Stochastic Causal Programming for Bounding Treatment Effects
This addresses causal inference challenges in natural and social sciences where continuous treatments and unmeasured confounding are common, representing a novel methodological advancement rather than an incremental improvement.
The paper tackles the problem of bounding causal effects of multivariate continuous treatments when unmeasured confounding prevents exact identification, by formulating causal effects as objective functions in a constrained optimization problem and using Monte Carlo methods to compute bounds. The result is a computationally stable framework called stochastic causal programming that avoids needing to fully specify hidden cause distributions, particularly in settings with clustered auxiliary variables.
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.