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arXiv 1702.06776cs.LGcs.AI
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基于随机复杂性的因果推理

Causal Inference by Stochastic Complexity

Max Planck Institute for Informatics(马克斯·普朗克信息学研究所);Saarland University(萨尔大学)

Kailash Budhathoki, Jilles Vreeken

摘要:

算法马尔可夫条件指出,两个随机变量X和Y之间最可能的因果方向可以被识别为具有最低柯尔莫哥洛夫复杂度的方向。然而,由于停机问题,这个概念是不可计算的。因此,我们建议做因果推理的随机复杂性。也就是说,我们建议通过最小描述长度(MDL)原则来近似Kolmogorov复杂度,使用一个关于所考虑的模型类的最小-最大最优得分。这意味着即使在对抗性设置中,例如当真实分布不在该类中时,我们仍然可以获得相对于该类的数据的最佳编码。我们实例化这个框架,我们称之为CISC,对单变量离散变量,使用类的多项式分布。实验表明,CISC对合成数据、基准数据以及真实数据都非常准确,远远优于最先进的技术水平,并且在样本和域大小方面具有非常好的扩展性。

英文摘要:

The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion is not computable. We hence propose to do causal inference by stochastic complexity. That is, we propose to approximate Kolmogorov complexity via the Minimum Description Length (MDL) principle, using a score that is mini-max optimal with regard to the model class under consideration. This means that even in an adversarial setting, such as when the true distribution is not in this class, we still obtain the optimal encoding for the data relative to the class. We instantiate this framework, which we call CISC, for pairs of univariate discrete variables, using the class of multinomial distributions. Experiments show that CISC is highly accurate on synthetic, benchmark, as well as real-world data, outperforming the state of the art by a margin, and scales extremely well with regard to sample and domain sizes.

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。

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