Bayesian and causal inference are fundamental processes for intelligence. Bayesian inference models observations: what can be inferred about y if we observe a related variable x? Causal inference models interventions: if we directly change x, how will y change? Predictive coding is a neuroscience-inspired method for performing Bayesian inference on continuous state variables using local information only. In this work, we go beyond Bayesian inference, and show how a simple change in the inference process of predictive coding enables interventional and counterfactual inference in scenarios where the causal graph is known. We then extend our results, and show how predictive coding can be generalized to cases where this graph is unknown, and has to be inferred from data, hence performing causal discovery. What results is a novel and straightforward technique that allows us to perform end-to-end causal inference on predictive-coding-based structural causal models, and demonstrate its utility for potential applications in machine learning.

翻译：贝叶斯推断与因果推断是智能的基本过程。贝叶斯推断建模观测结果：若我们观测到相关变量x，能推断出y的哪些信息？因果推断建模干预行为：若我们直接改变x，y将如何变化？预测编码是一种受神经科学启发的贝叶斯推断方法，仅利用局部信息对连续状态变量进行推断。本研究突破了贝叶斯推断的范畴，揭示了预测编码推断过程中的简单改变如何实现在已知因果图场景下的干预推断与反事实推断。我们进一步扩展研究结果，展示了预测编码如何推广至因果图未知、需从数据中推断（即进行因果发现）的场景。最终形成了一种新颖且直接的技术手段，使我们能够对基于预测编码的结构因果模型执行端到端因果推断，并论证了其在机器学习领域的潜在应用价值。