Research in the Project Group Mathematical Learning in Psychiatry

Sparse Partial Least Squares (SPLS) is an unsupervised multivariate method that identifies maximally associated latent components across two data domains while simultaneously performing feature selection. This makes SPLS well suited to high-dimensional psychiatric datasets, where the number of variables often exceeds the number of participants.

We have developed a MATLAB-based SPLS toolbox that embeds the method within a cross-validation framework to ensure robust and reproducible solutions. Using this framework, for example, we examined associations between peripheral inflammatory markers, childhood trauma, coping styles, and gray matter volume in early depression and psychosis.
 

Building on SPLS, we implement multi-block SPLS (MB SPLS), which generalizes the method to more than two data blocks. MB SPLS learns coupled latent components that maximize covariance across a user-defined set of modalities while enforcing sparsity for interpretability. A block–block coupling matrix specifies which domains are linked, and our implementation incorporates site correction, cross validated tuning, and permutation/bootstrapping procedures.

This framework is particularly suited to psychiatric risk research, where relevant information is distributed across brain, behavior, and environment. For example, we use MB SPLS to integrate clinical functioning, neurocognition, MRI-derived ROI features, adversity, premorbid adjustment, genetics, and resilience indicators, yielding transdiagnostic components that predict different clinical outcomes. In another project, we fuse structural MRI, plexus and ventricular system measures, polygenic scores (global and cell type specific), and clinical variables to probe shared mechanisms across diagnoses.
 

We explore Transformer-based architectures, originally developed for natural language processing, as flexible models for heterogeneous psychiatric and forensic datasets. The self attention mechanism allows Transformers to weigh the relative importance of different inputs and to capture long range, non-linear dependencies across time and feature space.

In psychiatry, we adapt tabular and sequential Transformers to neurocognitive data, genetic and transcriptomic information, diffusion MRI, EEG, and structured clinical assessments. Strategies such as pretraining, fine tuning, and multimodal fusion help us learn efficiently from limited and noisy datasets. In a proof of concept study, we pretrained a Tabular Transformer to discriminate healthy controls and individuals with schizophrenia using neurofilament light chain (NfL) data from the Steiner cohort, then fine tuned it on a smaller Clinical Deep Phenotyping (CDP) eye tracking dataset for the same classification task. This setup allowed us to quantify the benefit of pretraining relative to training from scratch.

Beyond clinical psychiatry, we extend these approaches to forensic psychiatry. Using the Dudeck dataset (approximately 525 women with rich demographic, psychiatric, legal, and treatment information), we investigate how tabular Transformers can model offending patterns and treatment outcomes. In the longitudinal FoDoBa dataset (Forensic Documentation Baden Württemberg), which combines static predictors (e.g. sex, diagnosis, index crime) with dynamic variables (e.g. evolving diagnoses, treatment history, institutional conduct), we compare traditional models such as logistic regression and discrete time hazard models with recurrent networks (LSTMs) and Transformer based architectures such as the Temporal Fusion Transformer. Our goal is to predict outcomes such as relapse, violent behavior, or reoffending while maintaining interpretability via attention mechanisms and allowing continuous model updating as new data become available.
 

In parallel to our unsupervised and representation learning work, we apply supervised machine learning methods—such as support vector machines (SVMs)—to develop and validate predictive models for clinically relevant outcomes. In close collaboration with the Precision Psychiatry groups of Nikolaos Koutsouleris at LMU and the Max Planck Institute of Psychiatry, we use the Neurominer software to implement rigorous cross validated workflows.

These pipelines combine innovative algorithms with multimodal datasets to support individualized risk prediction, treatment response modeling, and stratification across psychotic and affective disorders.
 

Radiomic analysis of structural MRI data offers a complementary route to identifying biomarkers of psychiatric risk. We apply radiomics pipelines—encompassing image acquisition, preprocessing, feature extraction, feature selection, and model development—to quantify subtle brain alterations using texture, shape, and intensity-based features.

Using advanced machine learning models and dimensionality reduction techniques, we build classifiers that distinguish healthy controls from individuals at clinical high risk (CHR) for psychiatric disorders. Model performance is evaluated using cross-validation and multiple performance metrics, and explainable AI tools are incorporated to enhance interpretability.

Beyond binary classification, we investigate whether distinct CHR subgroups can be identified based on their radiomic signatures, potentially revealing mechanistically meaningful trajectories of risk.