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.

翻译：因果效应估计对于自然科学与社会科学中的许多任务至关重要。我们针对连续部分识别问题设计了算法：在未测量混杂因素导致识别不可行的情况下，界定多变量连续处理变量的效应边界。具体而言，我们将因果效应表述为约束优化问题中的目标函数，并通过最小化/最大化这些函数来获得边界。我们结合灵活的学习算法与蒙特卡洛方法，实现了一族名为随机因果规划的解决方案。特别地，我们展示了如何在辅助变量被聚类为处理前集合与处理后集合（此时难以明确指定细粒度因果图）的场景中高效构建该通用框架。在这些场景中，我们无需完整指定隐藏共同原因的分布族，同时蒙特卡洛计算也得到极大简化，从而产生相比于替代方案在计算上更稳定的算法。