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Research Group Holger Rauhut

Link to Holger Rauhut

Holger Rauhut

Prof. Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Holger Rauhut

is Professor of Mathematical Data Science and Artificial Intelligence at LMU Munich.

His focus on the intersection of mathematics and artificial intelligence, aiming for both a mathematical understanding of artificial intelligence and artificial intelligence for mathematical problems.

Team members @MCML

Link to Sakirudeen Abdulsalaam

Sakirudeen Abdulsalaam

Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Link to Wiebke Bartolomaeus

Wiebke Bartolomaeus

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Link to Arinze Lawrence Folarin

Arinze Lawrence Folarin

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Link to Leonardo Galli

Leonardo Galli

Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Link to Garam Kim

Garam Kim

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Link to Gabin Maxime Nguegnang

Gabin Maxime Nguegnang

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Link to Laura Paul

Laura Paul

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Link to Shan Wei

Shan Wei

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Link to Tizian Wenzel

Tizian Wenzel

Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations

Publications @MCML

[5]
F. Hoppe, C. M. Verdun, H. Laus, F. Krahmer and H. Rauhut.
Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning.
38th Conference on Neural Information Processing Systems (NeurIPS 2024). Vancouver, Canada, Dec 10-15, 2024. To be published. Preprint at arXiv. arXiv.
Abstract

Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that applies both to classical regression approaches such as the LASSO as well as to neural networks. One of the most notable UQ techniques is the debiased LASSO, which modifies the LASSO to allow for the construction of asymptotic confidence intervals by decomposing the estimation error into a Gaussian and an asymptotically vanishing bias component. However, in real-world problems with finite-dimensional data, the bias term is often too significant to be neglected, resulting in overly narrow confidence intervals. Our work rigorously addresses this issue and derives a data-driven adjustment that corrects the confidence intervals for a large class of predictors by estimating the means and variances of the bias terms from training data, exploiting high-dimensional concentration phenomena. This gives rise to non-asymptotic confidence intervals, which can help avoid overestimating uncertainty in critical applications such as MRI diagnosis. Importantly, our analysis extends beyond sparse regression to data-driven predictors like neural networks, enhancing the reliability of model-based deep learning. Our findings bridge the gap between established theory and the practical applicability of such debiased methods.

MCML Authors
Link to Claudio Mayrink Verdun

Claudio Mayrink Verdun

Dr.

* Former member

A2 | Mathematical Foundations

Link to Hannah Laus

Hannah Laus

Optimization & Data Analysis

A2 | Mathematical Foundations

Link to Felix Krahmer

Felix Krahmer

Prof. Dr.

Optimization & Data Analysis

A2 | Mathematical Foundations

Link to Holger Rauhut

Holger Rauhut

Prof. Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations


[4]
F. Hoppe, C. M. Verdun, H. Laus, S. Endt, M. I. Menzel, F. Krahmer and H. Rauhut.
Imaging with Confidence: Uncertainty Quantification for High-dimensional Undersampled MR Images.
18th European Conference on Computer Vision (ECCV 2024). Milano, Italy, Sep 29-Oct 04, 2024. To be published.
MCML Authors
Link to Claudio Mayrink Verdun

Claudio Mayrink Verdun

Dr.

* Former member

A2 | Mathematical Foundations

Link to Hannah Laus

Hannah Laus

Optimization & Data Analysis

A2 | Mathematical Foundations

Link to Felix Krahmer

Felix Krahmer

Prof. Dr.

Optimization & Data Analysis

A2 | Mathematical Foundations

Link to Holger Rauhut

Holger Rauhut

Prof. Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations


[3]
F. Hoppe, C. M. Verdun, H. Laus, F. Krahmer and H. Rauhut.
Uncertainty Quantification For Learned ISTA.
IEEE Workshop on Machine Learning for Signal Processing (MLSP 2023). Rome, Italy, Sep 17-20, 2023. DOI.
MCML Authors
Link to Claudio Mayrink Verdun

Claudio Mayrink Verdun

Dr.

* Former member

A2 | Mathematical Foundations

Link to Hannah Laus

Hannah Laus

Optimization & Data Analysis

A2 | Mathematical Foundations

Link to Felix Krahmer

Felix Krahmer

Prof. Dr.

Optimization & Data Analysis

A2 | Mathematical Foundations

Link to Holger Rauhut

Holger Rauhut

Prof. Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations


[2]
F. Hoppe, F. Krahmer, C. M. Verdun, M. I. Menzel and H. Rauhut.
Sampling Strategies for Compressive Imaging Under Statistical Noise.
International Conference on Sampling Theory and Applications (SampTA 2023). Yale, CT, USA, Jul 10-14, 2023. DOI.
MCML Authors
Link to Felix Krahmer

Felix Krahmer

Prof. Dr.

Optimization & Data Analysis

A2 | Mathematical Foundations

Link to Claudio Mayrink Verdun

Claudio Mayrink Verdun

Dr.

* Former member

A2 | Mathematical Foundations

Link to Holger Rauhut

Holger Rauhut

Prof. Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations


[1]
H.-H. Chou, H. Rauhut and R. Ward.
Robust implicit regularization via weight normalization.
Preprint at arXiv (May. 2023). arXiv.
MCML Authors
Link to Hung-Hsu Chou

Hung-Hsu Chou

Dr.

Optimization & Data Analysis

A2 | Mathematical Foundations

Link to Holger Rauhut

Holger Rauhut

Prof. Dr.

Mathematical Data Science and Artificial Intelligence

A2 | Mathematical Foundations