Heidelberg University

Spectral Methods for High-Dimensional Biomedical Data

Seminar im Wintersemester 2026 / 2027

Organisation

Contact

For questions about the seminar, please contact: victoria.mezger@math.uni-heidelberg.de

Description

This seminar studies the mathematical foundations of spectral methods for high-dimensional biomedical data. Topics include principal component analysis under heterogeneous noise, spectral clustering, classification in latent factor models, estimation of shared subspaces, knowledge transfer, and entropic optimal transport.

Format

Each paper will be assigned to one student or a pair of two students. The presentations are theoretical in nature and should focus on the statistical model, the main mathematical results, and substantial parts of their proofs. Individual presentations are allocated 40 minutes in total, including discussion. Presentations by pairs are allocated 60 minutes in total, including discussion.

Dates and location

Organizational meeting: October 14, 2026, 2:15 pm
Room to be announced.

Students who are interested in participating but are unable to attend the organizational meeting are still welcome to join the seminar. Please contact us in advance to arrange the paper assignment individually.

Mathematical introduction: October 28, 2026, 2.15pm
Room to be announced.

Individual consultations: November 2026, by appointment

Block seminar

The final presentations will take place in two afternoon sessions:

  • December 9, 2026, 2:00–5:30 pm, room 4/414
  • December 15, 2026, 2:00–5:30 pm, room 4/414

Papers

Anru R. Zhang, T. Tony Cai and Yihong Wu (2022).
Heteroskedastic PCA: Algorithm, Optimality, and Applications.
Paper

Matthias Loeffler, Anderson Y. Zhang and Harrison H. Zhou (2021).
Optimality of Spectral Clustering in the Gaussian Mixture Model.
Paper

Xin Bing and Marten Wegkamp (2023).
Optimal Discriminant Analysis in High-Dimensional Latent Factor Models.
Paper

Zhengchi Ma and Rong Ma (2026).
Optimal Estimation of Shared Singular Subspaces across Multiple Noisy Matrices.
Paper

Feiqing Huang, Zongqi Xia, Rong Ma and Tianxi Cai (2026).
Enhancing Spectral Embedding through Robust and Flexible Knowledge Transfer in Electronic Health Records.
Paper

Boris Landa, Yuval Kluger and Rong Ma (2026).
Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets.
Paper

Zijian Guo, Domagoj Cevid and Peter Buehlmann (2022).
Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding.
Paper