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<title>Toni Karvonen — Publications</title>
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<h1>Toni Karvonen</h1>
<hr>
<p><b><a href="index.html">MAIN</a> — <u>PUBLICATIONS</u> — <a href="presentations.html">PRESENTATIONS</a> — <a href="cv.html">CV</a></b></p>
<p>See also my <a href="https://scholar.google.fi/citations?user=mXnYZN8AAAAJ" target="_blank">Google Scholar</a> profile.</p>
<div class="publications">
<h3>Preprints</h3>
<ol class="start">
<li>T. Karvonen & Y. Suzuki (2024). <strong>Approximation in Hilbert spaces of the Gaussian and related analytic kernels</strong>. arXiv:2209.12473.
<div class="links"><a href="https://arxiv.org/abs/2209.12473">arXiv</a></div></li>
<li>T. Karvonen, F. Cirak & M. Girolami (2024). <strong>Error analysis for a statistical finite element method</strong>. arXiv:2201.07543.
<div class="links"><a href="https://arxiv.org/abs/2201.07543">arXiv</a></div></li>
<li>Y. Suzuki, N. Hyvönen & T. Karvonen (2024). <strong>Möbius-transformed trapezoidal rule</strong>. arXiv:2407.13650.
<div class="links"><a href="https://arxiv.org/abs/2407.13650">arXiv</a></div></li>
<li>T. Karvonen & A. Zhigljavsky (2024). <strong>Maximum mean discrepancies of Farey sequences</strong>. arXiv:2407.10214.
<div class="links"><a href="https://arxiv.org/abs/2407.10214">arXiv</a></div></li>
<li>Y. Suzuki & T. Karvonen (2024). <strong>Construction of optimal algorithms for function approximation in Gaussian Sobolev spaces</strong>. arXiv:2402.02917.
<div class="links"><a href="https://arxiv.org/abs/2402.02917">arXiv</a></div></li>
<li>M. Korte-Stapff, T. Karvonen & E. Moulines (2024). <strong>Smoothness estimation for Whittle-Matérn processes on closed Riemannian manifolds</strong>. arXiv:2401.00510.
<div class="links"><a href="https://arxiv.org/abs/2401.00510">arXiv</a></div></li>
<li>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). <strong>ProbNum: Probabilistic numerics in Python</strong>. arXiv:2112.02100.
<div class="links"><a href="https://arxiv.org/abs/2112.02100">arXiv</a>|<a href="https://probnum.readthedocs.io/">ProbNum</a></div></li>
<li>T. Karvonen (2021). <strong>Estimation of the scale parameter for a misspecified Gaussian process model</strong>. arXiv:2110.02810.
<div class="links"><a href="https://arxiv.org/abs/2110.02810">arXiv</a></div></li>
<li>T. Karvonen (2021). <strong>On non-inclusion of certain functions in reproducing kernel Hilbert spaces</strong>. arXiv:2102.10628.
<div class="links"><a href="https://arxiv.org/abs/2102.10628">arXiv</a></div></li>
</ol>
<h3>Journal articles</h3>
<ol class="continue">
<li>C. J. Oates, T. Karvonen, A. L. Teckentrup, M. Strocchi & S. A. Niederer (2024+). <strong>Probabilistic Richardson extrapolation</strong>. <i>Journal of the Royal Statistical Society, Series B (Statistical Methodology)</i>. To appear.
<div class="links"><a href="https://arxiv.org/abs/2401.07562">arXiv</a></div></li>
<li>M. Naslidnyk, M. Kanagawa, T. Karvonen & M. Mahsereci (2024+). <strong>Comparing scale parameter estimators for Gaussian process interpolation with the Brownian motion prior: Leave-one-out cross validation and maximum likelihood</strong>. <i>SIAM/ASA Journal on Uncertainty Quantification</i>. To appear.
<div class="links"><a href="https://arxiv.org/abs/2307.07466">arXiv</a></div></li>
<li>F. Tronarp & T. Karvonen (2024). <strong>Orthonormal expansions for translation-invariant kernels</strong>. <i>Journal of Approximation Theory</i>, 302:106055.
<div class="links"><a href="https://doi.org/10.1016/j.jat.2024.106055">DOI</a>|<a href="pdf/JAT-2024.pdf">PDF</a>|<a href="pdf/JAT-2024_errors.pdf">errors</a></div></li>
<li>T. Karvonen (2023). <strong>Asymptotic bounds for smoothness parameter estimates in Gaussian process interpolation</strong>. <i>SIAM/ASA Journal on Uncertainty Quantification</i>, 11(4):1225–1257.
<div class="links"><a href="https://doi.org/10.1137/22M149288X">DOI</a>|<a href="pdf/JUQ-Smoothness-2023.pdf">PDF</a></div></li>
<li>T. Karvonen, J. Cockayne, F. Tronarp & S. Särkkä (2023). <strong>A probabilistic Taylor expansion with Gaussian processes</strong>. <i>Transactions on Machine Learning Research</i>.
<div class="links"><a href="https://openreview.net/pdf?id=2TneniEIDB">TMLR</a>|<a href="pdf/TMLR-2023.pdf">PDF</a></div></li>
<li>T. Karvonen & C. J. Oates (2023). <strong>Maximum likelihood estimation in Gaussian process regression is ill-posed</strong>. <i>Journal of Machine Learning Research</i>, 24(120):1–47.
<div class="links"><a href="https://jmlr.org/papers/v24/22-1153.html">JMLR</a>|<a href="pdf/JMLR-2023.pdf">PDF</a>|<a href="pdf/JMLR-2023-addendum.pdf">addendum</a></div></li>
<li>T. Karvonen (2023). <strong>Small sample spaces for Gaussian processes</strong>. <i>Bernoulli</i>, 29(2):875–900.
<div class="links"><a href="http://doi.org/10.3150/22-BEJ1483">DOI</a>|<a href="pdf/Bernoulli-2023.pdf">PDF</a></div></li>
<li>T. Karvonen (2022). <strong>Error bounds and the asymptotic setting in kernel-based approximation</strong>. <i>Dolomites Research Notes on Approximation</i>, 15(3):65–77.
<div class="links"><a href="http://doi.org/10.14658/pupj-drna-2022-3-7">DOI</a>|<a href="pdf/DRNA-2022.pdf">PDF</a>|<a href="pdf/DRNA-2022-addendum.pdf">addendum</a></div></li>
<li>L. F. South, T. Karvonen, C. Nemeth, M. Girolami & C. J. Oates (2022). <strong>Semi-exact control functionals from Sard's method</strong>. <i>Biometrika</i>, 109(2):351–367.
<div class="links"><a href="https://doi.org/10.1093/biomet/asab036">DOI</a>|<a href="pdf/Biometrika2021.pdf">PDF</a>|<a href="https://github.com/LeahPrice/ZVCV">code on GitHub</a></div></li>
<li>G. Santin, T. Karvonen & B. Haasdonk (2022). <strong>Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces</strong>. <i>BIT Numerical Mathematics</i>, 62:279–310.
<div class="links"><a href="https://doi.org/10.1007/s10543-021-00870-3">DOI</a>|<a href="pdf/BIT2021.pdf">PDF</a></div></li>
<li>Z. Zhao, T. Karvonen, R. Hostettler & S. Särkkä (2021). <strong>Taylor moment expansion for continuous-discrete Gaussian filtering and smoothing</strong>. <i>IEEE Transactions on Automatic Control</i>, 66(9):4460–4467.
<div class="links"><a href="https://www.doi.org/10.1109/TAC.2020.3047367">DOI</a>|<a href="pdf/Zhao-TAC2021.pdf">PDF</a></div></li>
<li>T. Karvonen, C. J. Oates & M. Girolami (2021). <strong>Integration in reproducing kernel Hilbert spaces of Gaussian kernels</strong>. <i>Mathematics of Computation</i>, 90(331):2209–2233.
<div class="links"><a href="https://doi.org/10.1090/mcom/3659">DOI</a>|<a href="pdf/MoC-2021.pdf">PDF</a></div></li>
<li>T. Karvonen, S. Särkkä & K. Tanaka (2021). <strong>Kernel-based interpolation at approximate Fekete points</strong>. <i>Numerical Algorithms</i>, 87(1):445–468.
<div class="links"><a href="https://doi.org/10.1007/s11075-020-00973-y">DOI</a>|<a href="pdf/Fekete-2021.pdf">PDF</a></div></li>
<li>J. Prüher, T. Karvonen, C. J. Oates, O. Straka & S. Särkkä (2021). <strong>Improved calibration of numerical integration error in sigma-point filters</strong>. <i>IEEE Transactions on Automatic Control</i>, 66(3):1286–1292.
<div class="links"><a href="https://doi.org/10.1109/TAC.2020.2991698">DOI</a>|<a href="pdf/TAC-2021.pdf">PDF</a></div></li>
<li>T. Karvonen & S. Särkkä (2020). <strong>Worst-case optimal approximation with increasingly flat Gaussian kernels</strong>. <i>Advances in Computational Mathematics</i>, 46:21.
<div class="links"><a href="https://doi.org/10.1007/s10444-020-09767-1">DOI</a>|<a href="pdf/Flat-Limit-ACOM-2020.pdf">PDF</a></div></li>
<li>T. Karvonen, S. Bonnabel, E. Moulines & S. Särkkä (2020). <strong>On stability of a class of filters for non-linear stochastic systems</strong>. <i>SIAM Journal on Control and Optimization</i>, 58(4):2023–2049.
<div class="links"><a href="https://doi.org/10.1137/19M1285974">DOI</a>|<a href="pdf/SICON2020.pdf">PDF</a>|<a href="pdf/SICON2020-errata.pdf">errata</a></div></li>
<li>T. Karvonen, G. Wynne, F. Tronarp, C. J. Oates & S. Särkkä (2020). <strong>Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions</strong>. <i>SIAM/ASA Journal on Uncertainty Quantification</i>, 8(3):926–958.
<div class="links"><a href="https://doi.org/10.1137/20M1315968">DOI</a>|<a href="pdf/JUQ-2020.pdf">PDF</a>|<a href="pdf/JUQ-2020-errata.pdf">errata</a></div></li>
<li>T. Karvonen, M. Kanagawa & S. Särkkä (2019). <strong>On the positivity and magnitudes of Bayesian quadrature weights</strong>. <i>Statistics and Computing</i>, 29(6):1317–1333.
<div class="links"><a href="https://doi.org/10.1007/s11222-019-09901-0">DOI</a>|<a href="pdf/KarvonenKanagawa2019.pdf">PDF</a></div></li>
<li>T. Karvonen, S. Särkkä & C. J. Oates (2019). <strong>Symmetry exploits for Bayesian cubature methods</strong>. <i>Statistics and Computing</i>, 29(6):1231–1248.
<div class="links"><a href="https://doi.org/10.1007/s11222-019-09896-8">DOI</a>|<a href="pdf/Karvonen2019-SymmetryExploits.pdf">PDF</a>|<a href="https://github.com/tskarvone/bc-symmetry-exploits">code on GitHub</a></div></li>
<li>T. Karvonen & S. Särkkä (2019). <strong>Gaussian kernel quadrature at scaled Gauss–Hermite nodes</strong>. <i>BIT Numerical Mathematics</i>, 59(4):877–902.
<div class="links"><a href="http://doi.org/10.1007/s10543-019-00758-3">DOI</a>|<a href="pdf/BIT2019.pdf">PDF</a>|<a href="https://github.com/tskarvone/gauss-mercer">code on GitHub</a></div></li>
<li>F. Tronarp, T. Karvonen & S. Särkkä (2019). <strong>Student's <i>t</i>-filters for noise scale estimation</strong>. <i>IEEE Signal Processing Letters</i>, 26(2):352–356.
<div class="links"><a href="http://doi.org/10.1109/LSP.2018.2889440">DOI</a>|<a href="pdf/SPL2019.pdf">PDF</a></div></li>
<li>T. Karvonen & S. Särkkä (2018). <strong>Fully symmetric kernel quadrature</strong>. <i>SIAM Journal on Scientific Computing</i>, 40(2):A697–A720.
<div class="links"><a href="https://doi.org/10.1137/17M1121779">DOI</a>|<a href="pdf/KarvonenSarkka2018-fss.pdf">PDF</a>|<a href="https://github.com/tskarvone/fskq">code on GitHub</a></div></li>
</ol>
<h3>Conference articles</h3>
<ol class="continue">
<li>K. Li, D. Giles, T. Karvonen, S. Guillas & F.-X. Briol (2023). <strong>Multilevel Bayesian quadrature</strong>. In the <i>26th International Conference on Artificial Intelligence and Statistics, PMLR</i>, 206:1845–1868.
<div class="links"><a href="https://proceedings.mlr.press/v206/li23a.html">PMLR</a>|<a href="pdf/AISTATS2023.pdf">PDF</a>|<a href="https://github.com/CeciliaKaiyu/MLBQ">code on GitHub</a></div></li>
<li>O. Teymur, C. N. Foley, P. G. Green, T. Karvonen & C. J. Oates (2021). <strong>Black box probabilistic numerics</strong>. In <i>Advances in Neural Information Processing Systems 34</i>, pp. 23452–23464.
<div class="links"><a href="https://papers.nips.cc/paper/2021/hash/c4de8ced6214345614d33fb0b16a8acd-Abstract.html">NeurIPS</a>|<a href="pdf/NeurIPS2021.pdf">PDF</a></div></li>
<li>S. Särkkä, C. Merkatas & T. Karvonen (2021). <strong>Gaussian approximations of SDEs in Metropolis-adjusted Langevin algorithms</strong>. In the <i>31st IEEE International Workshop on Machine Learning for Signal Processing</i>.
<div class="links"><a href="https://doi.org/10.1109/MLSP52302.2021.9596301">DOI</a>|<a href="pdf/MLSP2021.pdf">PDF</a></div></li>
<li>T. Karvonen, F. Tronarp & S. Särkkä (2019). <strong>Asymptotics of maximum likelihood parameter estimation for Gaussian processes: the Ornstein–Uhlenbeck prior</strong>. In the <i>29th IEEE International Workshop on Machine Learning for Signal Processing</i>.
<div class="links"><a href="https://doi.org/10.1109/MLSP.2019.8918767">DOI</a>|<a href="pdf/MLSP2019.pdf">PDF</a></div></li>
<li>T. Karvonen, C. J. Oates & S. Särkkä (2018). <strong>A Bayes–Sard cubature method</strong>. In <i>Advances in Neural Information Processing Systems 31</i>, pp. 5882–5893.
<div class="links"><a href="http://papers.nips.cc/paper/7829-a-bayes-sard-cubature-method">NeurIPS</a>|<a href="pdf/NIPS2018-full.pdf">PDF</a></div></li>
<li>T. Karvonen, S. Bonnabel, E. Moulines & S. Särkkä (2018). <strong>Bounds on the covariance matrix of a class of Kalman–Bucy filters for systems with non-linear dynamics</strong>. In the <i>57th IEEE Conference on Decision and Control</i>, pp. 7176–7181.
<div class="links"><a href="https://doi.org/10.1109/CDC.2018.8619726">DOI</a>|<a href="pdf/CDC2018.pdf">PDF</a></div>
</li>
<li>F. Tronarp, T. Karvonen & S. Särkkä (2018). <strong>Mixture representation of the Matérn class with applications in state space approximations and Bayesian quadrature</strong>. In the <i>28th IEEE International Workshop on Machine Learning for Signal Processing</i>.
<div class="links"><a href="https://doi.org/10.1109/MLSP.2018.8516992">DOI</a>|<a href="pdf/TronarpKarvonenSarkka2018-MLSP.pdf">PDF</a></div></li>
<li>T. Karvonen & S. Särkkä (2017). <strong>Classical quadrature rules via Gaussian processes</strong>. In the <i>27th IEEE International Workshop on Machine Learning for Signal Processing</i>.
<div class="links"><a href="https://doi.org/10.1109/MLSP.2017.8168195">DOI</a>|<a href="pdf/KarvonenSarkka2017-MLSP.pdf">PDF</a></div></li>
<li>J. Prüher, F. Tronarp, T. Karvonen, S. Särkkä & O. Straka (2017). <strong>Student-<i>t</i> process quadratures for filtering of non-linear systems with heavy-tailed noise</strong>. In the <i>20th International Conference on Information Fusion</i>. <i><font color="#284d00">Tammy Blair Best Student Paper Award</i>, first runner-up</font>.
<div class="links"><a href="https://doi.org/10.23919/ICIF.2017.8009742">DOI</a>|<a href="pdf/PruherEtal2017-FUSION.pdf">PDF</a></div></li>
<li>T. Karvonen & S. Särkkä (2016). <strong>Approximate state-space Gaussian processes via spectral transformation</strong>. In the <i>26th IEEE International Workshop on Machine Learning for Signal Processing</i>.
<div class="links"><a href="http://dx.doi.org/10.1109/MLSP.2016.7738812">DOI</a>|<a href="pdf/KarvonenSarkka2016-MLSP.pdf">PDF</a>|<a href="pdf/KarvonenSarkka2016-MLSP_errors.pdf">errors</a></div></li>
<li>T. Karvonen & S. Särkkä (2016). <strong>Fourier–Hermite series for stochastic stability analysis of non-linear Kalman filters</strong>. In the <i>19th International Conference on Information Fusion</i>, pp. 1829–1836.
<div class="links"><a href="http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7528105">IEEE Xplore</a>|<a href="pdf/KarvonenSarkka2016-FUSION.pdf">PDF</a>|<a href="code/2016-fusion-code.zip">code</a></div></li>
</ol>
<h3>Theses</h3>
<ol class="continue">
<li>T. Karvonen (2019). <i><strong>Kernel-Based and Bayesian Methods for Numerical Integration</strong></i>. Doctoral dissertation. Department of Electrical Engineering and Automation, Aalto University.
<div class="links"><a href="http://urn.fi/URN:ISBN:978-952-60-8704-7">Aaltodoc</a>|<a href="pdf/PhD-thesis.pdf">PDF</a></div></li>
<li>T. Karvonen (2014). <i><strong>Stability of Linear and Non-Linear Kalman Filters</strong></i>. Master's thesis. Department of Mathematics and Statistics, University of Helsinki.
<div class="links"><a href="http://hdl.handle.net/10138/144334">E-thesis</a>|<a href="pdf/Karvonen2014-masters_thesis.pdf">PDF</a>|<a href="pdf/Karvonen2014-masters_thesis_errors.pdf">errors</a></div></li>
<li>T. Karvonen (2014). <i><strong>Mittojen disintegraatio</strong></i>. Bachelors's thesis. Department of Mathematics and Statistics, University of Helsinki.
</li>
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