Toni Karvonen

MAIN — PUBLICATIONS — PRESENTATIONS — CV

See also my Google Scholar profile.

Preprints

  1. T. Karvonen & C. J. Oates (2026). Why not to use the Gaussian kernel. arXiv:2608.26974. [arXiv]
  2. T. Karvonen (2026). Bumps and polynomials in RKHSs of translation-invariant kernels. arXiv:2102.10628. [arXiv]
  3. T. Karvonen & R. K. H. Sørensen (2026). Gaussian processes with sample paths in reproducing kernel Banach spaces. arXiv:2605.28106. [arXiv]
  4. C. J. Oates, R. Howey & T. Karvonen (2026). Sparse probabilistic Richardson extrapolation. arXiv:2604.02072. [arXiv]
  5. T. Karvonen & F. Bachoc (2025). Scale estimation and rate-unbiasedness for Gaussian processes under smoothness misspecification. arXiv:2110.02810. [arXiv]
  6. J. Koskela, T. Karvonen, K. Łatuszyński & D. Spanò (2025). A debiased Bernoulli factory and unbiased estimation of a probability. arXiv:2510.01941. [arXiv]

Books & surveys

  1. M. Mahsereci & T. Karvonen (2026). Bayesian quadrature. Foundations and Trends in Machine Learning, 19(2–3):121–240. [DOI | PDF]

Journal articles

  1. T. Karvonen, G. Santin & T. Wenzel (2026+). General superconvergence for kernel-based approximation. IMA Journal of Numerical Analysis. To appear. [arXiv]
  2. T. Karvonen & S. Särkkä (2026+). Wasserstein bounds for non-linear Gaussian filters. IEEE Transactions on Automatic Control. To appear. [DOI | PDF]
  3. T. Karvonen & Y. Suzuki (2026). Approximation in Hilbert spaces of the Gaussian and related analytic kernels. IMA Journal of Numerical Analysis, 46(4):2344–2376. [DOI | PDF]
  4. Y. Suzuki & T. Karvonen (2026). Construction of optimal algorithms for function approximation in Gaussian Sobolev spaces. BIT Numerical Mathematics, 66:23. [DOI | PDF]
  5. Y. Suzuki, N. Hyvönen & T. Karvonen (2026). Möbius-transformed trapezoidal rule. Mathematics of Computation, 95(359):1491–1515. [DOI | PDF]
  6. T. Karvonen & A. Zhigljavsky (2025). Maximum mean discrepancies of Farey sequences. Acta Mathematica Hungarica, 177(2):351–362. [DOI | PDF]
  7. T. Karvonen, F. Cirak & M. Girolami (2025). Error analysis for a statistical finite element method. Journal of Multivariate Analysis, 210:105468. [DOI | PDF]
  8. M. Korte-Stapff, T. Karvonen & É. Moulines (2025). Smoothness estimation for Whittle-Matérn processes on closed Riemannian manifolds. Stochastic Processes and their Applications, 189:104685. [DOI | PDF]
  9. M. Naslidnyk, M. Kanagawa, T. Karvonen & M. Mahsereci (2025). Comparing scale parameter estimators for Gaussian process interpolation with the Brownian motion prior: Leave-one-out cross validation and maximum likelihood. SIAM/ASA Journal on Uncertainty Quantification, 13(2):679–717. [DOI | PDF]
  10. C. J. Oates, T. Karvonen, A. L. Teckentrup, M. Strocchi & S. A. Niederer (2025). Probabilistic Richardson extrapolation. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 87(2):457–479. [DOI | PDF]
  11. F. Tronarp & T. Karvonen (2024). Orthonormal expansions for translation-invariant kernels. Journal of Approximation Theory, 302:106055. [DOI | PDF | errors]
  12. T. Karvonen (2023). Asymptotic bounds for smoothness parameter estimates in Gaussian process interpolation. SIAM/ASA Journal on Uncertainty Quantification, 11(4):1225–1257. [DOI | PDF]
  13. T. Karvonen, J. Cockayne, F. Tronarp & S. Särkkä (2023). A probabilistic Taylor expansion with Gaussian processes. Transactions on Machine Learning Research. [TMLR | PDF]
  14. T. Karvonen & C. J. Oates (2023). Maximum likelihood estimation in Gaussian process regression is ill-posed. Journal of Machine Learning Research, 24(120):1–47. [JMLR | PDF | addendum]
  15. T. Karvonen (2023). Small sample spaces for Gaussian processes. Bernoulli, 29(2):875–900. [DOI | PDF]
  16. T. Karvonen (2022). Error bounds and the asymptotic setting in kernel-based approximation. Dolomites Research Notes on Approximation, 15(3):65–77. [DOI | PDF | addendum]
  17. L. F. South, T. Karvonen, C. Nemeth, M. Girolami & C. J. Oates (2022). Semi-exact control functionals from Sard's method. Biometrika, 109(2):351–367. [DOI | PDF | code on GitHub]
  18. G. Santin, T. Karvonen & B. Haasdonk (2022). Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces. BIT Numerical Mathematics, 62:279–310. [DOI | PDF]
  19. Z. Zhao, T. Karvonen, R. Hostettler & S. Särkkä (2021). Taylor moment expansion for continuous-discrete Gaussian filtering and smoothing. IEEE Transactions on Automatic Control, 66(9):4460–4467. [DOI | PDF]
  20. T. Karvonen, C. J. Oates & M. Girolami (2021). Integration in reproducing kernel Hilbert spaces of Gaussian kernels. Mathematics of Computation, 90(331):2209–2233. [DOI | PDF]
  21. T. Karvonen, S. Särkkä & K. Tanaka (2021). Kernel-based interpolation at approximate Fekete points. Numerical Algorithms, 87(1):445–468. [DOI | PDF]
  22. J. Prüher, T. Karvonen, C. J. Oates, O. Straka & S. Särkkä (2021). Improved calibration of numerical integration error in sigma-point filters. IEEE Transactions on Automatic Control, 66(3):1286–1292. [DOI | PDF]
  23. T. Karvonen & S. Särkkä (2020). Worst-case optimal approximation with increasingly flat Gaussian kernels. Advances in Computational Mathematics, 46:21. [DOI | PDF]
  24. T. Karvonen, S. Bonnabel, E. Moulines & S. Särkkä (2020). On stability of a class of filters for non-linear stochastic systems. SIAM Journal on Control and Optimization, 58(4):2023–2049. [DOI | PDF | errata]
  25. T. Karvonen, G. Wynne, F. Tronarp, C. J. Oates & S. 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. [DOI | PDF | errata]
  26. T. Karvonen, M. Kanagawa & S. Särkkä (2019). On the positivity and magnitudes of Bayesian quadrature weights. Statistics and Computing, 29(6):1317–1333. [DOI | PDF]
  27. T. Karvonen, S. Särkkä & C. J. Oates (2019). Symmetry exploits for Bayesian cubature methods. Statistics and Computing, 29(6):1231–1248. [DOI | PDF | code on GitHub]
  28. T. Karvonen & S. Särkkä (2019). Gaussian kernel quadrature at scaled Gauss–Hermite nodes. BIT Numerical Mathematics, 59(4):877–902. [DOI | PDF | code on GitHub]
  29. F. Tronarp, T. Karvonen & S. Särkkä (2019). Student's t-filters for noise scale estimation. IEEE Signal Processing Letters, 26(2):352–356. [DOI | PDF]
  30. T. Karvonen & S. Särkkä (2018). Fully symmetric kernel quadrature. SIAM Journal on Scientific Computing, 40(2):A697–A720. [DOI | PDF | code on GitHub]

Conference articles

  1. T. Karvonen, G. Santin & T. Wenzel (2026+). Piecewise linear interpolation via kernels. In ENUMATH 2025. To appear. [arXiv]
  2. A. Tokmak, T. Karvonen, T. B. Schön & D. Baumann (2026). Safe learning-based control via function-based uncertainty quantification. In the 65th IEEE Conference on Decision and Control. To appear. [arXiv]
  3. Z. Chen, T. Karvonen, H. Kanagawa, F.-X. Briol & C. J. Oates (2026). Stationary MMD points. In the 43rd International Conference on Machine Learning. To appear. [arXiv]
  4. S. S. Kang, F.-X. Briol, T. Karvonen & Z. Chen (2026). BayesSum: Bayesian quadrature in discrete spaces. In the 2nd International Conference on Probabilistic Numerics, PMLR, 341:73–89. [PMLR | PDF | GitHub]
  5. T. Weiland, T. Karvonen & P. Hennig (2026). Hierarchical Bayesian quadrature. In the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR, 337:7273–7289. [PMLR | PDF | GitHub]
  6. F.-X. Briol, A. Gessner, T. Karvonen & M. Mahsereci (2025). A dictionary of closed-form kernel mean embeddings. In the 1st International Conference on Probabilistic Numerics, PMLR, 271:84–94. [PMLR | PDF | GitHub]
  7. K. Li, D. Giles, T. Karvonen, S. Guillas & F.-X. Briol (2023). Multilevel Bayesian quadrature. In the 26th International Conference on Artificial Intelligence and Statistics, PMLR, 206:1845–1868. [PMLR | PDF | GitHub]
  8. O. Teymur, C. N. Foley, P. G. Green, T. Karvonen & C. J. Oates (2021). Black box probabilistic numerics. In Advances in Neural Information Processing Systems 34, pp. 23452–23464. [NeurIPS | PDF]
  9. S. Särkkä, C. Merkatas & T. Karvonen (2021). Gaussian approximations of SDEs in Metropolis-adjusted Langevin algorithms. In the 31st IEEE International Workshop on Machine Learning for Signal Processing. [DOI | PDF]
  10. T. Karvonen, F. Tronarp & S. Särkkä (2019). Asymptotics of maximum likelihood parameter estimation for Gaussian processes: the Ornstein–Uhlenbeck prior. In the 29th IEEE International Workshop on Machine Learning for Signal Processing. [DOI | PDF]
  11. T. Karvonen, C. J. Oates & S. Särkkä (2018). A Bayes–Sard cubature method. In Advances in Neural Information Processing Systems 31, pp. 5882–5893. [NeurIPS | PDF]
  12. T. Karvonen, S. Bonnabel, E. Moulines & S. Särkkä (2018). Bounds on the covariance matrix of a class of Kalman–Bucy filters for systems with non-linear dynamics. In the 57th IEEE Conference on Decision and Control, pp. 7176–7181. [DOI | PDF]
  13. F. Tronarp, T. Karvonen & S. Särkkä (2018). Mixture representation of the Matérn class with applications in state space approximations and Bayesian quadrature. In the 28th IEEE International Workshop on Machine Learning for Signal Processing. [DOI | PDF]
  14. T. Karvonen & S. Särkkä (2017). Classical quadrature rules via Gaussian processes. In the 27th IEEE International Workshop on Machine Learning for Signal Processing. [DOI | PDF]
  15. J. Prüher, F. Tronarp, T. Karvonen, S. Särkkä & O. Straka (2017). Student-t process quadratures for filtering of non-linear systems with heavy-tailed noise. In the 20th International Conference on Information Fusion. Tammy Blair Best Student Paper Award, first runner-up. [DOI | PDF]
  16. T. Karvonen & S. Särkkä (2016). Approximate state-space Gaussian processes via spectral transformation. In the 26th IEEE International Workshop on Machine Learning for Signal Processing. [DOI | PDF | errors]
  17. T. Karvonen & S. Särkkä (2016). Fourier–Hermite series for stochastic stability analysis of non-linear Kalman filters. In the 19th International Conference on Information Fusion, pp. 1829–1836. [IEEE Xplore | PDF | code]

Technical reports

  1. J. Wenger, N. Krämer, M. Pförtner, J. Schmidt, N. Bosch, N. Effenberger, J. Zenn, A. Gessner, T. Karvonen, F.-X. Briol, M. Mahsereci & P. Hennig (2021). ProbNum: Probabilistic numerics in Python. arXiv:2112.02100. [arXiv | ProbNum]

Theses

  1. T. Karvonen (2019). Kernel-Based and Bayesian Methods for Numerical Integration. Doctoral dissertation. Department of Electrical Engineering and Automation, Aalto University. [Aaltodoc | PDF]
  2. T. Karvonen (2014). Stability of Linear and Non-Linear Kalman Filters. Master's thesis. Department of Mathematics and Statistics, University of Helsinki. [E-thesis | PDF | errors]
  3. T. Karvonen (2014). Mittojen disintegraatio. Bachelors's thesis. Department of Mathematics and Statistics, University of Helsinki.