Causal inference from observation data is a core problem in many scientific fields. Here we present a general supervised deep learning framework that infers causal interactions by transforming the input vectors to an image-like representation for every pair of inputs. Given a training dataset we first construct a normalized empirical probability density distribution (NEPDF) matrix. We then train a convolutional neural network (CNN) on NEPDFs for causality predictions. We tested the method on several different simulated and real world data and compared it to prior methods for causal inference. As we show, the method is general, can efficiently handle very large datasets and improves upon prior methods.

翻译：从观测数据得出的因果推断是许多科学领域的一个核心问题。 这里我们提出了一个受监督的总体深层次学习框架, 通过将输入矢量转换成每对投入的图像表示方式来推断因果关系。 根据一个培训数据集,我们首先构建了一个标准化的经验概率密度分布矩阵(NEPDF) 。 然后,我们用NEPDFs培训了一个关于因果关系预测的进化神经网络(CNN ) 。 我们用几种不同的模拟和真实的世界数据测试了该方法,并将其与先前的因果推断方法进行了比较。 正如我们所显示的,该方法是一般性的,可以有效地处理非常大的数据元并改进先前的方法。