Monte Carlo Dependency Estimation

Abstract: Estimating the dependency of variables is a fundamental task in data analysis. Identifying the relevant attributes in databases leads to better data understanding and also improves the performance of learning algorithms, both in terms of runtime and quality. In data streams, dependency monitoring provides key insights into the underlying process, but is challenging. In this paper, we propose Monte Carlo Dependency Estimation (MCDE), a theoretical framework to estimate multivariate dependency in static and dynamic data. MCDE quantifies dependency as the average discrepancy between marginal and conditional distributions via Monte Carlo simulations. Based on this framework, we present Mann-Whitney P (MWP), a novel dependency estimator. We show that MWP satisfies a number of desirable properties and can accommodate any kind of numerical data. We demonstrate the superiority of our estimator by comparing it to the state-of-the-art multivariate dependency measures.