基于神经网络的因果结构学习的前置MDL
Prequential MDL for Causal Structure Learning with Neural Networks
摘要：
从观测中学习贝叶斯网络的结构和因果关系是多个科学和技术领域的共同目标。我们发现，先决条件的最小描述长度原则（MDL）可以用来推导出一个实用的评分函数贝叶斯网络时，灵活的和overparametrized神经网络被用来模拟观测变量之间的条件概率分布。MDL代表了奥卡姆剃刀的一个实施例，我们获得合理的和简约的图形结构，而不依赖于稀疏诱导先验或其他正则化，必须调整。从经验上讲，我们在合成数据和真实数据上展示了竞争结果。即使在变量之间存在强烈的非线性关系的情况下，分数也经常恢复正确的结构;一种情况是先前的方法难以实现，通常会失败。此外，我们还讨论了如何与最近的工作，推断因果结构的适应速度时，观察来自一个源进行分布转移的先决条件的分数。
英文摘要：
Learning the structure of Bayesian networks and causal relationships from observations is a common goal in several areas of science and technology. We show that the prequential minimum description length principle (MDL) can be used to derive a practical scoring function for Bayesian networks when flexible and overparametrized neural networks are used to model the conditional probability distributions between observed variables. MDL represents an embodiment of Occam's Razor and we obtain plausible and parsimonious graph structures without relying on sparsity inducing priors or other regularizers which must be tuned. Empirically we demonstrate competitive results on synthetic and real-world data. The score often recovers the correct structure even in the presence of strongly nonlinear relationships between variables; a scenario were prior approaches struggle and usually fail. Furthermore we discuss how the the prequential score relates to recent work that infers causal structure from the speed of adaptation when the observations come from a source undergoing distributional shift.
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