Toni Karvonen

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See also my Google Scholar profile.

Preprints

  1. T. Karvonen & Y. Suzuki (2024). Approximation in Hilbert spaces of the Gaussian and related analytic kernels. arXiv:2209.12473.
    arXiv
  2. T. Karvonen, F. Cirak & M. Girolami (2024). Error analysis for a statistical finite element method. arXiv:2201.07543.
    arXiv
  3. Y. Suzuki, N. Hyvönen & T. Karvonen (2024). Möbius-transformed trapezoidal rule. arXiv:2407.13650.
    arXiv
  4. T. Karvonen & A. Zhigljavsky (2024). Maximum mean discrepancies of Farey sequences. arXiv:2407.10214.
    arXiv
  5. Y. Suzuki & T. Karvonen (2024). Construction of optimal algorithms for function approximation in Gaussian Sobolev spaces. arXiv:2402.02917.
    arXiv
  6. M. Korte-Stapff, T. Karvonen & E. Moulines (2024). Smoothness estimation for Whittle-Matérn processes on closed Riemannian manifolds. arXiv:2401.00510.
    arXiv
  7. 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
  8. T. Karvonen (2021). Estimation of the scale parameter for a misspecified Gaussian process model. arXiv:2110.02810.
    arXiv
  9. T. Karvonen (2021). On non-inclusion of certain functions in reproducing kernel Hilbert spaces. arXiv:2102.10628.
    arXiv

Journal articles

  1. C. J. Oates, T. Karvonen, A. L. Teckentrup, M. Strocchi & S. A. Niederer (2024+). Probabilistic Richardson extrapolation. Journal of the Royal Statistical Society, Series B (Statistical Methodology). To appear.
    arXiv
  2. M. Naslidnyk, M. Kanagawa, T. Karvonen & M. Mahsereci (2024+). 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. To appear.
    arXiv
  3. F. Tronarp & T. Karvonen (2024). Orthonormal expansions for translation-invariant kernels. Journal of Approximation Theory, 302:106055.
    DOI|PDF|errors
  4. 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
  5. T. Karvonen, J. Cockayne, F. Tronarp & S. Särkkä (2023). A probabilistic Taylor expansion with Gaussian processes. Transactions on Machine Learning Research.
    TMLR|PDF
  6. 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
  7. T. Karvonen (2023). Small sample spaces for Gaussian processes. Bernoulli, 29(2):875–900.
    DOI|PDF
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. T. Karvonen, S. Särkkä & K. Tanaka (2021). Kernel-based interpolation at approximate Fekete points. Numerical Algorithms, 87(1):445–468.
    DOI|PDF
  14. 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
  15. T. Karvonen & S. Särkkä (2020). Worst-case optimal approximation with increasingly flat Gaussian kernels. Advances in Computational Mathematics, 46:21.
    DOI|PDF
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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. 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|code on GitHub
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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

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.