Reproduce “Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction” on OpenResearch

About this paper

Afsaneh Mastouri, Yuchen Zhu, Limor Gultchin, Anna Korba, Ricardo Silva, Matt J. Kusner, Arthur Gretton, Krikamol Muandet

The authors develop KPV and PMMR, kernel methods for estimating nonlinear treatment effects when an unmeasured confounder has two proxy measurements. KPV uses two regression stages, while PMMR fits a kernel moment-restriction objective. In a nonlinear simulation at n=1000, PMMR’s c-MAE was 0.472 ± 0.358 versus 0.607 ± 0.379 for ordinary proxy adjustment; real-data results varied, with KernelRidge-W best in one case.

Key insights

• Kernel-based methods can consistently estimate Average Treatment Effects in proximal causal learning settings, effectively handling unobserved confounding and non-linear relationships through proxy variables.
• The two-stage regression (KPV) and maximum moment restriction (PMMR) approaches are theoretically linked, with KPV's objective function representing an upper bound of PMMR's, indicating shared underlying principles.
• Rigorous theoretical consistency guarantees and convergence rates can be established for these kernel-based estimators, providing strong statistical validity for complex causal inference problems.

Summary by alphaXiv.