Working papers

• T. Stillfjord and F. Tronarp (2023). Computing the matrix exponential and the Cholesky factor of a related finite horizon Gramian. [arXiv]

• N. P. Subramaniyam, F. Tronarp, S. Särkkä, and L. Parkkonen (2020). Joint estimation of neural sources and their functional connections from MEG data. [bioRxiv]

Journal papers

• N. Bosch, A. Corenflos, F. Yaghoobi, F. Tronarp, P. Hennig and S. Särkkä (2024). Parallel-in-Time Probabililstic Numerical ODE Solvers . Journal of Machine Learning Research. [arXiv] [DOI]

• F. Tronarp and T. Karvonen (2024). Orthonormal expansions for translation-invariant kernels. Journal of Approximation Theory. [arXiv] [DOI]

• T. Karvonen, J. Cockayne, F. Tronarp and S. Särkkä (2023). A probabilistic Taylor expansion with applications in filtering and differential equations. Transactions on Machine Learning Research (TMLR). [arXiv] [DOI]

• F. Tronarp, S. Särkkä, P. Hennig (2021). Bayesian ODE Solvers: The Maximum A Posteriori Estimate. Statistics and Computing. [arXiV] [DOI]

• R. Gao, F. Tronarp, and S. Särkkä (2020). Variable Splitting Methods for Constrained State Estimation in Partially Observed Markov Processes. IEEE, Signal Processing Letters. [arXiV] [DOI]

• T. Karvonen, G. Wynne, Filip 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. [arXiV] [DOI]

• Roland Hostettler, F. Tronarp, Á. F. García-Fernández, and S. Särkkä (2020). Importance Densities for Particle Filtering Using Iterated Conditional Expectations. IEEE Signal Processing Letters. [DOI]

• F. Tronarp, H. Kersting, S. Särkkä, and P. Henning (2019). Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective. Springer, Statistics and Computing. [arXiV] [DOI]

• F. Tronarp and S. Särkkä (2019). Iterative Statistical Linear Regression for Gaussian Smoothing in Continuous-Time Non-linear Stochastic Dynamic Systems. Elsevier, Signal Processing 159.[arXiV] [DOI]

• R. Gao, F. Tronarp, S. Särkkä (2019). Iterated Extended Kalman Smoother-based Variable Splitting for $L_1$-Regularized State Estimation. IEEE, Transactions on Signal Processing. [arXiV] [DOI]

• Á. F. García-Fernández, F. Tronarp, and S. Särkkä (2019). Gaussian Target Tracking With Direction-of-Arrival von Mises–Fisher Measurements. IEEE, Transactions on Signal Processing 67 (11). [DOI]

• Á. F. García-Fernández, F. Tronarp, and S. Särkkä (2019). Gaussian Process Classification Using Posterior Linearization. IEEE, Signal Processing Letters 26 (5). [arXiV] [DOI]

• F. Tronarp, T. Karvonen, and S. Särkkä (2019). Student’s -Filters for Noise Scale Estimation. IEEE, Signal Processing Letters 26 (2) 2019. [DOI]

• F. Tronarp, Á. F. García-Fernández, and S. Särkkä (2018). Iterative Filtering and Smoothing In Non-Linear and Non-Gaussian Systems Using Conditional Moments. IEEE, Signal Processing Letters 25 (3). [DOI]

Conference papers

• F. Tronarp (2024). Numerically robust square root implementations of statistical linear regression filters and smoothers. To appear in 32nd European Signal Processing Conference (EUSIPCO 2024). [arXiv]

• A. Lahr, F. Tronarp, N. Bosch, J. Schmidt, P. Hennig, M. N. Zeilinger (2023). Probabilistic ODE Solvers for Integration Error-Aware Model Predictive Control. The 6th Annual Learning for Dynamics & Control Conference (L4DC), 2024. [arXiv] [DOI]

• N. Bosch, P. Hennig, and F. Tronarp (2023). Probabilistic Exponential Integrators. Advances in Neural Information Processing Systems, 2023. [arXiv] [DOI]

• J. Schmidt,P. Hennig, J. Nick, F. Tronarp (2023). The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering In High Dimensions. Advances in Neural Information Processing Systems, 2023. [arXiv] [DOI]

• F. Tronarp, N. Bosch, and Philipp Hennig (2022). Fenrir: Physics-Enhanced Regression for Initial Value Problems. The Thirty-ninth International Conference on Machine Learning. [arXiV] [DOI]

• F. Tronarp and S. Särkkä (2022). Continuous-discrete filtering and smoothing on submanifolds of Euclidean space. 25th International Conference on Information Fusion (FUSION). [arXiV] [DOI]

• N. Bosch, F. Tronarp, and P. Hennig (2022). Pick-and-Mix Information Operators for Probabilistic ODE Solvers. The 25th International Conference on Artificial Intelligence and Statistics. [arXiV] [DOI]

• N. Bosch, P. Hennig, and F. Tronarp (2021). Calibrated Adaptive Probabilistic ODE Solvers. The 24th International Conference on Artificial Intelligence and Statistics. [arXiV] [DOI]

• Z. Zhao, F. Tronarp, R. Hostettler, and S. Särkkä (2020). State-Space Gaussian Process for Drift Estimation in Stochastic Differential Equations. In proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP). [DOI]

• F. Tronarp and S. Särkkä (2019). Updates in Bayesian Filtering by Continuous Projections on a Manifold of Densities. In proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP). [DOI]

• T. Karvonen, F. Tronarp, and S. Särkkä (2019). Asymptotics of maximum likelihood parameter estimates for Gaussian processes: the Ornstein-Uhlenbeck prior. In proceedings of Machine learning in Signal Processing (MLSP). [DOI]

• R. Gao, F. Tronarp, and S. Särkkä (2019). Regularized State estimation and Parameter learning via augmented Lagrangian Kalman smoother method. In proceedings of Machine learning in Signal Processing (MLSP). [DOI]

• R. Hostettler, F. Tronarp, and S. Särkkä (2019). Joint Calibration of Inertial Sensors and Magnetometers Using Von Mises-Fisher Filtering and Expectation Maximization. In Proceedings of the 22th International Conference on Information Fusion (FUSION). [DOI]

• F. Tronarp, R. Hostettler, and S. Särkkä. Continuous-Discrete Von Mises-Fisher Filtering on $S^2$ for Reference Vector Tracking. In Proceedings of the 21th International Conference on Information Fusion (FUSION). [DOI]

• F. Tronarp and S. Särkkä (2018). Non-Linear Continuous-Discrete Smoothing by Basis Function Expansions of Brownian Motion. In Proceedings of the 21th International Conference on Information Fusion (FUSION). [DOI]

• F. Tronarp, T. Karvonen, and S. Särkkä (2018). Mixture Representation of The Matérn Class with Applications in State Space Approximations and Bayesian Quadrature. In proceedings of Machine learning in Signal Processing (MLSP). [DOI]

• F. Tronarp, N. P. Subramaniyam, S. Särkkä, and L. Parkkonen (2018). Tracking of dynamic functional connectivity from MEG data with Kalman filtering. In proceedings of 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). [DOI]

• R. Hostettler, F. Tronarp, and S. Särkkä (2018). Modeling the drift function in stochastic differential equations using reduced rank Gaussian processes. In 18th IFAC Symposium on System Identification (SYSID), Stockholm, Sweden. [DOI]

• R. Gao, F. Tronarp, and S. Särkkä (2018). Combined Analysis-$l_1$ and Total Variation ADMM with Applications to MEG Brain Imaging and Signal Reconstruction. In Proceedings of European Signal Processing Conference (EUSIPCO). [DOI]

• J. Prüher, F. Tronarp, T. Karvonen, O. Straka, and S. Särkkä (2017). Student-t Process Quadratures for Filtering of Non-linear Systems with Heavy-Tailed Noise. In Proceedings of the 20th International Conference on Information Fusion (FUSION). [arXiV] [DOI]

• N. P. Subramaniyam, F. Tronarp, S. Särkkä, and L. Parkkonen (2017). Expectation–maximization algorithm with a nonlinear Kalman smoother for MEG/EEG connectivity estimation. In Proceedings of the Joint Conference of European Medical and Biological Engineering Conference (EMBEC) and Nordic-Baltic Conference on Biomedical Engineering and Medical Physics (NBC). [DOI]

• T. Karvonen, A. Solin, Á. F. García-Fernández, F. Tronarp, S. Särkkä and F.-H. Lin. Where is physiological noise lurking in $k$-space?. Proceedings of ISMRM 2017, Annual Meeting & Exhibition.

• F. Tronarp, R. Hostettler, and S. Särkkä. Sigma-Point Filtering for Non-linear Systems with Non-Additive Heavy-Tailed Noise. In Proceedings of the 19th International Conference on Information Fusion (FUSION). [DOI]