最大熵与不充分理由原理的因果版本
Causal versions of Maximum Entropy and Principle of Insufficient Reason
摘要：
不充分理由原理（PIR）是指在没有理由的情况下，对随机试验中的每一种选择都赋予相等的概率。最大熵原理（MaxEnt）将PIR推广到给定期望等统计信息的情况。众所周知，这两个原则都会导致因果关系的联合分布的自相矛盾的概率更新。这是因为对条件P（效应）的约束|原因）导致P（原因）的变化，将更高的概率分配给那些为结果提供更多选择的原因值，这表明“故意行为”。因此，早期的工作建议根据因果顺序依次最大化（条件）熵，但没有进一步的理由，除了玩具例子的可解释性。我们证明因果关系的修改PIR和MaxEnt分离的限制，限制的原因和限制的机制，产生的影响，从原因。我们进一步勾勒为什么因果PIR也需要“信息几何因果推断“。我们简要地讨论了推广的因果版本的MaxEnt任意因果DAG的问题。
英文摘要：
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.
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