2013/01/26 by David N. Reshef, Yakir Reshef, Reshef, David +5 · 3 citations
Mathematics · Computer Science · #Advanced Statistical Methods and Models #Statistical Methods and Inference #Bayesian Modeling and Causal Inference
paper · pdf · doi:10.48550/arxiv.1301.6314
A measure of dependence is said to be equitable if it gives similar scores to\nequally noisy relationships of different types. Equitability is important in\ndata exploration when the goal is to identify a relatively small set of\nstrongest associations within a dataset as opposed to finding as many non-zero\nassociations as possible, which often are too many to sift through. Thus an\nequitable statistic, such as the maximal information coefficient (MIC), can be\nuseful for analyzing high-dimensional data sets. Here, we explore both\nequitability and the properties of MIC, and discuss several aspects of the\ntheory and practice of MIC. We begin by presenting an intuition behind the\nequitability of MIC through the exploration of the maximization and\nnormalization steps in its definition. We then examine the speed and optimality\nof the approximation algorithm used to compute MIC, and suggest some directions\nfor improving both. Finally, we demonstrate in a range of noise models and\nsample sizes that MIC is more equitable than natural alternatives, such as\nmutual information estimation and distance correlation.\n