我们不是你真正的父母：使用MDL区分因果关系和混淆
We Are Not Your Real Parents: Telling Causal from Confounded using MDL
摘要：
鉴于数据变量$(X_1,...,X_m, Y)$，我们考虑的问题，找出是否$X$共同导致$Y$或是否他们都混淆了一个未观察到的潜在变量$Z$。为此，我们采用基于柯尔莫哥洛夫复杂度的信息论方法。简而言之，我们遵循这样一个假设：首先对真正的原因进行编码，然后对给定原因的结果进行编码，这比观察变量的任何其他编码都要短。理想的分数是不可计算的，因此我们必须近似它。我们建议使用最小描述长度（MDL）原则。我们比较了$X$导致$Y$的模型和存在潜在变量$Z$混淆$X$和$Y$的模型下的MDL得分，并显示我们的得分是一致的。为了找到潜在的混杂因素，我们建议使用潜在因素建模，特别是概率PCA（PPCA）。对合成数据和真实数据的实证评估表明，我们的方法CoCa表现非常好-即使数据的真实生成过程与我们使用的模型所做的假设相差甚远。此外，它是强大的，因为它的准确性与它的信心齐头并进。
英文摘要：
Given data over variables $(X_1,...,X_m, Y)$ we consider the problem of finding out whether $X$ jointly causes $Y$ or whether they are all confounded by an unobserved latent variable $Z$. To do so, we take an information-theoretic approach based on Kolmogorov complexity. In a nutshell, we follow the postulate that first encoding the true cause, and then the effects given that cause, results in a shorter description than any other encoding of the observed variables. The ideal score is not computable, and hence we have to approximate it. We propose to do so using the Minimum Description Length (MDL) principle. We compare the MDL scores under the models where $X$ causes $Y$ and where there exists a latent variables $Z$ confounding both $X$ and $Y$ and show our scores are consistent. To find potential confounders we propose using latent factor modeling, in particular, probabilistic PCA (PPCA). Empirical evaluation on both synthetic and real-world data shows that our method, CoCa, performs very well -- even when the true generating process of the data is far from the assumptions made by the models we use. Moreover, it is robust as its accuracy goes hand in hand with its confidence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
