Scalable Bayesian Statistical Machine Learning for Multi-modal Data with Applications to Multiple Sclerosis

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Within this project, we undertake the challenge of effectively managing extensive and complex datasets, as exemplified by the NO.MS clinical dataset. The primary objective is to streamline the inherent complexity of these datasets by uncovering underlying latent variables. This simplification is particularly vital when contending with high-dimensional data, where the challenge lies in distilling an abundance of dimensions into a more concise set of broader covariates that remain accurate representations of the data. This concept of distilling latent variables extends its relevance to diverse fields beyond our immediate study.The NO.MS dataset, provided by Novartis, serves as a focal point of interest. It encompasses a wealth of data on individuals affected by multiple sclerosis, distinguishing itself as one of the largest datasets of its kind. This distinction arises from the inclusion of numerous MRI brain scans, contributing to its high dimensionality due to the myriad of pixels within each scan. Consequently, this dataset bears significant potential for unravelling insights into the disease. However, from an analytical standpoint, it presents considerable challenges. This complexity stems from the dataset's amalgamation of discrete data, such as disability scores, and continuous data, exemplified by the pixel values within the MRI scans. Furthermore, the dataset draws from multiple studies, each capturing distinct facets of patient visits, resulting in a substantial amount of missing data.The project's core objectives comprise of two pivotal contributions:First and foremost, we aim to construct a model that can effectively unveil an interpretable representation of the lower-dimensional latent space. Our approach relies heavily on Bayesian statistics, a statistical framework that integrates prior beliefs into modelling, subsequently updating them based on the incoming data. This model must possess the versatility to accommodate both continuous and discrete data, offering a solution for datasets like NO.MS. Furthermore, we prioritize scalability, recognizing the impracticality of conventional methods for managing large, high-dimensional datasets, such as the Novartis multiple sclerosis data. In addition, our model should autonomously determine the optimal number of latent variables required to represent the data accurately. While existing models may address individual aspects of these challenges, the unique aspect of our approach is the integration of solutions into a cohesive whole.Secondly, we intend to apply this comprehensive model to the NO.MS dataset to deepen our understanding of multiple sclerosis. This can be achieved by analysing the latent factors unveiled, in collaboration with medical experts. Additionally. These latent factors furnish a simplified representation of the data, which can, in turn, be employed in conjunction with more computationally intensive models. This streamlined representation enhances the efficiency of our analyses compared to conventional approaches.This project falls within the EPSRC Statistics and Applied Probability research area and is carried out in collaboration with Novartis, it is supervised by Dr Habib Ganjgahi, Prof Tom Nichols and Prof Chris Holmes.