About Me
Since 2018, Johannes Schmidt-Hieber is professor of statistics at the University of Twente. Click here here to access the personal webpage.
Expertise
Mathematics
# Activation Function
# Contraction
# Gaussian Process
# Neural Networks
# Nonparametric Regression
# Recovery
Business & Economics
# Bayesian Analysis
# Nonparametric Regression
Organisations
Research
Articles
- Bayesian variance estimation in the Gaussian sequence model with partial information on the means preprint
With Gianluca Finocchio. - Posterior consistency for n in the binomial (n,p) problem with both parameters unknown - with applications to quantitative nanoscopy. preprint
With Laura Schneider, Thomas Staudt, Andrea Krajina, Timo Aspelmeier and Axel Munk. - Posterior contraction rates for support boundary recovery preprint
With Markus Reiss. - Nonparametric regression using deep neural networks with ReLU activation function preprint
To appear as a discussion article in the Annals of Statistics - Tests for qualitative features in the random coefficients model preprint
With Fabian Dunker, Konstantin Eckle, and Katharina Proksch.
To appear in Electronic Journal of Statistics - Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery preprint
With Markus Reiss.
To appear in Annals of Statistics - Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities preprint
With Kolyan Ray.
To appear in Annales de l'Institut Henri Poincaré B. - A comparison of deep networks with ReLU activation function and linear spline-type methods pdf
Neural Networks, Volume 110, 232-242, 2019.
With Konstantin Eckle. - The Le Cam distance between density estimation, Poisson processes and Gaussian white noise article preprint
Mathematical Statistics and Learning. Volume 1, Issue 2, 101-170, 2018. With Kolyan Ray. - A regularity class for the roots of non-negative functions. pdf arXiv
Annali di Matematica Pura ed Applicata. Volume 196, Number 6, 2091-2103, 2017. With Kolyan Ray. - Minimax theory for a class of non-linear statistical inverse problems. article revised preprint
Inverse Problems. Volume 32, Number 6, 065003, 2016. With Kolyan Ray. - Conditions for posterior contraction in the sparse normal means problem. pdf
Electronic Journal of Statistics. Volume 10, Number 1, 976-1000, 2016. With Stéphanie van der Pas and JB Salomond. - Bayesian linear regression with sparse priors. pdf arXiv
Annals of Statistics. Volume 43, Number 5, 1986-2018, 2015. With Ismael Castillo and Aad van der Vaart. - On adaptive posterior concentration rates. pdf
Annals of Statistics. Volume 43, Number 5, 2259-2295, 2015. With Marc Hoffmann and Judith Rousseau. - Spot volatility estimation for high-frequency data: adaptive estimation in practice. pdf arXiv
Springer Lecture Notes in Statistics: Modeling and Stochastic Learning for Forecasting in High Dimension. 213-241, 2015. With Till Sabel and Axel Munk. - Asymptotic equivalence for regression under fractional noise. pdf arXiv
Annals of Statistics, Volume 42, Number 6, 2557-2585, 2014. - Asymptotically efficient estimation of a scale parameter in Gaussian time series and closed-form expressions for the Fisher information. pdf arXiv supplement
Bernoulli, Volume 20, Number 2, 747-774, 2014. With Till Sabel. - On an estimator achieving the adaptive rate in nonparametric regression under Lp-loss for all 1≤p≤∞. preprint
This is an update of the working paper pdf. In the first version, we only consider simultaneous adaptation with respect to L2- and L∞-loss. This article might be easier to read and includes a small numerical study. - Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features.pdfsupplement
Annals of Statistics, Volume 41, Number 3, 1299-1328, 2013. With Axel Munk and Lutz Dümbgen.
A first draft of this paper appeared under the title: "Multiscale methods for shape constraints in deconvolution" in 2011.pdf. It contains essentially the same results, but under a very strong assumption on the decay of the Fourier transform of the error density. The first version is much easier to read and does not require the theory of pseudo-differential operators. - Adaptive wavelet estimation of the diffusion coefficient under additive error measurements. pdf software
Annales de l'Institut Henri Poincaré, 48, 1186-1216. With Marc Hoffmann and Axel Munk.
An earlier version of this paper was published as a working paper under the title "Nonparametric estimation of the volatility under microstructure noise: wavelet adaptation." pdf. - Nonparametric methods in spot volatility estimation. pdf
Dissertation. Universität Göttingen und Universtät Bern, 2010. - Lower bounds for volatility estimation in microstructure noise models. pdf
Borrowing Strength: Theory Powering Applications - A Festschrift for Lawrence D. Brown, IMS Collections, 6, 43-55, 2010. With Axel Munk. - Nonparametric estimation of the volatility function in a high-frequency model corrupted by noise. pdf
Electronic Journal of Statistics, 4, 781-821, 2010. With Axel Munk. - Sharp minimax estimation of the variance of Brownian motion corrupted with Gaussian noise. pdf (including supplementary material).
Statistica Sinica, 20, 1011-1024, 2010 . With T. Tony Cai and Axel Munk.
Publications
Recent
Derumigny, A.
, & Schmidt-Hieber, A. J. (2023).
On lower bounds for the bias-variance trade-off.
Annals of the Institute of Statistical Mathematics,
51(4), 1510 - 1533.
https://doi.org/10.1214/23-AOS2279
Imaizumi, M.
, & Schmidt-Hieber, A. J. (2023).
On Generalization Bounds for Deep Networks Based on Loss Surface Implicit Regularization.
IEEE transactions on information theory,
69(2), 1203- 1223.
https://doi.org/10.1109/TIT.2022.3215088
Finocchio, G.
, & Schmidt-Hieber, A. J. (2023).
Posterior Contraction for Deep Gaussian Process Priors.
Journal of machine learning research,
24(66), 1-49.
https://jmlr.org/papers/volume24/21-0556/21-0556.pdf
Bos, T.
, & Schmidt-Hieber, A. J. (2022).
Convergence rates of deep ReLU networks for multiclass classification.
Electronic Journal of Statistics,
16(1), 2724 - 2773.
https://doi.org/10.1214/22-EJS2011
Schmidt-Hieber, A. J., Schneider, L., Staudt, T., Krajina, A., Aspelmeier, T., & Munk, A. (2021).
Posterior analysis of n in the binomial (n,p) problem with both parameters unknown—with applications to quantitative nanoscopy.
Annals of statistics,
49(6), 3534-3558.
https://doi.org/10.1214/21-AOS2096
Finocchio, G. (2021).
Two perspectives on high-dimensional estimation problems: posterior contraction and median-of-means. [PhD Thesis - Research UT, graduation UT, University of Twente]. University of Twente.
https://doi.org/10.3990/1.9789036552356
Schmidt-Hieber, A. J. (2021).
The Kolmogorov–Arnold representation theorem revisited.
Neural networks,
137, 119-126.
https://doi.org/10.1016/j.neunet.2021.01.020
Langer, S. (2020).
Ein Beitrag zur Statistischen Theorie des Deep Learnings. [PhD Thesis - Research external, graduation external, Technische Universitat Darmstadt]. Verlag Dr. Hut.
Reiss, M.
, & Schmidt-Hieber, J. (2020).
Posterior contraction rates for support boundary recovery.
Stochastic processes and their applications,
130(11), 6638.
https://doi.org/10.1016/j.spa.2020.06.005
Schmidt-Hieber, A. J. (2020).
Nonparametric regression using deep neural networks with ReLU activation function.
Annals of statistics,
48(4), 1875-1897.
https://doi.org/10.1214/19-AOS1875
Schmidt-Hieber, A. J. (2020).
Rejoinder: “Nonparametric regression using deep neural networks with ReLU activation function”.
Annals of statistics,
48(4), 1916-1921.
https://doi.org/10.1214/19-AOS1931
Reiss, M.
, & Schmidt-Hieber, A. J. (2020).
Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery.
Annals of statistics,
48(3), 1432-1451.
https://doi.org/10.1214/19-AOS1853
Finocchio, G.
, & Schmidt-Hieber, J. (2020).
Bayesian variance estimation in the Gaussian sequence model with partial information on the means.
Electronic Journal of Statistics,
14(1), 239-271.
https://doi.org/10.1214/19-EJS1671
Eckle, K.
, & Schmidt-Hieber, A. J. (2019).
A comparison of deep networks with ReLU activation function and linear spline-type methods.
Neural networks,
110, 232-242.
https://doi.org/10.1016/j.neunet.2018.11.005
Dunker, F., Eckle, K.
, Proksch, K.
, & Schmidt-Hieber, A. J. (2019).
Tests for qualitative features in the random coefficients model.
Electronic Journal of Statistics,
13(2), 2257-2306.
https://doi.org/10.1214/19-EJS1570
UT Research Information System
Courses Academic Year 2023/2024
Courses in the current academic year are added at the moment they are finalised in the Osiris system. Therefore it is possible that the list is not yet complete for the whole academic year.
Courses Academic Year 2022/2023
Contact Details
Visiting Address
University of Twente
Faculty of Electrical Engineering, Mathematics and Computer Science
Zilverling
(building no. 11), room 2057
Hallenweg 19
7522NH Enschede
The Netherlands
Mailing Address
University of Twente
Faculty of Electrical Engineering, Mathematics and Computer Science
Zilverling
2057
P.O. Box 217
7500 AE Enschede
The Netherlands