The Principle of Insufficient Reason (PIR) assigns equal probabilities to each alternative of a random experiment whenever there is no reason to prefer one over the other. The Maximum Entropy Principle (MaxEnt) generalizes PIR to the case where statistical information like expectations are given. It is known that both principles result in paradoxical probability updates for joint distributions of cause and effect. This is because constraints on the conditional P(effect|cause) result in changes of P(cause) that assign higher probability to those values of the cause that offer more options for the effect, suggesting "intentional behaviour". Earlier work therefore suggested sequentially maximizing (conditional) entropy according to the causal order, but without further justification apart from plausibility on toy examples. We justify causal modifications of PIR and MaxEnt by separating constraints into restrictions for the cause and restrictions for the mechanism that generates the effect from the cause. We further sketch why Causal PIR also entails "Information Geometric Causal Inference". We briefly discuss problems of generalizing the causal version of MaxEnt to arbitrary causal DAGs.
翻译:理由不足原则(PIR)为随机试验的每一种选择分配了相等的概率,只要没有理由选择一种选择而选择另一种选择。最大负载原则(MaxEnt)将PIR笼统地适用于提供类似预期的统计资料的情况。众所周知,这两项原则都导致对因果关系的共同分布产生自相矛盾的概率更新,这是因为对有条件的P(效果)的限制导致P(原因)的改变,从而给产生效果的原因的数值带来更大的概率,从而建议“故意行为”。因此,早期的工作建议根据因果关系顺序(有条件)的旋转,但除了对微小例子的可信任性之外,不提出进一步的理由。我们有理由将PIR和MaxEnt的因果修改分为对原因的限制和对产生效果的机制的限制。我们进一步描述了Causal PIR为什么还包含“信息性大地测量引力”的问题。我们简要讨论了将因果版本概括为任意因果关系的DAGs的问题。