  Detecting statistical interactions between input features is a crucial and
challenging task. Recent advances demonstrate that it is possible to extract
learned interactions from trained neural networks. It has also been observed
that, in neural networks, any interacting features must follow a strongly
weighted connection to common hidden units. Motivated by the observation, in
this paper, we propose to investigate the interaction detection problem from a
novel topological perspective by analyzing the connectivity in neural networks.
Specially, we propose a new measure for quantifying interaction strength, based
upon the well-received theory of persistent homology. Based on this measure, a
Persistence Interaction detection~(PID) algorithm is developed to efficiently
detect interactions. Our proposed algorithm is evaluated across a number of
interaction detection tasks on several synthetic and real world datasets with
different hyperparameters. Experimental results validate that the PID algorithm
outperforms the state-of-the-art baselines.
