Most causal discovery algorithms find causal structure among a set of observed variables. Learning the causal structure among latent variables remains an important open problem, particularly when using high-dimensional data. In this paper, we address a problem for which it is known that inputs cause outputs, and these causal relationships are encoded by a causal network among a set of an unknown number of latent variables. We developed a deep learning model, which we call a redundant input neural network (RINN), with a modified architecture and a regularized objective function to find causal relationships between input, hidden, and output variables. More specifically, our model allows input variables to directly interact with all latent variables in a neural network to influence what information the latent variables should encode in order to generate the output variables accurately. In this setting, the direct connections between input and latent variables makes the latent variables partially interpretable; furthermore, the connectivity among the latent variables in the neural network serves to model their potential causal relationships to each other and to the output variables. A series of simulation experiments provide support that the RINN method can successfully recover latent causal structure between input and output variables.

本文介绍了一种基于深度学习的RINN模型，通过直接连接输入和潜在变量，使用修改后的结构和正则化目标函数来解决在高维数据中学习到潜在变量间因果结构的问题，并在模拟实验中验证了该方法的有效性。

用多余输入的神经网络学习潜在因果结构