A polynomial-time algorithm for learning nonparametric causal graphs

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.

Authors

• Ming Gao School of Management Science and Engineering, Key Laboratory of Big Data Management Optimization and Decision of Liaoning Province, Dongbei University of Finance and Economics Center for Post-doctoral Studies of Computer Science, Northeastern University
• Yi Ding
• Bryon Aragam

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