Combining geometry-aware statistical and deep learning for neuroimaging data

点击翻译按钮获取中文摘要

This project will develop methods for data that constitute non-vectorial structured objects (object data) lying on a constrained manifold, which play a key role in biomedical imaging. In particular, we will focus on the two important special cases: 1) connectivity matrices obtained from functional magnetic resonance imaging (fMRI) and 2) shapes of brain structures obtained from structural magnetic resonance imaging (MRI), which are relevant both as inputs (e.g. for disease classification) and as outputs (e.g. as disease markers). Connectivity matrices are symmetric positive definite matrices, and shapes are equivalence classes with respect to translation, rotation and/or scale, but the geometric structure of the Riemannian manifolds they live on is often ignored. This can lead for instance to invalid predictions outside the space (e.g. non positive definite connectivity matrices) for object outputs and suboptimal results in classification for object inputs. Additional challenges in neuroimaging data are confounding variables such as age or sex that are often not controlled for, and the dependence between objects on the same subject in longitudinal studies. A further desideratum are interpretable models that can aid in developing a better understanding of the underlying relationship between health outcomes, neurobiological markers and other factors such as age or sex, while showing good predictive performance.In this project, we will develop and benchmark methods for both types of object data as either inputs or outputs that respect their geometry. We combine the strengths of flexible model-based statistical learning approaches - interpretability, adjustment for confounders and temporal dependence structure - with those from deep learning - in particular predictive performance and scalable software solutions. To better understand the relationship of object biomarkers with a number of health-related variables including age and disease status, by building more valid and interpretable models, we will test these methods in three data sets for both types of object data. These are 1) fMRI connectivity matrices in the UK Biobank and the Human Connectome Project and 2) shape data in the longitudinal Alzheimer’s Disease Neuroimaging Initiative database.