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Abstract:
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We study the causal inference when not all confounders are observed and instead negative controls are available. Recent work has shown how negative controls can enable identification and efficient estimation of average treatment effects via two so-called bridge functions. In this paper, we consider a generalized average causal effect (GACE) with general interventions (discrete or continuous) and tackle the central challenge to causal inference using negative controls: the estimation of the two bridge functions. Previous work has largely relied on the uniqueness of these functions, which may be implausible in practice, assumed completeness assumptions, which my hard tor reason about, and focused on estimating these functions parametrically. We show GACE can be identified via two analogous bridge functions and provide a new identification strategy that avoids both uniqueness and completeness. And, we provide new estimators for the (possibly nonunique) bridge functions based on minimax learning that can accommodate general function classes such as Reproducing Kernel Hilbert spaces and neural networks. We study finite-sample convergence results both for estimating bridge function themse
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