Johannes Maly

Welcome to my page!

I am an assistant professor working on mathematics of data science and machine learning. My former research has been focused on compressed sensing and the influence of quantization on signal reconstruction.
I am currently interested in the recovery of multi-structured signals, covariance estimation, approximation properties of neural networks, and the implicit bias of gradient descent (and particularly in theoretically understanding the influence of coarse quantization in all of these fields).

Contact

Current address: Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence, LMU Munich, Akademiestr. 7, D-80799 München

E-mail: maly(at)math(dot)lmu(dot)de

Short CV

10/2022 - now: Assistant professor for “Mathematical Data Science” at the chair of Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence at LMU, Munich
11/2020 - 09/2022: PostDoc (akademischer Rat auf Zeit) at the Department of Scientific Computing at Catholic University of Eichstaett-Ingolstadt
02/2019 - 10/2020: PostDoc at the Chair for Mathematics of Data Processing at RWTH Aachen University
01/2016 - 01/2019: PhD at the Chair for Applied and Numerical Analysis and Optimization and Data Analysis at TUM, Munich, under supervision of Prof. Massimo Fornasier
10/2013 - 09/2015: M.Sc. in mathematics at TUM, Munich
05/2011 - 09/2013: B.Sc. in mathematics at TUM, Munich

Teaching

LMU

10/2023 - 03/2024: “High-dimensional Probability” (Lecture)
04/2023 - 09/2023: “Convex Optimization for Data Science” (Lecture)
10/2022 - 03/2023: “Mathematical Signal and Image Processing” (Lecture)

Catholic University of Eichstaett/Ingolstadt

04/2022 - 09/2022: “Introduction to Scientific Computing” (Lecture+Exercises)
10/2021 - 03/2022: “Mathematics for Economics” (Lecture)
04/2021 - 09/2021: “Introduction to Scientific Computing” (Lecture+Exercises)
11/2020 - 03/2021: “Introduction to Numerical Analysis” (Lecture+Exercises)

RWTH Aachen University

04/2020 - 09/2020: Teaching assistant for “Optimization”
10/2019 - 03/2020: Teaching assistant for “Repetitorium - Higher Mathematics II”
04/2019 - 09/2019: Teaching assistant for “Higher Mathematics II”

Technical University of Munich

04/2018 - 09/2018: Teaching assistant for “Foundations of Data Analysis”

Publications

Preprints

H.–H. Chou, J. Maly, and D. Stöger: “How to induce regularization in generalized linear models: A guide to reparametrizing gradient flow”, 2023, arXiv preprint
H.–H. Chou, J. Maly, and C. Mayrink Verdun: “Non-negative Least Squares via Overparametrization”, 2022, arXiv preprint

Journal publications

2024

S. Dirksen, J. Maly: “Tuning-free one-bit covariance estimation using data-driven dithering”, 2024, IEEE Transactions on Information Theory, (arXiv)
H.–H. Chou, C. Gieshoff, J. Maly, and H. Rauhut: “Gradient Descent for Deep Matrix Factorization: Dynamics and Implicit Bias towards Low Rank”, 2024, Applied and Computational Harmonic Analysis, (arXiv)
T. Yang, J. Maly, S. Dirksen, and G. Caire: “Plug-in Channel Estimation with Dithered Quantized Signals in Spatially Non-Stationary Massive MIMO Systems”, 2024, IEEE Transactions on Communications, (arXiv)

2023

J. Maly: “Robust Sensing of Low-Rank Matrices with Non-Orthogonal Sparse Decomposition”, 2023, Applied and Computational Harmonic Analysis, (arXiv)
J. Maly and R. Saab: “A simple approach for quantizing neural networks”, 2023, Applied and Computational Harmonic Analysis, (arXiv)
H.–H. Chou, J. Maly, and H. Rauhut: “More is Less: Inducing Sparsity via Overparameterization”, 2023, Information and Inference: A Journal of the IMA, (arXiv)

2022

S. Dirksen, J. Maly, and H. Rauhut: “Covariance estimation under one-bit quantization”, 2022, Annals of Statistics, (arXiv)
A. Caragea, D. G. Lee, J. Maly, G. Pfander, and F. Voigtlaender: “Quantitative approximation results for complex-valued neural networks”, 2022, SIAM Journal on Mathematics of Data Science (SIMODS), (arXiv)

2021

F. Boßmann, S. Krause-Solberg, J. Maly, and N. Sissouno: “Structural Sparsity in Multiple Measurements”, 2021, IEEE Transactions on Signal Processing, (arXiv)
Z. Kereta, J. Maly, and V. Naumova: “Computational approaches to non-convex, sparsity-inducing multi-penalty regularization”, 2021, Inverse Problems, (arXiv)
M. Iwen, F. Krahmer, S. Krause-Solberg, and J. Maly: “On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds”, 2021, Discrete and Computational Geometry, (arXiv)
H. C. Jung, J. Maly, L. Palzer, and A. Stollenwerk: “Quantized Compressed Sensing by Rectified Linear Units”, 2021, IEEE Transactions on Information Theory, (arXiv)

2020

M. Fornasier, J. Maly and V. Naumova: “Robust Recovery of Low-Rank Matrices with Non-Orthogonal Sparse Decomposition from Incomplete Measurements”, 2020, Applied Mathematics and Computation, (arXiv)

2019

J. Maly and L. Palzer: “Analysis of Hard-Thresholding for Distributed Compressed Sensing with One-Bit Measurements”, 2019, Information and Inference: A Journal of the IMA, (arXiv)

Conference publications

2023

C. Kümmerle, J. Maly: “Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares”, 2023, NeurIPS 2023, (arXiv)

2021

S. Dirksen, J. Maly, and H. Rauhut: “Covariance estimation under one-bit quantization”, 2021, Proceedings in Applied Mathematics and Mechanics — PAMM
H. C. Jung, J. Maly, L. Palzer, and A. Stollenwerk: “Quantized Compressed Sensing by Rectified Linear Units”, 2021, Proceedings in Applied Mathematics and Mechanics — PAMM

2020

A. Guth, C. Culotta-López, J. Maly, H. Rauhut, and D. Heberling: “Polyhedral Sampling Structures for Phaseless Spherical Near-Field Antenna Measurements”, 2020, 42nd Antenna Measurement Techniques Association Symposium (AMTA)
H. C. Jung, J. Maly, L. Palzer, and A. Stollenwerk: “Quantized Compressed Sensing by Rectified Linear Units”, 2020, iTWIST’20

2019

S. Dirksen, M. Iwen, S. Krause-Solberg, and J. Maly: “Robust One-bit Compressed Sensing With Manifold Data”, 2019, International Conference on Sampling Theory and Applications (SampTA)
H. C. Jung, J. Maly, L. Palzer, and A. Stollenwerk: “One-Bit Compressed Sensing by Convex Relaxation of the Hamming Distance”, 2019, SPARS workshop
Z. Kereta, J. Maly, and V. Naumova: Linear convergence and support recovery for non-convex multi-penalty regularisation, 2019, SPARS workshop

2017

M. Fornasier, J. Maly and V. Naumova: “Robust Recovery of Low-Rank Matrices using Multi-Penalty Regularization”, 2017, NIPS workshop Optimization for Machine Learning
S. Krause-Solberg and J. Maly: “A tractable approach for one-bit Compressed Sensing on manifolds”, 2017, International Conference on Sampling Theory and Applications (SampTA)

Book chapters

J. Maly, T. Yang, S. Dirksen, H. Rauhut, and G. Caire: “New challenges in covariance estimation: multiple structures and coarse quantization” in Compressed Sensing in Information Processing, 2021, Springer, (arXiv)

Theses

J. Maly: “Recovery Algorithms for Quantized Compressed Sensing”, 2019, Phd thesis
J. Maly: “Weighted Energy-Dissipation Approximation for an Optimal Control Problem”, 2015, Master’s thesis

Code

Supplementary material for “Tuning-free one-bit covariance estimation using data-driven dithering”
Supplementary material for “Robust Sensing of Low-Rank Matrices with Non-Orthogonal Sparse Decomposition”
Supplementary material for “Robust Recovery of Low-Rank Matrices with Non-Orthogonal Sparse Decomposition from Incomplete Measurements”
Supplementary material for “On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds”