Project P7 develops methods for inputs and outputs that are non-vectorial structured objects lying on a constrained Riemannian manifold, respecting the geometry of such object data. The project in particular focuses on shapes of brain structures and connectivity matrices, both important in biomedical imaging. The project combines methods from geometry-aware statistical and deep learning and thus develops interpretable hybrid models, improving adjustment for confounders in deep learning models for biomedical data. This project will closely collaborate with P5 and P6 on semi-structured deep regression models, and will use tests developed by P1 to assess significance of associations conditional on confounders.