Johannes Schmidt-Hieber

Articles

Generalization bounds for transformer-based next-token prediction in a language model preprint
With Insung Kong and Niklas Dexheimer.
Hyper input convex neural networks for shape constrained learning and optimal transport preprint
With Shayan Hundrieser and Insung Kong.
Central limit theorems for the outputs of fully convolutional neural networks with time series input preprint
With Annika Betken and Giorgio Micali
Semi-supervised learning on graphs using graph neural networks preprint
With Juntong Chen, Claire Donnat, and Olga Klopp
On the universal representation property of spiking neural networks preprint
With Shayan Hundrieser, Philipp Tuchel, and Insung Kong.
Training diagonal linear networks with stochastic sharpness-aware minimization preprint
With Gabriel Clara and Sophie Langer
Interpreting learning in biological neural networks as zero-order optimization method preprint
Hebbian learning inspired estimation of the linear regression parameters from queries preprint
With Wouter Koolen
Improving the convergence rates of forward gradient descent with repeated sampling preprint
With Niklas Dexheimer
To appear in Information and Inference
On frequentist coverage of Bayesian credible sets for estimation of the mean under constraints preprint
With Kevin Duisters
To appear as book chapter within Springer IISA series on Statistics and Data Science.
On the expressivity of deep Heaviside networks article preprint
With Insung Kong, Juntong Chen, and Sophie Langer.
Constructive Approximation, 2026.
Asymptotics of stochastic gradient descent with dropout regularization in linear models article bibtex
With Jiaqi Li and Wei Biao Wu
Journal of Machine Learning Research (JMLR), Volume 27 (83), 1-78, 2026.
A novel statistical approach to analyze image classification pdf preprint bibtex
With Juntong Chen and Sophie Langer
Annals of Statistics, Volume 54, Number 3, 1566-1593, 2026.
(also selected as poster at ICML 2026)
Statistical guarantees for high-dimensional stochastic gradient descent article bibtex
With Jiaqi Li, Zhipeng Lou and Wei Biao Wu
Advances in Neural Information Processing Systems 38 (NeurIPS 2025), 94854-94890.
Spike-timing-dependent Hebbian learning as noisy gradient descent article source code bibtex
With Niklas Dexheimer and Sascha Gaudlitz.
Advances in Neural Information Processing Systems 38 (NeurIPS 2025), 106580-106620.
On the VC dimension of deep group convolutional neural networks article bibtex
With Anna Sepliarskaia and Sophie Langer
Advances in Neural Information Processing Systems 38 (NeurIPS 2025), 119377-119405.
Ordinal patterns based change point detection article
With Annika Betken and Giorgio Micali
Test, 2025.
Understanding the effect of GCN convolutions in regression tasks article preprint code
With Juntong Chen, Claire Donnat, and Olga Klopp
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:4573-4581, 2025.
A supervised deep learning method for nonparametric density estimation paper bibtex
With Thijs Bos
Electronic Journal of Statistics, Volume 18 (2), 5601-5658, 2024.
Dropout regularization versus ℓ2-penalization in the linear model article bibtex
With Gabriel Clara and Sophie Langer
Journal of Machine Learning Research (JMLR), Volume 25 (204), 1-48, 2024.
Lower bounds for the trade-off between bias and mean absolute deviation preprint article
With Alexis Derumigny
Statistics and Probability Letters, Volume 213, 110182, 2024.
Codivergences and information matrices article
With Alexis Derumigny
Information Geometry, Volume 7, 253–282, 2024.
Local convergence rates of the least squares estimator with applications to transfer learning preprint article bibtex
With Petr Zamolodtchikov
Bernoulli, Volume 30, Number 3, 1845-1877, 2024.
Convergence guarantees for forward gradient descent in the linear regression model preprint article
With Thijs Bos
Journal of Statistical Planning and Inference, Volume 233, 106174, 2024.
On lower bounds for the bias-variance trade-off preprint article
With Alexis Derumigny
Annals of Statistics, Volume 51, Number 4, 1510-1533, 2023.
Posterior contraction for deep Gaussian process priors preprint article bibtex
With Gianluca Finocchio
Journal of Machine Learning Research, Volume 24, Number 66, 1-49, 2023.
On generalization bounds for deep networks based on loss surface implicit regularization preprint article
With Masaaki Imaizumi
IEEE Transactions on Information Theory, Volume 69, Issue 2, 1203 - 1223, 2023.
On the inability of Gaussian process regression to optimally learn compositional functions preprint article bibtex
With Matteo Giordano and Kolyan Ray
36th Conference on Neural Information Processing Systems (NeurIPS 2022), Volume 35, 22341-22353, 2022.
Convergence rates of deep ReLU networks for multiclass classification article
With Thijs Bos
Electronic Journal of Statistics, Volume 16, Number 1, 2724-2773, 2022.
Posterior consistency for n in the binomial (n,p) problem with both parameters unknown - with applications to quantitative nanoscopy. article preprint
With Laura Schneider, Thomas Staudt, Andrea Krajina, Timo Aspelmeier and Axel Munk.
Annals of Statistics, Volume 49, Number 6, 3534-3558, 2021.
The Kolmogorov-Arnold representation theorem revisited article
Neural Networks, Volume 137, 119-126, 2021.
Posterior contraction rates for support boundary recovery preprint article
Stochastic Processes and their Applications, Volume 130, Issue 11, 6638-6656, 2020. With Markus Reiss.
Nonparametric regression using deep neural networks with ReLU activation function article pdf preprint corrections
Annals of Statistics, Volume 48, Number 4, 1875-1897, 2020.
This article has been discussed by
- Behrooz Ghorbani, Song Mei, Theodor Misiakiewicz, and Andrea Montanari
- Gitta Kutyniok
- Michael Kohler and Sophie Langer
- Ohad Shamir
Rejoinder: "Nonparametric regression using deep neural networks with ReLU activation function" article pdf
Annals of Statistics, Volume 48, Number 4, 1916-1921, 2020.
Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery article pdf preprint
Annals of Statistics, Volume 48, Number 3, 1432-1451, 2020. With Markus Reiss.
Bayesian variance estimation in the Gaussian sequence model with partial information on the means. article
Electronic Journal of Statistics, Volume 14, Number 1, 239-271, 2020. With Gianluca Finocchio.
Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities preprint article
Annales de l'Institut Henri Poincaré B, Volume 55, Number 4, 2195-2208, 2019. With Kolyan Ray.
Tests for qualitative features in the random coefficients model pdf
Electronic Journal of Statistics, Volume 3, 2257-2306, 2019. With Fabian Dunker, Konstantin Eckle, and Katharina Proksch.
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 $L^{p}$ -loss for all $1 \leq p \leq \infty$ . preprint
This is an update of the working paper pdf. In the first version, we only consider simultaneous adaptation with respect to $L^{2}$ - and $L^{\infty}$ -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. pdf supplement
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. article
Annales de l'Institut Henri Poincaré, 48, 1186-1216. With Marc Hoffmann and Axel Munk.
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.

Reports

Book review "K. Spiliopoulos, R.B. Sowers, J. Sirignano: “Mathematical Foundations of Deep Learning Models and Algorithms”" pdf
Jahresbericht der Deutschen Mathematiker-Vereinigung, 2026.
Poorbita Kundu’s and Johannes Schmidt-Hieber’s contribution to the Discussion of 'Statistical exploration of the Manifold Hypothesis' by Whiteley et al pdf
Journal of the Royal Statistical Society, Series B, 2026. With Poorbita Kundu.
Challenges and opportunities for statistics in the era of data science article
(The text was written by a consortium of statisticians.)
Harvard Data Science Review, 7(2), 2025.
Towards a statistical foundation for machine learning methods pdf
Proceedings of the International Congress of Basic Science 2025.
Johannes Schmidt-Hieber’s contribution to the Discussion of ”Automatic change-point detection in time series via deep learning” by Jie Li, Paul Fearnhead, Piotr Fryzlewicz, and Tengyao Wang.
Journal of the Royal Statistical Society, Series B, Volume 86, Issue 2, Page 329, 2024.
Statistical theory for deep neural networks with ReLU activation function. pdf
Oberwolfach Reports, 2018.
Nonparametric Bayes for an irregular model. pdf
Oberwolfach Reports, 2017.
Asymptotic equivalence for regression under dependent noise. pdf
Oberwolfach Reports, 2015.
Reconstruction of risk measures from financial data. pdf
Nieuw Archief voor Wiskunde, 2014.
Simultaneously adaptive estimation for $L^{2}$ - and $L^{\infty}$ -loss. pdf
Oberwolfach Reports,2014.
Detection of qualitative features in statistical inverse problems. pdf
Oberwolfach Reports, 2012.
Obtaining qualitative statements in deconvolution models. pdf
Oberwolfach Reports, 2012.
The Estimation of different scales in microstructure noise models from a nonparametric regression perspective. pdf
Oberwolfach Reports, 2009. With Axel Munk.

Johannes Schmidt-Hieber

Reports

Invited Talks (2009-2026)