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.

我们提出了一种名为本地相关解释（CorEx）的新方法，通过首先基于数据流形上的接近程度对数据点进行聚类，以在局部尺度上捕获高阶变量相互作用（HOIs），以解决在复杂的生态系统、合作关系和人脑等领域中准确表征 HOIs 变得困难并且当 HOIs 在数据中变化时进一步加剧的问题。然后，我们使用一种名为总相关性的多变量互信息构建每个聚类中数据的潜在因子表示，以学习局部 HOIs。我们使用本地 CorEx 探索合成和真实世界数据中的 HOIs，以提取有关数据结构的隐藏见解。最后，我们演示了本地 CorEx 用于探索和解释经过训练的神经网络内部运作的适用性。