KI-FOR 5363 DeSBi
Fusing Deep Learning and Statistics towards Understanding Structured Biomedical Data (DeSBi)
Publications
Elastic Full Procrustes Analysis of Plane Curves via Hermitian Covariance Smoothing (Stöcker, A., Pfeuffer, M., Steyer, L., & Greven, S.)
Published in: Journal of Computational and Graphical Statistics
Abstract: For shapes of plane curves, the coordinate systems and parametrizations used are often arbitrary and not of interest. In statistical shape analysis, curves are thus frequently considered as equivalence classes of parameterized curves with respect to the shape invariances translation, rotation and scale, as well as re-parameterization (warping), based on the square-root-velocity (SRV) framework. We propose a novel elastic full Procrustes mean for samples of plane curve shapes. Identifying the real plane with the complex numbers, we establish a connection to covariance estimation in irregular/sparse functional data analysis. We introduce Hermitian covariance smoothing and employ it for mean estimation, thereby newly covering the sparse case and improving robustness to outlier contamination compared to existing methods. Necessary for our approach but also of independent interest, we characterize the covariance structure of rotation-invariant bivariate stochastic processes via complex representations, and identify sampling schemes that allow for observing derivatives/SRV transforms of sparsely sampled curves. In addition, we develop one- and two-way ANOVA for sparse curve shape data, where exact distance computation is not feasible. We demonstrate the performance of our approach in different realistic simulation settings and use it for an ANOVA of tongue shapes during speech production. Proposed methods are implemented in the R package elastes.
Deep Nonparametric Conditional Independence Tests for Images (Marco Simnacher, Xiangnan Xu, Hani Park, Christoph Lippert, Sonja Greven)
Published in: Journal of Machine Learning Research 27 (2026) 1-73
Abstract: Conditional independence tests (CITs) test for conditional dependence between random variables given a vector of conditioning or confounder variables. As existing CITs are limited in their applicability to complex, high-dimensional variables such as images, we introduce deep nonparametric CITs (DNCITs). The DNCITs combine embedding maps, which extract feature representations of high-dimensional variables, with nonparametric CITs applicable to these feature representations. For the embedding maps, we derive general properties on their parameter estimators to obtain valid DNCITs and show that these properties include embedding maps learned through (conditional) unsupervised or transfer learning. For the nonparametric CITs, appropriate tests are selected and adapted to be applicable to feature representations. Through simulations, we investigate the performance of the DNCITs for different embedding maps and nonparametric CITs under varying confounder dimensions and confounder relationships. We apply the DNCITs to brain MRI scans and behavioral traits, given confounders, of healthy individuals from the UKBiobank, confirming null results from a number of ambiguous personality neuroscience studies, now with a larger data set and with our more powerful tests. In addition, in a confounder control study, we apply the DNCITs to brain MRI scans and a confounder set to test for sufficient confounder control. We provide an R package implementing the proposed DNCITs.
Pioneering newpaths: theroleofgenerativemodelling inneurological disease research (Seiler, M., & Ritter, K.)
Published in: Pflügers Archiv- European Journal of Physiology (2025) 477:571–589
Abstract: Recently, deep generative modelling has become an increasingly powerful tool with seminal work in a myriad of disciplines. This powerful modelling approach is supposed to not only have the potential to solve current problems in the medical field but also to enable personalised precision medicine and revolutionise healthcare through applications such as digital twins of patients. Here, the core concepts of generative modelling and popular modelling approaches are first introduced to consider the potential based on methodological concepts for the generation of synthetic data and the ability to learn a representation of observed data. These potentials will be reviewed using current applications in neuroimaging for data synthesis and disease decomposition in Alzheimer’s disease and multiple sclerosis. Finally, challenges for further research and applications will be discussed, including computational and data requirements, model evaluation, and potential privacy risks.






