Kernel Single Proxy Control for Deterministic Confounding
This work addresses causal inference challenges in settings with unobserved confounders, offering a novel solution for deterministic outcomes, though it is incremental in generalizing to continuous treatments.
The paper tackles the problem of causal effect estimation with anobserved confounders using a single proxy variable, showing that recovery is possible if the outcome is generated deterministically, and proposes two kernel-based methods that consistently estimate the effect, as demonstrated on synthetic benchmarks.
We consider the problem of causal effect estimation with an unobserved confounder, where we observe a single proxy variable that is associated with the confounder. Although it has been shown that the recovery of an average causal effect is impossible in general from a single proxy variable, we show that causal recovery is possible if the outcome is generated deterministically. This generalizes existing work on causal methods with a single proxy variable to the continuous treatment setting. We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.