标题： 将马尔可夫过程与结构因果建模相结合，可在复杂系统中进行反事实推断 显示英文标题

标题： Integrating Markov processes with structural causal modeling enables counterfactual inference in complex systems

摘要： 本手稿提出了一种通用且实用的框架，将处于平衡状态的系统的马尔可夫过程模型转化为结构因果模型，并进行反事实推断。 马尔可夫过程从数学上描述系统中的机制，并预测干预后系统的平衡行为，但不支持反事实推断。 相反，结构因果模型支持反事实推断，但无法识别机制。 本手稿利用了这两种方法的优势。 我们根据马尔可夫过程模型的参数和平衡动态来定义结构因果模型，反事实推断由此得出。 所提出的方法缓解了结构因果模型的可识别性缺点，因为反事实推断与从马尔可夫过程模型中模拟的反事实轨迹一致。 我们在具有非线性动力学的复杂生物分子系统的案例研究中展示了该框架的优势。 我们说明了在存在马尔可夫过程模型误设的情况下，反事实推断利用先验数据，因此比直接模拟更准确地估计干预的结果。 显示英文摘要

摘要： This manuscript contributes a general and practical framework for casting a Markov process model of a system at equilibrium as a structural causal model, and carrying out counterfactual inference. Markov processes mathematically describe the mechanisms in the system, and predict the system's equilibrium behavior upon intervention, but do not support counterfactual inference. In contrast, structural causal models support counterfactual inference, but do not identify the mechanisms. This manuscript leverages the benefits of both approaches. We define the structural causal models in terms of the parameters and the equilibrium dynamics of the Markov process models, and counterfactual inference flows from these settings. The proposed approach alleviates the identifiability drawback of the structural causal models, in that the counterfactual inference is consistent with the counterfactual trajectories simulated from the Markov process model. We showcase the benefits of this framework in case studies of complex biomolecular systems with nonlinear dynamics. We illustrate that, in presence of Markov process model misspecification, counterfactual inference leverages prior data, and therefore estimates the outcome of an intervention more accurately than a direct simulation.