Multiple Linear Regression: Bayesian Inference for Distributed and Big Data in the Medical Informatics Platform of the Human Brain Project

We propose a Multiple Linear Regression (MLR) methodology for the analysis of distributed and Big Data in the framework of the Medical Informatics Platform (MIP) of the Human Brain Project (HBP). MLR is a very versatile model, and is considered one of the workhorses for estimating dependences between clinical, neuropsychological and neurophysiological variables in the field of neuroimaging. One of the main concepts behind MIP is to federate data, which is stored locally in geographically distributed sites (hospitals, customized databases, etc.) around the world. We restrain from using a unique federation node for two main reasons: first the maintenance of data privacy, and second the efficiency in management of big volumes of data in terms of latency and storage resources needed in the federation node. Considering these conditions and the distributed nature of data, MLR cannot be estimated in the classical way, which raises the necessity of modifications of the standard algorithms. We use the Bayesian formalism that provides the armamentarium necessary to implement the MLR methodology for distributed Big Data. It allows us to account for the heterogeneity of the possible mechanisms that explain data sets across sites expressed through different models of explanatory variables. This approach enables the integration of highly heterogeneous data coming from different subjects and hospitals across the globe. Additionally, it offers general and sophisticated ways, which are extendable to other statistical models, to suit high-dimensional and distributed multimodal data. This work forms part of a series of papers related to the methodological developments embedded in the MIP.