Toni Karvonen

MAIN — PUBLICATIONS — PRESENTATIONS

See also my Google Scholar profile.

Preprints

  1. Y. Suzuki and T. Karvonen (2024). Construction of optimal algorithms for function approximation in Gaussian Sobolev spaces. arXiv:2402.02917.
    arXiv
  2. C. J. Oates, T. Karvonen, A. L. Teckentrup, M. Strocchi and S. A. Niederer (2024). Probabilistic Richardson extrapolation. arXiv:2401.07562.
    arXiv
  3. M. Korte-Stapff, T. Karvonen and E. Moulines (2023). Smoothness estimation for Whittle-Matérn processes on closed Riemannian manifolds. arXiv:2401.00510.
    arXiv
  4. M. Naslidnyk, M. Kanagawa, T. Karvonen and M. Mahsereci (2023). Comparing scale parameter estimators for Gaussian process regression: cross validation and maximum likelihood. arXiv:2307.07466.
    arXiv
  5. F. Tronarp and T. Karvonen (2023). Orthonormal expansions for translation-invariant kernels. arXiv:2206.08648.
    arXiv
  6. T. Karvonen (2022). Approximation in Hilbert spaces of the Gaussian and other weighted power series kernels. arXiv:2209.12473.
    arXiv
  7. T. Karvonen, F. Cirak and M. Girolami (2022). Error analysis for a statistical finite element method. arXiv:2201.07543.
    arXiv
  8. J. Wenger, N. Krämer, M. Pförtner, J. Schmidt, N. Bosch, N. Effenberger, J. Zenn, A. Gessner, T. Karvonen, F.-X. Briol, M. Mahsereci and P. Hennig (2021). ProbNum: Probabilistic numerics in Python. arXiv:2112.02100.
    arXiv|ProbNum
  9. T. Karvonen (2021). Estimation of the scale parameter for a misspecified Gaussian process model. arXiv:2110.02810.
    arXiv
  10. T. Karvonen (2021). On non-inclusion of certain functions in reproducing kernel Hilbert spaces. arXiv:2102.10628.
    arXiv

Journal articles

  1. 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
  2. T. Karvonen, J. Cockayne, F. Tronarp and S. Särkkä (2023). A probabilistic Taylor expansion with Gaussian processes. Transactions on Machine Learning Research.
    TMLR|PDF
  3. T. Karvonen and 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
  4. T. Karvonen (2023). Small sample spaces for Gaussian processes. Bernoulli, 29(2):875–900.
    DOI|PDF
  5. 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
  6. L. F. South, T. Karvonen, C. Nemeth, M. Girolami and C. J. Oates (2022). Semi-exact control functionals from Sard's method. Biometrika, 109(2):351–367.
    DOI|PDF|code on Github
  7. G. Santin, T. Karvonen and B. Haasdonk (2022). Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces. BIT Numerical Mathematics, 62:279–310.
    DOI|PDF
  8. Z. Zhao, T. Karvonen, R. Hostettler and S. Särkkä (2021). Taylor moment expansion for continuous-discrete Gaussian filtering and smoothing. IEEE Transactions on Automatic Control, 66(9):4460–4467.
    DOI|PDF
  9. T. Karvonen, C. J. Oates and M. Girolami (2021). Integration in reproducing kernel Hilbert spaces of Gaussian kernels. Mathematics of Computation, 90(331):2209–2233.
    DOI|PDF
  10. T. Karvonen, S. Särkkä and K. Tanaka (2021). Kernel-based interpolation at approximate Fekete points. Numerical Algorithms, 87(1):445–468.
    DOI|PDF
  11. J. Prüher, T. Karvonen, C. J. Oates, O. Straka and S. Särkkä (2021). Improved calibration of numerical integration error in sigma-point filters. IEEE Transactions on Automatic Control, 66(3):1286–1292.
    DOI|PDF
  12. T. Karvonen and S. Särkkä (2020). Worst-case optimal approximation with increasingly flat Gaussian kernels. Advances in Computational Mathematics, 46:21.
    DOI|PDF
  13. T. Karvonen, S. Bonnabel, E. Moulines and 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
  14. T. Karvonen, G. Wynne, F. Tronarp, C. J. Oates and 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
  15. T. Karvonen, M. Kanagawa and S. Särkkä (2019). On the positivity and magnitudes of Bayesian quadrature weights. Statistics and Computing, 29(6):1317–1333.
    DOI|PDF
  16. T. Karvonen, S. Särkkä and C. J. Oates (2019). Symmetry exploits for Bayesian cubature methods. Statistics and Computing, 29(6):1231–1248.
    DOI|PDF|code on GitHub
  17. T. Karvonen and S. Särkkä (2019). Gaussian kernel quadrature at scaled Gauss–Hermite nodes. BIT Numerical Mathematics, 59(4):877–902.
    DOI|PDF|code on GitHub
  18. F. Tronarp, T. Karvonen and S. Särkkä (2019). Student's t-filters for noise scale estimation. IEEE Signal Processing Letters, 26(2):352–356.
    DOI|PDF
  19. T. Karvonen and S. Särkkä (2018). Fully symmetric kernel quadrature. SIAM Journal on Scientific Computing, 40(2):A697–A720.
    DOI|PDF|code on GitHub

Conference proceedings

  1. K. Li, D. Giles, T. Karvonen, S. Guillas and F.-X. Briol (2023). Multilevel Bayesian quadrature. In the 26th International Conference on Artificial Intelligence and Statistics, PMLR, 206:1845–1868.
    PMLR|PDF|code on GitHub
  2. O. Teymur, C. N. Foley, P. G. Green, T. Karvonen and C. J. Oates (2021). Black box probabilistic numerics. In Advances in Neural Information Processing Systems 34, pp. 23452–23464.
    NeurIPS|PDF
  3. S. Särkkä, C. Merkatas and 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
  4. T. Karvonen, F. Tronarp and 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
  5. T. Karvonen, C. J. Oates and S. Särkkä (2018). A Bayes–Sard cubature method. In Advances in Neural Information Processing Systems 31, pp. 5882–5893.
    NeurIPS|PDF
  6. T. Karvonen, S. Bonnabel, E. Moulines and 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
  7. F. Tronarp, T. Karvonen and 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
  8. T. Karvonen and S. Särkkä (2017). Classical quadrature rules via Gaussian processes. In the 27th IEEE International Workshop on Machine Learning for Signal Processing.
    DOI|PDF
  9. J. Prüher, F. Tronarp, T. Karvonen, S. Särkkä and 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
  10. T. Karvonen and 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
  11. T. Karvonen and 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

Theses