Learning DAGs from Fourier-Sparse Data

Panagiotis Misiakos, Chris Wendler, Markus Püschel

Keywords: directed acyclic graph, DAG learning, causal Fourier analysis, structural equation models, additive noise, Fourier-sparse

TL;DR: We leverage recent causal Fourier analysis to pose the novel problem of learning DAGs from data with sparse spectrum and propose a solution that has better performance over existing DAG learning methods.

Abstract: We present a novel perspective on learning directed acyclic graphs (DAGs) from data, leveraging a recent novel form of causal Fourier analysis on DAGs. We build on prior work that learned DAGs from data generated by a structural equation model (SEM). First, we show that data generated by linear SEMs can be characterized in the frequency domain as having dense spectra with random coefficients. Then we propose the new problem of learning DAGs from approximately Fourier-sparse data, which we solve by minimizing the $L^1$ norm of the spectrum. We provide a motivation for this problem and compare our method to prior DAG learning methods, showing superior performance.

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