Gaussian processes with optimal kernel construction for neuro-degenerative clinical onset prediction

Gaussian Processes (GP) are a powerful tool to capture the complex time-variations of a dataset. In the context of medical imaging analysis, they allow a robust modelling even in case of highly uncertain or incomplete datasets. Predictions from GP are dependent of the covariance kernel function selected to explain the data variance. To overcome this limitation, we propose a framework to identify the optimal covariance kernel function to model the data.The optimal kernel is defined as a composition of base kernel functions used to identify correlation patterns between data points. Our approach includes a modified version of the Compositional Kernel Learning (CKL) algorithm, in which we score the kernel families using a new energy function that depends both the Bayesian Information Criterion (BIC) and the explained variance score. We applied the proposed framework to model the progression of neurodegenerative diseases over time, in particular the progression of autosomal dominantly-inherited Alzheimer's disease, and use it to predict the time to clinical onset of subjects carrying genetic mutation.