Learning Dependence Representations with CNNs

To measure statistical dependence, correlations have been widely used in the fields of statistics and machine learning. However, due to a large amount of types of nonlinear dependence, it is very challenging to distinguish the types with a correlation coefficient. In this paper, we present a new approach to capturing the dependence from 2D histograms, which has a potential to learn task-specific representations of dependence. With the representations learned on 427 datasets, our models are able to predict Pearson's correlation coefficient and distance correlation coefficient almost perfectly. Furthermore, in terms of computing speed of distance correlation, our proposed method is faster than Huo's method [1], when a sample size is large.