基于算法信息论的加性噪声模型因果发现
Justifying additive-noise-model based causal discovery via algorithmic information theory
摘要：
最近的一种因果发现方法在许多情况下能够推断出X导致Y还是Y导致X，只有两个观察变量X和Y。它基于以下观察：存在（非高斯）联合分布P（X，Y），其中Y可以被写为X的函数，直到独立于X的加性噪声项，并且从Y到X不存在这样的模型。在这种情况下，人们倾向于因果模型X-> Y。在这里，我们证明了这种方法，表明因果假设Y--> X是不可能的，因为它需要在P（Y）和P（X）之间进行特定的调整|Y）以生成允许从X到Y的加性噪声模型的分布。为了量化所需的调整量，我们推导出P（Y）和P（X）共享的算法信息的下限|Y）。这样，我们的理由是一致的，最近的方法使用算法信息论的因果推理。我们将这一原理推广到P（X，Y）几乎包含加性噪声模型的情形。我们的结果表明，当P（Y）的复杂度较高时，上述结论更可靠。
英文摘要：
A recent method for causal discovery is in many cases able to infer whether X causes Y or Y causes X for just two observed variables X and Y. It is based on the observation that there exist (non-Gaussian) joint distributions P(X,Y) for which Y may be written as a function of X up to an additive noise term that is independent of X and no such model exists from Y to X. Whenever this is the case, one prefers the causal model X--> Y. Here we justify this method by showing that the causal hypothesis Y--> X is unlikely because it requires a specific tuning between P(Y) and P(X|Y) to generate a distribution that admits an additive noise model from X to Y. To quantify the amount of tuning required we derive lower bounds on the algorithmic information shared by P(Y) and P(X|Y). This way, our justification is consistent with recent approaches for using algorithmic information theory for causal reasoning. We extend this principle to the case where P(X,Y) almost admits an additive noise model. Our results suggest that the above conclusion is more reliable if the complexity of P(Y) is high.
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