Detecting Associations Based on the Multi-Variable Maximum Information Coefficient

The maximum information coefficient (MIC) is a novel and widely-using measure of association detection in large datasets. The most outstanding feature of MIC is that it has both generality and equability. However, MIC can only deal with two variables and cannot precisely estimate coupling associations of multiple variables. In this paper, we propose an extension of MIC to deal with multi-variable datasets, called the multi-variable maximum information coefficient (MMIC). Some inherited and novel properties of MMIC are proved, including generality, equability, monotonicity, and subadditivity. We design an algorithm based on greedy stepwise strategy and upper confidence bound (UCB) for an approximate calculation of MMIC. The tests of MMIC on generated datasets and examples on real datasets are carried out to detect known and novel associations.