Toni Karvonen

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Publications (Google Scholar)

Preprints

1. Toni Karvonen, Chris J. Oates and Mark Girolami (2020). Integration in reproducing kernel Hilbert spaces of Gaussian kernels. arXiv:2004.12654.
   arXiv
2. Gabriele Santin, Toni Karvonen and Bernard Haasdonk (2020). Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces. arXiv:2004.00556.
   arXiv
3. Leah F. South, Toni Karvonen, Chris Nemeth, Mark Girolami and Chris J. Oates (2020). Semi-exact control functionals from Sard's method. arXiv:2002.00033.
   arXiv|code on Github
4. Zheng Zhao, Toni Karvonen, Roland Hostettler and Simo Särkkä (2020). Taylor moment expansion for continuous-discrete Gaussian filtering and smoothing. arxiv:2001.02466.
   arXiv

Journal articles

1. 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. To appear.
   DOI|PDF
2. Toni Karvonen, Simo Särkkä and Ken'ichiro Tanaka (2020). Kernel-based interpolation at approximate Fekete points. Numerical Algorithms. To appear.
   DOI|arXiv
3. 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. To appear.
   arXiv
4. 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. To appear.
   arXiv
5. Toni Karvonen and Simo Särkkä (2020). Worst-case optimal approximation with increasingly flat Gaussian kernels. Advances in Computational Mathematics.
   DOI|PDF
6. Toni Karvonen, Motonobu Kanagawa and Simo Särkkä (2019). On the positivity and magnitudes of Bayesian quadrature weights. Statistics and Computing, 29(6):1317–1333.
   DOI|PDF
7. Toni Karvonen, Simo Särkkä and Chris J. Oates (2019). Symmetry exploits for Bayesian cubature methods. Statistics and Computing, 29(6):1231–1248.
   DOI|PDF|code on GitHub
8. Toni Karvonen and Simo Särkkä (2019). Gaussian kernel quadrature at scaled Gauss–Hermite nodes. BIT Numerical Mathematics, 59(4):877–902.
   DOI|PDF|code on GitHub
9. Filip Tronarp, Toni Karvonen and Simo Särkkä (2019). Student's t-filters for noise scale estimation. IEEE Signal Processing Letters, 26(2):352–356.
   DOI|PDF
10. Toni Karvonen and Simo Särkkä (2018). Fully symmetric kernel quadrature. SIAM Journal on Scientific Computing, 40(2):A697–A720.
    DOI|PDF|code on GitHub

Conference proceedings

1. 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.
   DOI|PDF
2. 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.
   NeurIPS proceedings|PDF
3. 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.
   DOI|PDF
4. 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.
   DOI|PDF
5. Toni Karvonen and Simo Särkkä (2017). Classical quadrature rules via Gaussian processes. In 27th IEEE International Workshop on Machine Learning for Signal Processing.
   DOI|PDF
6. 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.
   DOI|PDF
7. 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.
   DOI|PDF|errata
8. 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.
   IEEE Xplore|PDF|code

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.
  Aaltodoc|PDF
• 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.
  E-thesis|PDF|errata
• 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.

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Talks and posters

Upcoming

• August 9–14, 2020. Talk. 14th International Conference in Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing, Oxford, UK.
• September 10, 2020. Talk. The Royal Statistical Society Conference 2020 (Session: Quantifying Uncertainty due to Discretisation Error in Numerical Computation), Bournemouth, UK.

Past

• February 17–18, 2020. Poster. Workshop on Functional Inference and Machine Intelligence, EURECOM, Sophia Antipolis, France.
• October 29, 2019. Talk. The Alan Turing Institute, London, UK.
• October 17, 2019. Talk. Department of Statistics, Pennsylvania State University, State College, Pennsylvania, USA.
• October 15, 2019. Poster. The 29th IEEE International Workshop on Machine Learning for Signal Processing, Pittsburgh, Pennsylvania, USA.
• September 11, 2019. Talk. The 8th Workshop on High-Dimensional Approximation (HDA2019), ETH Zurich, Switzerland.
• July 10, 2019. Talk “Methods for large-scale and high-dimensional probabilistic integration”. The 12th International Conference on Monte Carlo Methods and Applications (Session: Probabilistic Numerical Methods), Sydney, Australia.
• June 27, 2019. Talk “Kernel-based numerical integration”. The Institute of Statistical Mathematics, Tokyo, Japan.
• June 26, 2019. Talk “Approximation with Gaussians, power series kernels and polynomials”. Mathematics Informatics 3rd Laboratory Seminar, Department of Mathematical Informatics, University of Tokyo, Japan.
• June 21, 2019. Talk “On stability of a class of filters for non-linear stochastic systems”. SIAM Conference on Control and Its Applications 2019 (CP8: Stability in Estimation and Control), Chengdu, China.
• May 20, 2019. Talk “Computational methods for kernel-based cubature”. Approximation Theory 16 (MS: Probabilistic Numerics and Kernel-Based Methods), Nashville, Tennessee, USA.
• April 26, 2019. Talk “Classical approximation and Gaussian process regression”. Algorithms & Computationally Intensive Inference Seminar, Department of Statistics, University of Warwick, UK.
• December 6, 2018. Poster “A Bayes–Sard cubature method”. The 32nd Conference on Neural Information Processing Systems, Montréal, Canada.
• May 29, 2018. Talk “Numerical integration as a statistical inference problem”. The 38th Finnish Summer School on Probability and Statistics, Lammi, Finland.
• April 27, 2018. Talk “Stability of Kalman filters”. DELTA Spring Workshop 2018, Tampere, Finland.
• April 17, 2018. Talk “Fully symmetric sets for efficient large-scale probabilistic integration”. SIAM Conference on Uncertainty Quantification 2018 (MS32: Probabilistic Numerical Methods for Quantification of Discretisation Error), Garden Grove, California, USA.
• April 12, 2018. Talk “A Bayes–Sard cubature method”. SAMSI-Lloyds-Turing Workshop on Probabilistic Numerical Methods, The Alan Turing Institute, London, UK.
• March 9, 2018. Talk. “On stability of a class of Kalman–Bucy filters for systems with non-linear dynamics”. SFB 1294 Seminar, Institute for Mathematics, University of Potsdam, Germany.
• March 5, 2018. Poster. “Classical quadrature rules via Gaussian processes”. Spring School “Structural Inference” 2018, Lübbenau, Germany.
• December 14, 2017. Talk “Concentration inequalities for the extended Kalman–Bucy filter”. The 23rd Inverse Days, Oulu, Finland.
• August 31, 2017. Poster “Backward simulation smoothing for Gaussian process state-space models”. Sequential Monte Carlo Workshop 2017, Uppsala University, Sweden.
• July 4, 2017. Talk “Some parallels between classical and kernel quadrature”. Max Planck Institute for Intelligent Systems, Tübingen, Germany.
• April 27, 2017. E-poster “Where is physiological noise lurking in k-space?”. ISMRM 25th Annual Meeting & Exhibition, Honolulu, Hawaii, USA.
• March 7, 2017. Poster “Large-scale probabilistic integration”. Spring School “Structural Inference” 2017, Bad Malente, Germany.
• February 9, 2017. Talk “Second order Poincaré inequalities for non-linear Kalman filtering”. Department of Cybernetics, University of West Bohemia, Plzeň, Czech Republic.
• December 16, 2016. Talk “Increasing length-scale in probabilistic numerics”. FOMICS Winter School on Uncertainty Quantification, University of Lugano, Switzerland.
• December 13, 2016. Talk “Non-linear state estimation with Kalman filters”. The 22nd Inverse Days, Kuopio, Finland.
• September 16, 2016. Poster “Approximate state-space Gaussian processes via spectral transformation”. The 26th IEEE International Workshop on Machine Learning for Signal Processing, Salerno, Italy.
• July 8, 2016. Talk “Fourier–Hermite series for stochastic stability analysis of non-linear Kalman filters”. The 19th International Conference on Information Fusion, Heidelberg, Germany.
• April 25, 2016. Talk on covariance function length-scale parameter in Bayesian quadrature. Probabilistic Numerics PhD Meeting, Max Planck Institute for Intelligent Systems, Tübingen, Germany.
• February 12, 2016. Talk “Stability of state estimators for nonlinear stochastic dynamic systems”. Statistics Day 2, Aalto University, Espoo, Finland.