A polynomial-time algorithm for learning nonparametric causal graphs

Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)

Bibtex »Paper »Supplemental »

Bibtek download is not availble in the pre-proceeding


Authors

Ming Gao, Yi Ding, Bryon Aragam

Abstract

We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity, independent noise, or faithfulness. Instead, we impose a condition on the residual variances that is closely related to previous work on linear models with equal variances. Compared to an optimal algorithm with oracle knowledge of the variable ordering, the additional cost of the algorithm is linear in the dimension $d$ and the number of samples $n$. Finally, we compare the proposed algorithm to existing approaches in a simulation study.