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和社会科学中的许多任务至关重要。我们设计了针对连续部分识别问题的算法：当未测量混杂因素导致识别不可能时，对多变量连续处理效应进行边界界定。具体而言，我们将因果效应作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取边界。我们将灵活的学习算法与蒙特卡洛方法相结合，以随机因果规划为名实现了一系列解决方案。特别地，我们展示了在辅助变量被聚类为处理前和处理后集合（此时无法轻易指定细粒度因果图）的场景中，如何高效地构建这一通用框架。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大为简化，从而得到比替代方案计算更稳定的算法。