In domains such as ecological systems, collaborations, and the human brain the variables interact in complex ways. Yet accurately characterizing higher-order variable interactions (HOIs) is a difficult problem that is further exacerbated when the HOIs change across the data. To solve this problem we propose a new method called Local Correlation Explanation (CorEx) to capture HOIs at a local scale by first clustering data points based on their proximity on the data manifold. We then use a multivariate version of the mutual information called the total correlation, to construct a latent factor representation of the data within each cluster to learn the local HOIs. We use Local CorEx to explore HOIs in synthetic and real world data to extract hidden insights about the data structure. Lastly, we demonstrate Local CorEx's suitability to explore and interpret the inner workings of trained neural networks.

翻译：在生态系统、协作系统以及人脑等领域中，变量之间以复杂的方式相互作用。然而，准确刻画高阶变量交互（HOIs）是一个难题，当HOIs随数据变化时这一问题更加突出。为解决该问题，我们提出一种名为局部相关性解释（Local Correlation Explanation, Local CorEx）的新方法，通过基于数据流形上邻近性对数据点进行聚类，在局部尺度上捕捉HOIs。随后，我们利用一种名为总相关性（total correlation）的多变量互信息形式，在每个聚类内构建数据的潜在因子表示，以学习局部HOIs。我们使用局部CorEx在合成数据和真实世界数据中探索HOIs，以提取关于数据结构的隐藏信息。最后，我们证明局部CorEx在探索和解释已训练神经网络内部工作机制方面的适用性。