Toni Karvonen


MAINPUBLICATIONS

See also my Google Scholar profile.

Preprints

  1. K. Li, D. Giles, T. Karvonen, S. Guillas and F.-X. Briol (2022). Multilevel Bayesian quadrature. arXiv:2210.08329.
  2. T. Karvonen (2022). Approximation in Hilbert spaces of the Gaussian and other weighted power series kernels. arXiv:2209.12473.
  3. F. Tronarp and T. Karvonen (2022). Orthonormal expansions for translation-invariant kernels. arXiv:2206.08648.
  4. T. Karvonen and C. J. Oates (2022). Maximum likelihood estimation in Gaussian process regression is ill-posed. arXiv:2203.09179.
  5. T. Karvonen (2022). Asymptotic bounds for smoothness parameter estimates in Gaussian process interpolation. arXiv:2203.05400.
  6. T. Karvonen, F. Cirak and M. Girolami (2022). Error analysis for a statistical finite element method. arXiv:2201.07543.
  7. 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.
  8. T. Karvonen (2021). Estimation of the scale parameter for a misspecified Gaussian process model. arXiv:2110.02810.
  9. T. Karvonen (2021). On non-inclusion of certain functions in reproducing kernel Hilbert spaces. arXiv:2102.10628.
  10. T. Karvonen, J. Cockayne, F. Tronarp and S. Särkkä (2021). A probabilistic Taylor expansion with applications in filtering and differential equations. arXiv:2102.00877.

Journal articles

  1. T. Karvonen (2022). Small sample spaces for Gaussian processes. Bernoulli. To appear.
  2. T. Karvonen (2022). Error bounds and the asymptotic setting in kernel-based approximation. Dolomites Research Notes on Approximation, 15(3):65–77.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. T. Karvonen, S. Särkkä and K. Tanaka (2021). Kernel-based interpolation at approximate Fekete points. Numerical Algorithms, 87(1):445–468.
  8. 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.
  9. T. Karvonen and S. Särkkä (2020). Worst-case optimal approximation with increasingly flat Gaussian kernels. Advances in Computational Mathematics, 46:21.
  10. 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.
  11. 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.
  12. T. Karvonen, M. Kanagawa and S. Särkkä (2019). On the positivity and magnitudes of Bayesian quadrature weights. Statistics and Computing, 29(6):1317–1333.
  13. T. Karvonen, S. Särkkä and C. J. Oates (2019). Symmetry exploits for Bayesian cubature methods. Statistics and Computing, 29(6):1231–1248.
  14. T. Karvonen and S. Särkkä (2019). Gaussian kernel quadrature at scaled Gauss–Hermite nodes. BIT Numerical Mathematics, 59(4):877–902.
  15. F. Tronarp, T. Karvonen and S. Särkkä (2019). Student's t-filters for noise scale estimation. IEEE Signal Processing Letters, 26(2):352–356.
  16. T. Karvonen and S. Särkkä (2018). Fully symmetric kernel quadrature. SIAM Journal on Scientific Computing, 40(2):A697–A720.

Conference proceedings

  1. 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.
  2. S. Särkkä, C. Merkatas and T. Karvonen (2021). Gaussian approximations of SDEs in Metropolis-adjusted Langevin algorithms. In 31st IEEE International Workshop on Machine Learning for Signal Processing.
  3. T. Karvonen, F. Tronarp and S. 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.
  4. 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.
  5. 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 57th IEEE Conference on Decision and Control, pp. 7176–7181.
  6. F. Tronarp, T. Karvonen and S. 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.
  7. T. Karvonen and S. Särkkä (2017). Classical quadrature rules via Gaussian processes. In 27th IEEE International Workshop on Machine Learning for Signal Processing.
  8. 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 20th International Conference on Information Fusion. Tammy Blair Best Student Paper Award, first runner-up.
  9. T. Karvonen and S. Särkkä (2016). Approximate state-space Gaussian processes via spectral transformation. In 26th IEEE International Workshop on Machine Learning for Signal Processing.
  10. T. Karvonen and S. 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