Johannes Schmidt-Hieber

Central limit theorems for the outputs of fully convolutional neural networks with time series input

A. Betken, G. Micali, J. Schmidt-Hieber

Semi-supervised learning on graphs using graph neural networks

J. Chen, C. Donnat, O. Klopp, J. Schmidt-Hieber

On the universal representation property of spiking neural networks

S. Hundrieser, P. Tuchel, I. Kong, J. Schmidt-Hieber

Training diagonal linear networks with stochastic sharpness-aware minimization

G. Clara, S. Langer, J. Schmidt-Hieber

Hebbian learning inspired estimation of the linear regression parameters from queries

W. Koolen, J. Schmidt-Hieber

On frequentist coverage of Bayesian credible sets for estimation of the mean under constraints

K. Duisters, J. Schmidt-Hieber
To appear as book chapter, Springer IISA series on Statistics and Data Science

Hyper input convex neural networks for shape constrained learning and optimal transport

S. Hundrieser, I. Kong, J. Schmidt-Hieber
To appear in Advances in Neural Information Processing Systems 39 (NeurIPS 2026)

Improving the convergence rates of forward gradient descent with repeated sampling

N. Dexheimer, J. Schmidt-Hieber
Information and Inference: A Journal of the IMA, Volume 15, Issue 3, September 2026, iaag035

On the expressivity of deep Heaviside networks

I. Kong, J. Chen, S. Langer, J. Schmidt-Hieber
Constructive Approximation, 2026.

Asymptotics of stochastic gradient descent with dropout regularization in linear models

J. Li, W.B. Wu, J. Schmidt-Hieber
Journal of Machine Learning Research (JMLR), Volume 27 (83), 1-78, 2026.

A novel statistical approach to analyze image classification

J. Chen, S. Langer, J. Schmidt-Hieber
Annals of Statistics, Volume 54, Number 3, 1566-1593, 2026. (also selected as poster at ICML 2026)

pdf preprint bibtex

Statistical guarantees for high-dimensional stochastic gradient descent

J. Li, Z. Lou, W.B. Wu, J. Schmidt-Hieber
Advances in Neural Information Processing Systems 38 (NeurIPS 2025), 94854-94890.

Spike-timing-dependent Hebbian learning as noisy gradient descent

N. Dexheimer, S. Gaudlitz, J. Schmidt-Hieber
Advances in Neural Information Processing Systems 38 (NeurIPS 2025), 106580-106620.

article code bibtex

On the VC dimension of deep group convolutional neural networks

A. Sepliarskaia, S. Langer, J. Schmidt-Hieber
Advances in Neural Information Processing Systems 38 (NeurIPS 2025), 119377-119405.

Ordinal patterns based change point detection

A. Betken, G. Micali, J. Schmidt-Hieber
Test, 2025.

Understanding the effect of GCN convolutions in regression tasks

J. Chen, C. Donnat, O. Klopp, J. Schmidt-Hieber
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:4573-4581, 2025.

article preprint code

A supervised deep learning method for nonparametric density estimation

T. Bos, J. Schmidt-Hieber
Electronic Journal of Statistics, Volume 18 (2), 5601-5658, 2024.

paper bibtex

Dropout regularization versus ℓ2-penalization in the linear model

G. Clara, S. Langer, J. Schmidt-Hieber
Journal of Machine Learning Research (JMLR), Volume 25 (204), 1-48, 2024.

Lower bounds for the trade-off between bias and mean absolute deviation

A. Derumigny, J. Schmidt-Hieber
Statistics and Probability Letters, Volume 213, 110182, 2024.

Codivergences and information matrices

A. Derumigny, J. Schmidt-Hieber
Information Geometry, Volume 7, 253–282, 2024.

Local convergence rates of the least squares estimator with applications to transfer learning

P. Zamolodtchikov, J. Schmidt-Hieber
Bernoulli, Volume 30, Number 3, 1845-1877, 2024.

preprint article bibtex

Convergence guarantees for forward gradient descent in the linear regression model

T. Bos, J. Schmidt-Hieber
Journal of Statistical Planning and Inference, Volume 233, 106174, 2024.

On lower bounds for the bias-variance trade-off

A. Derumigny, J. Schmidt-Hieber
Annals of Statistics, Volume 51, Number 4, 1510-1533, 2023.

Posterior contraction for deep Gaussian process priors

G. Finocchio, J. Schmidt-Hieber
Journal of Machine Learning Research, Volume 24, Number 66, 1-49, 2023.

preprint article bibtex

On generalization bounds for deep networks based on loss surface implicit regularization

M. Imaizumi, J. Schmidt-Hieber
IEEE Transactions on Information Theory, Volume 69, Issue 2, 1203-1223, 2023.

On the inability of Gaussian process regression to optimally learn compositional functions

M. Giordano, K. Ray, J. Schmidt-Hieber
36th Conference on Neural Information Processing Systems (NeurIPS 2022), Volume 35, 22341-22353, 2022.

preprint article bibtex

Convergence rates of deep ReLU networks for multiclass classification

T. Bos, J. Schmidt-Hieber
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

L. Schneider, T. Staudt, A. Krajina, T. Aspelmeier, A. Munk, J. Schmidt-Hieber
Annals of Statistics, Volume 49, Number 6, 3534-3558, 2021.

The Kolmogorov-Arnold representation theorem revisited

J. Schmidt-Hieber
Neural Networks, Volume 137, 119-126, 2021.

Posterior contraction rates for support boundary recovery

M. Reiss, J. Schmidt-Hieber
Stochastic Processes and their Applications, Volume 130, Issue 11, 6638-6656, 2020.

article pdf preprint corrections

Nonparametric regression using deep neural networks with ReLU activation function

J. Schmidt-Hieber
Annals of Statistics, Volume 48, Number 4, 1875-1897, 2020.
Discussion article with contributions by Ghorbani, Mei, Misiakiewicz & Montanari; Kutyniok; Kohler & Langer; and Shamir.

Discussion 1 Discussion 2 Discussion 3 Discussion 4 Rejoinder

Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery

M. Reiss, J. Schmidt-Hieber
Annals of Statistics, Volume 48, Number 3, 1432-1451, 2020.

article pdf preprint

Bayesian variance estimation in the Gaussian sequence model with partial information on the means

G. Finocchio, J. Schmidt-Hieber
Electronic Journal of Statistics, Volume 14, Number 1, 239-271, 2020.

Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities

K. Ray, J. Schmidt-Hieber
Annales de l'Institut Henri Poincaré B, Volume 55, Number 4, 2195-2208, 2019.

Tests for qualitative features in the random coefficients model

F. Dunker, K. Eckle, K. Proksch, J. Schmidt-Hieber
Electronic Journal of Statistics, Volume 3, 2257-2306, 2019.

A comparison of deep networks with ReLU activation function and linear spline-type methods

K. Eckle, J. Schmidt-Hieber
Neural Networks, Volume 110, 232-242, 2019.

The Le Cam distance between density estimation, Poisson processes and Gaussian white noise

K. Ray, J. Schmidt-Hieber
Mathematical Statistics and Learning, Volume 1, Issue 2, 101-170, 2018.

A regularity class for the roots of non-negative functions

K. Ray, J. Schmidt-Hieber
Annali di Matematica Pura ed Applicata, Volume 196, Number 6, 2091-2103, 2017.

Minimax theory for a class of non-linear statistical inverse problems

K. Ray, J. Schmidt-Hieber
Inverse Problems, Volume 32, Number 6, 065003, 2016.

article revised preprint

Conditions for posterior contraction in the sparse normal means problem

S. van der Pas, J.B. Salomond, J. Schmidt-Hieber
Electronic Journal of Statistics, Volume 10, Number 1, 976-1000, 2016.

Bayesian linear regression with sparse priors

I. Castillo, A. van der Vaart, J. Schmidt-Hieber
Annals of Statistics, Volume 43, Number 5, 1986-2018, 2015.

On adaptive posterior concentration rates

M. Hoffmann, J. Rousseau, J. Schmidt-Hieber
Annals of Statistics, Volume 43, Number 5, 2259-2295, 2015.

Spot volatility estimation for high-frequency data: adaptive estimation in practice

T. Sabel, A. Munk, J. Schmidt-Hieber
Springer Lecture Notes in Statistics: Modeling and Stochastic Learning for Forecasting in High Dimension, 213-241, 2015.

Asymptotic equivalence for regression under fractional noise

J. Schmidt-Hieber
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

T. Sabel, J. Schmidt-Hieber
Bernoulli, Volume 20, Number 2, 747-774, 2014.

pdf arXiv supplement

Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

A. Munk, L. Dümbgen, J. Schmidt-Hieber
Annals of Statistics, Volume 41, Number 3, 1299-1328, 2013.

pdf supplement

Adaptive wavelet estimation of the diffusion coefficient under additive error measurements

M. Hoffmann, A. Munk, J. Schmidt-Hieber
Annales de l'Institut Henri Poincaré, 48, 1186-1216.

Nonparametric methods in spot volatility estimation

J. Schmidt-Hieber
Dissertation, Universität Göttingen und Universität Bern, 2010.

Lower bounds for volatility estimation in microstructure noise models

A. Munk, J. Schmidt-Hieber
Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown, IMS Collections, 6, 43-55, 2010.

Nonparametric estimation of the volatility function in a high-frequency model corrupted by noise

A. Munk, J. Schmidt-Hieber
Electronic Journal of Statistics, 4, 781-821, 2010.

Sharp minimax estimation of the variance of Brownian motion corrupted with Gaussian noise

T.T. Cai, A. Munk, J. Schmidt-Hieber
Statistica Sinica, Volume 20, 1011-1024, 2010 (including supplementary material).

Reports

Book review of "Mathematical Foundations of Deep Learning Models and Algorithms" by K. Spiliopoulos, R.B. Sowers, J. Sirignano

J. Schmidt-Hieber
Jahresbericht der Deutschen Mathematiker-Vereinigung, 2026

Contribution to the Discussion of 'Statistical exploration of the Manifold Hypothesis' by Whiteley et al.

P. Kundu, J. Schmidt-Hieber
Journal of the Royal Statistical Society, Series B, 2026

Challenges and opportunities for statistics in the era of data science

J. Schmidt-Hieber
Harvard Data Science Review, 7(2), 2025. (Written by a consortium of statisticians.)

Towards a statistical foundation for machine learning methods

J. Schmidt-Hieber
Proceedings of the International Congress of Basic Science 2025

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

J. Schmidt-Hieber
Journal of the Royal Statistical Society, Series B, Volume 86, Issue 2, Page 329, 2024

Deep ReLU network approximation of functions on a manifold

J. Schmidt-Hieber
arXiv preprint arXiv:1908.00695

Statistical theory for deep neural networks with ReLU activation function

J. Schmidt-Hieber
Oberwolfach Reports, 2018

Nonparametric Bayes for an irregular model

J. Schmidt-Hieber
Oberwolfach Reports, 2017

Asymptotic equivalence for regression under dependent noise

J. Schmidt-Hieber
Oberwolfach Reports, 2015

Reconstruction of risk measures from financial data

J. Schmidt-Hieber
Nieuw Archief voor Wiskunde, 2014

On an estimator achieving the adaptive rate in nonparametric regression under Lp-loss for all 1≤p≤∞

J. Schmidt-Hieber
This is an update of an earlier working paper (which only considered simultaneous adaptation w.r.t. L2- and L∞-loss); this version is easier to read and includes a small numerical study.

Simultaneously adaptive estimation for L2- and L∞-loss

J. Schmidt-Hieber
Oberwolfach Reports, 2014

Detection of qualitative features in statistical inverse problems

J. Schmidt-Hieber
Oberwolfach Reports, 2012

Obtaining qualitative statements in deconvolution models

J. Schmidt-Hieber
Oberwolfach Reports, 2012

The estimation of different scales in microstructure noise models from a nonparametric regression perspective

J. Schmidt-Hieber, A. Munk
Oberwolfach Reports, 2009