Learning Gene Regulatory Networks under Few Root Causes assumption.

Panagiotis Misiakos, Chris Wendler, Markus Püschel

Keywords: directed acyclic graph, few causes, Fourier analysis, structural equation models, linear SEMs, additive noise, Fourier-sparse

TL;DR: We attempt the CausalBench Challenge by assuming that gene expression data are generated from a few root causes.

Abstract: We present a novel directed acyclic graph (DAG) learning method for data generated by a linear structural equation model (SEM) and apply it to learn from gene expression data. In prior work, linear SEMs can be viewed as a linear transformation of a dense input vector of random valued root causes (as we define). In our novel setting we further impose the assumption that the output data are generated via a sparse input vector, or equivalently few root causes. Interestingly, this assumption can be viewed as a form of Fourier sparsity based on a recently proposed theory of causal Fourier analysis. Our setting is identifiable and the true DAG is the global minimizer of the $L^0$-norm of the vector of root causes. Application to the CausalBench Challenge shows superior performance over the provided baselines.