Fourier-Hermite series for stochastic stability analysis of non-linear Kalman filters. - Toni Karvonen; Simo Särkkä (FUSION, 2016)

Approximate state-space Gaussian processes via spectral transformation. - Toni Karvonen; Simo Särkkä (MLSP, 2016)

Student-t process quadratures for filtering of non-linear systems with heavy-tailed noise. - Jakub Prüher; Filip Tronarp; Toni Karvonen; Simo Särkkä; Ondrej Straka (FUSION, 2017)

Classical quadrature rules via Gaussian processes. - Toni Karvonen; Simo Särkkä (MLSP, 2017)

Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics. - Toni Karvonen; Silvère Bonnabel; Eric Moulines; Simo Särkkä (CDC, 2018)

Mixture Representation of the MatéRn class with Applications in State Space Approximations and Bayesian quadrature. - Filip Tronarp; Toni Karvonen; Simo Särkkä (MLSP, 2018)

A Bayes-Sard Cubature Method. - Toni Karvonen; Chris J. Oates; Simo Särkkä (NeurIPS, 2018)

Fully Symmetric Kernel Quadrature. - Toni Karvonen; Simo Särkkä (SIAM J. Sci. Comput., 2018)

Asymptotics of Maximum Likelihood Parameter Estimates For Gaussian Processes: The Ornstein-Uhlenbeck Prior. - Toni Karvonen; Filip Tronarp; Simo Särkkä (MLSP, 2019)

On the positivity and magnitudes of Bayesian quadrature weights. - Toni Karvonen; Motonobu Kanagawa; Simo Särkkä (Stat. Comput., 2019)

Symmetry exploits for Bayesian cubature methods. - Toni Karvonen; Simo Särkkä; Chris J. Oates (Stat. Comput., 2019)

Student's $t$-Filters for Noise Scale Estimation. - Filip Tronarp; Toni Karvonen; Simo Särkkä (IEEE Signal Process. Lett., 2019)

Worst-case optimal approximation with increasingly flat Gaussian kernels. - Toni Karvonen; Simo Särkkä (Adv. Comput. Math., 2020)

Sampling based approximation of linear functionals in Reproducing Kernel Hilbert Spaces. - Gabriele Santin; Toni Karvonen; Bernard Haasdonk (CoRR, 2020)

Maximum Likelihood Estimation and Uncertainty Quantification for Gaussian Process Approximation of Deterministic Functions. - Toni Karvonen; George Wynne; Filip Tronarp; Chris J. Oates; Simo Särkkä (SIAM/ASA J. Uncertain. Quantification, 2020)

On Stability of a Class of Filters for Nonlinear Stochastic Systems. - Toni Karvonen; Silvère Bonnabel; Eric Moulines; Simo Särkkä (SIAM J. Control. Optim., 2020)

Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms. - Simo Särkkä; Christos Merkatas; Toni Karvonen (MLSP, 2021)

Black Box Probabilistic Numerics. - Onur Teymur; Christopher N. Foley; Philip G. Breen; Toni Karvonen; Chris J. Oates (NeurIPS, 2021)

A Probabilistic Taylor Expansion with Applications in Filtering and Differential Equations. - Toni Karvonen; Jon Cockayne; Filip Tronarp; Simo Särkkä (CoRR, 2021)

ProbNum: Probabilistic Numerics in Python. - Jonathan Wenger; Nicholas Krämer; Marvin Pförtner; Jonathan Schmidt 001; Nathanael Bosch; Nina Effenberger; Johannes Zenn; Alexandra Gessner; Toni Karvonen; François-Xavier Briol; Maren Mahsereci; Philipp Hennig (CoRR, 2021)

Integration in reproducing kernel Hilbert spaces of Gaussian kernels. - Toni Karvonen; Chris J. Oates; Mark Girolami (Math. Comput., 2021)

Kernel-based interpolation at approximate Fekete points. - Toni Karvonen; Simo Särkkä; Ken'ichiro Tanaka (Numer. Algorithms, 2021)

Correction to: Kernel-based interpolation at approximate Fekete points. - Toni Karvonen; Simo Särkkä; Ken'ichiro Tanaka (Numer. Algorithms, 2021)

Improved Calibration of Numerical Integration Error in Sigma-Point Filters. - Jakub Prüher; Toni Karvonen; Chris J. Oates; Ondrej Straka; Simo Särkkä (IEEE Trans. Autom. Control., 2021)

Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering. - Zheng Zhao 004; Toni Karvonen; Roland Hostettler; Simo Särkkä (IEEE Trans. Autom. Control., 2021)

Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Regression. - Toni Karvonen (CoRR, 2022)

Approximation in Hilbert spaces of the Gaussian and other weighted power series kernels. - Toni Karvonen (CoRR, 2022)

Multilevel Bayesian Quadrature. - Kaiyu Li; Daniel Giles; Toni Karvonen; Serge Guillas; François-Xavier Briol (AISTATS, 2023)

Maximum likelihood estimation in Gaussian process regression is ill-posed. - Toni Karvonen; Chris J. Oates (J. Mach. Learn. Res., 2023)

A probabilistic Taylor expansion with Gaussian processes. - Toni Karvonen; Jon Cockayne; Filip Tronarp; Simo Särkkä (Trans. Mach. Learn. Res., 2023)

Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation. - Toni Karvonen (SIAM/ASA J. Uncertain. Quantification, 2023)

Probabilistic Richardson Extrapolation. - Chris J. Oates; Toni Karvonen; Aretha L. Teckentrup; Marina Strocchi; Steven A. Niederer (CoRR, 2024)

Construction of Optimal Algorithms for Function Approximation in Gaussian Sobolev Spaces. - Yuya Suzuki; Toni Karvonen (CoRR, 2024)

Möbius-Transformed Trapezoidal Rule. - Yuya Suzuki; Nuutti Hyvönen; Toni Karvonen (CoRR, 2024)

Orthonormal expansions for translation-invariant kernels. - Filip Tronarp; Toni Karvonen (J. Approx. Theory, 2024)

Comparing Scale Parameter Estimators for Gaussian Process Interpolation with the Brownian Motion Prior: Leave-One-Out Cross Validation and Maximum Likelihood. - Masha Naslidnyk; Motonobu Kanagawa; Toni Karvonen; Maren Mahsereci (SIAM/ASA J. Uncertain. Quantification, 2025)

Error analysis for a statistical finite element method. - Toni Karvonen; Fehmi Cirak; Mark Girolami (J. Multivar. Anal., 2025)

A Dictionary of Closed-Form Kernel Mean Embeddings. - François-Xavier Briol; Alexandra Gessner; Toni Karvonen; Maren Mahsereci (CoRR, 2025)

General superconvergence for kernel-based approximation. - Toni Karvonen; Gabriele Santin; Tizian Wenzel (CoRR, 2025)

Stationary MMD Points for Cubature. - Zonghao Chen; Toni Karvonen; Heishiro Kanagawa; François-Xavier Briol; Chris J. Oates (CoRR, 2025)