Universal Dependency Analysis

Abstract: Most data is multi-dimensional. Discovering whether any subset of dimensions, or subspaces, of such data is significantly correlated is a core task in data mining. To do so, we require a measure that quantifies how correlated a subspace is. For practical use, such a measure should be universal in the sense that it captures correlation in subspaces of any dimensionality and allows to meaningfully compare correlation scores across different subspaces, regardless how many dimensions they have and what specific statistical properties their dimensions possess. Further, it would be nice if the measure can non-parametrically and efficiently capture both linear and non-linear correlations. In this paper, we propose UDS, a multivariate correlation measure that fulfills all of these desiderata. In short, we define \uds based on cumulative entropy and propose a principled normalization scheme to bring its scores across different subspaces to the same domain, enabling universal correlation assessment. UDS is purely non-parametric as we make no assumption on data distributions nor types of correlation. To compute it on empirical data, we introduce an efficient and non-parametric method. Extensive experiments show that UDS outperforms state of the art.