). Small sample spaces for Gaussian processes. arXiv:2103.03169.
- Toni Karvonen (2021). On non-inclusion of certain functions in reproducing kernel Hilbert spaces. arXiv:2102.10628.
- Toni Karvonen, Jon Cockayne, Filip Tronarp and Simo Särkkä (2021). A probabilistic Taylor expansion with applications in filtering and differential equations. arXiv:2102.00877.
Journal articles
- Leah F. South, Toni Karvonen, Chris Nemeth, Mark Girolami and Chris J. Oates (2021). Semi-exact control functionals from Sard's method. Biometrika. To appear.
- Gabriele Santin, Toni Karvonen and Bernard Haasdonk (2021). Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces. BIT Numerical Mathematics. To appear.
- Toni Karvonen, Chris J. Oates and Mark Girolami (2021). Integration in reproducing kernel Hilbert spaces of Gaussian kernels. Mathematics of Computation, 90(331):2209–2233.
- Zheng Zhao, Toni Karvonen, Roland Hostettler and Simo Särkkä (2021). Taylor moment expansion for continuous-discrete Gaussian filtering and smoothing. IEEE Transactions on Automatic Control. To appear.
- Toni Karvonen, Simo Särkkä and Ken'ichiro Tanaka (2021). Kernel-based interpolation at approximate Fekete points. Numerical Algorithms, 87(1):445–468.
- Jakub Prüher, Toni Karvonen, Chris J. Oates, Ondřej Straka and Simo Särkkä (2021). Improved calibration of numerical integration error in sigma-point filters. IEEE Transactions on Automatic Control, 66(3):1286–1292.
- Toni Karvonen and Simo Särkkä (2020). Worst-case optimal approximation with increasingly flat Gaussian kernels. Advances in Computational Mathematics, 46:21.
- Toni Karvonen, Silvère Bonnabel, Eric Moulines and Simo Särkkä (2020). On stability of a class of filters for non-linear stochastic systems. SIAM Journal on Control and Optimization, 58(4):2023–2049.
- Toni Karvonen, George Wynne, Filip Tronarp, Chris J. Oates and Simo Särkkä (2020). Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions. SIAM/ASA Journal on Uncertainty Quantification, 8(3):926–958.
- Toni Karvonen, Motonobu Kanagawa and Simo Särkkä (2019). On the positivity and magnitudes of Bayesian quadrature weights. Statistics and Computing, 29(6):1317–1333.
- Toni Karvonen, Simo Särkkä and Chris J. Oates (2019). Symmetry exploits for Bayesian cubature methods. Statistics and Computing, 29(6):1231–1248.
- Toni Karvonen and Simo Särkkä (2019). Gaussian kernel quadrature at scaled Gauss–Hermite nodes. BIT Numerical Mathematics, 59(4):877–902.
- Filip Tronarp, Toni Karvonen and Simo Särkkä (2019). Student's t-filters for noise scale estimation. IEEE Signal Processing Letters, 26(2):352–356.
- Toni Karvonen and Simo Särkkä (2018). Fully symmetric kernel quadrature. SIAM Journal on Scientific Computing, 40(2):A697–A720.
Conference proceedings
- Toni Karvonen, Filip Tronarp and Simo Särkkä (2019). Asymptotics of maximum likelihood parameter estimation for Gaussian processes: the Ornstein–Uhlenbeck prior. In 29th IEEE International Workshop on Machine Learning for Signal Processing.
- Toni Karvonen, Chris J. Oates and Simo Särkkä (2018). A Bayes–Sard cubature method. In Advances in Neural Information Processing Systems 31 (NeurIPS 2018), pp. 5882–5893.
- Toni Karvonen, Silvère Bonnabel, Eric Moulines and Simo Särkkä (2018). Bounds on the covariance matrix of a class of Kalman–Bucy filters for systems with non-linear dynamics. In 57th IEEE Conference on Decision and Control, pp. 7176–7181.
- Filip Tronarp, Toni Karvonen and Simo Särkkä (2018). Mixture representation of the Matérn class with applications in state space approximations and Bayesian quadrature. In 28th IEEE International Workshop on Machine Learning for Signal Processing.
- Toni Karvonen and Simo Särkkä (2017). Classical quadrature rules via Gaussian processes. In 27th IEEE International Workshop on Machine Learning for Signal Processing.
- Jakub Prüher, Filip Tronarp, Toni Karvonen, Simo Särkkä and Ondřej Straka (2017). Student-t process quadratures for filtering of non-linear systems with heavy-tailed noise. In 20th International Conference on Information Fusion. Tammy Blair Best Student Paper Award, first runner-up.
- Toni Karvonen and Simo Särkkä (2016). Approximate state-space Gaussian processes via spectral transformation. In 26th IEEE International Workshop on Machine Learning for Signal Processing.
- Toni Karvonen and Simo Särkkä (2016). Fourier–Hermite series for stochastic stability analysis of non-linear Kalman filters. In 19th International Conference on Information Fusion, pp. 1829–1836.
Theses
- Toni Karvonen (2019). Kernel-Based and Bayesian Methods for Numerical Integration. Doctoral dissertation. Supervisor Prof. Simo Särkkä. Department of Electrical Engineering and Automation, Aalto University.
- Toni Karvonen (2014). Stability of Linear and Non-Linear Kalman Filters. Master's thesis. Instructor Dr. Simo Särkkä (Aalto University), supervisor Dr. Dario Gasbarra (University of Helsinki). Department of Mathematics and Statistics, University of Helsinki.
- Toni Karvonen (2014). Mittojen disintegraatio. Bachelors's thesis (in Finnish). Instructor Dr. Ilkka Holopainen (University of Helsinki). Department of Mathematics and Statistics, University of Helsinki.
Updated on July 26, 2021.