📖Pearl的因果性理论中，在自然的最小性和稳定性假设下，仅依据观测数据能恢复因果模型，且能确定观测分布的完美映射（若存在）与因果模型的关系。

🤔作者对该理论中与因果性的实际关联存在疑问，如最小性和稳定性虽能缩小贝叶斯网络中箭头方向的范围，但与因果意义上的箭头方向的关系尚不明确。

🌐Pearl在其时间偏差猜想中提到，在大多数自然现象中，物理时间与至少一个统计时间一致，且猜想这可能是因为人类语言的优化使得我们对现实的变量选择和分解使得时间偏差为真，但作者对此不太理解且认为不太满意。

Published on August 3, 2024 12:39 PM GMT

Chapter 2 of Pearl's Causality book claims you can recover causal models given only the observational data, under very natural assumptions of minimality and stability^[1].

In graphical models lingo, Pearl identifies a causal model of the observational distribution with the distribution's perfect map (if they exist).

But I'm confused about a pretty fundamental point: "What does this have to do at all with causality??" More precisely:

"Okay, it's pretty cool that minimality and stability alone lets us narrow down such a large number of arrow directions (in the Bayes Net independency sense) of the minimal network. But ... what does this have to do with arrow directions in the causal sense, i.e. [independent stable mechanisms of reality that, by the virtue of its independence, respond to interventions in a modular way]"?

To be clear, Pearl acknowledges this in his Temporal Bias Conjecture (2.8.2):

"In most natural phenomenon, the physical time coincides with at least one statistical time."

And Pearl conjectures that the reason for this is possibly because human language is optimized such that our [choice of variables / factorization of reality] makes the Temporal Bias true.

I ... guess that could be an explanation? But honestly I don't think I understand his point very well and I find it pretty unsatisfying. I would appreciate any explanation as to why it makes sense to identify perfect maps with Causal Models.

1. ^{^}

   Minimality: Choose the network structure that is minimally expressive among those that can express the observational distribution.

   This is pretty reasonable imo, occam's razor blah blah

   Stability: Assume that there exists a network structure that perfectly captures all and only the independencies implied by the observational distribution. i.e. independencies are structural.

   Stability is a reasonable assumption since it would be pretty unlikely for the conditional probability distributions to be fine-tuned as to cancel each other out and induce an independency not present in the network.