We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the "abduction, action, and prediction" approach to answer counterfactual queries and handles two key challenges where (1) the states are hidden and (2) the model is dynamic. Recognizing the lack of knowledge on the underlying causal mechanism and the possibility of infinitely many such mechanisms, we optimize over this space and compute upper and lower bounds on the counterfactual quantity of interest. Our work brings together ideas from causality, state-space models, simulation, and optimization, and we apply it on a breast cancer case study. To the best of our knowledge, we are the first to compute lower and upper bounds on a counterfactual query in a dynamic latent-state model.

翻译：我们提出一个基于优化的框架，用于在具有隐状态的动态模型中执行反事实分析。该框架基于"归因、行动与预测"方法回答反事实查询，并应对两个关键挑战：（1）状态是隐式的，（2）模型是动态的。鉴于对底层因果机制认知的缺乏以及可能存在无限多种此类机制，我们在该空间上进行优化，计算目标反事实量的上下界。本研究融合了因果推断、状态空间模型、模拟与优化领域的理念，并以乳腺癌案例进行应用验证。据我们所知，这是首次在动态隐状态模型中计算反事实查询的上下界。