In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and thus can be recovered using autoregressive normalizing flows (NFs). Second, we analyze different design and learning choices for causal normalizing flows to capture the underlying causal data-generating process. Third, we describe how to implement the do-operator in causal NFs, and thus, how to answer interventional and counterfactual questions. Finally, in our experiments, we validate our design and training choices through a comprehensive ablation study; compare causal NFs to other approaches for approximating causal models; and empirically demonstrate that causal NFs can be used to address real-world problems, where the presence of mixed discrete-continuous data and partial knowledge on the causal graph is the norm. The code for this work can be found at https://github.com/psanch21/causal-flows.
- Pub Date:
- June 2023
- Computer Science - Machine Learning;
- Computer Science - Artificial Intelligence;
- Statistics - Methodology;
- Statistics - Machine Learning
- 31 pages, 15 figures. Under submission