Stochastic Causal Programming for Bounding Treatment Effects

Kirtan Padh, Jakob Zeitler, David Watson, Matt Kusner, Ricardo Silva, Niki Kilbertus

Keywords: Causal effects, partial identification, shape constraints

TL;DR: We provide a framework to perform partial identification for high-dimensional, continuous variables without common assumptions such as additivity and monotonicity

Abstract: Causal effect estimation is important for many tasks in the natural and social sciences. We design algorithms for the continuous partial identification problem: bounding the effects of multivariate, continuous treatments when unmeasured confounding makes identification impossible. Specifically, we cast causal effects as objective functions within a constrained optimization problem, and minimize/maximize these functions to obtain bounds. We combine flexible learning algorithms with Monte Carlo methods to implement a family of solutions under the name of stochastic causal programming. In particular, we show how the generic framework can be efficiently formulated in settings where auxiliary variables are clustered into pre-treatment and post-treatment sets, where no fine-grained causal graph can be easily specified. In these settings, we can avoid the need for fully specifying the distribution family of hidden common causes. Monte Carlo computation is also much simplified, leading to algorithms which are more computationally stable against alternatives.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2202.10806/code)