Causal Inference using Gaussian Processes with Structured Latent Confounders
Sam Witty,u00a0Kenta Takatsu,u00a0David Jensen,u00a0Vikash Mansinghka
Latent confoundersu2014unobserved variables that influence both treatment and outcomeu2014can bias estimates of causal effects. In some cases, these confounders are shared across observations, e.g. all students taking a course are influenced by the courseu2019s difficulty in addition to any educational interventions they receive individually. This paper shows how to semiparametrically model latent confounders that have this structure and thereby improve estimates of causal effects. The key innovations are a hierarchical Bayesian model, Gaussian processes with structured latent confounders (GP-SLC), and a Monte Carlo inference algorithm for this model based on elliptical slice sampling. GP-SLC provides principled Bayesian uncertainty estimates of individual treatment effect with minimal assumptions about the functional forms relating confounders, covariates, treatment, and outcome. Finally, this paper shows GP-SLC is competitive with or more accurate than widely used causal inference techniques on three benchmark datasets, including the Infant Health and Development Program and a dataset showing the effect of changing temperatures on state-wide energy consumption across New England.
