Deep Learning of Causal Structures in High Dimensions

arXiv (Cornell University)

Abstract

Recent years have seen rapid progress at the intersection between causality and machine learning. Motivated by scientific applications involving high-dimensional data, in particular in biomedicine, we propose a deep neural architecture for learning causal relationships between variables from a combination of empirical data and prior causal knowledge. We combine convolutional and graph neural networks within a causal risk framework to provide a flexible and scalable approach. Empirical results include linear and nonlinear simulations (where the underlying causal structures are known and can be directly compared against), as well as a real biological example where the models are applied to high-dimensional molecular data and their output compared against entirely unseen validation experiments. These results demonstrate the feasibility of using deep learning approaches to learn causal networks in large-scale problems spanning thousands of variables.

Authors 4

1. Kai Lagemann

   German Center for Neurodegenerative Diseases

   Affiliation as printed

   Statistics and Machine Learning , DZNE , Bonn , Germany

2. Christian Lagemann Aachen Institute of Aerodynamics

   RWTH Aachen University

   Affiliation as printed

   Institute of Aerodynamics , RWTH Aachen University , Aachen , Germany

3. Bernd Taschler

   University of Oxford · Wellcome Centre for Integrative Neuroimaging

   Affiliation as printed

   Wellcome Centre for Integrative Neuroimaging , University of Oxford , Oxford , UK

4. Sach Mukherjee

   University of Cambridge · German Center for Neurodegenerative Diseases · MRC Biostatistics Unit

   Affiliation as printed

   MRC Biostatistics Unit , University of Cambridge , Cambridge , UK

   Statistics and Machine Learning , DZNE , Bonn , Germany