||Quantifying dependencies among variables is a fundamental task in data analysis. It allows to understand data and to identify the variables required to answer specific questions. Recent studies have positioned Monte Carlo Dependency Estimation (MCDE) as a state-of-the-art tool in this field.
MCDE quantifies dependencies as the average discrepancy between marginal and conditional distributions. In practice, this value is approximated with a dependency estimator. However, the original implementation of this estimator converges rather slowly, which leads to suboptimal results in terms of statistical power. Moreover, MCDE is only able to quantify dependencies among univariate random variables, but not multivariate ones. In this thesis, we make 2 major improvements to MCDE. First, we propose 4 new dependency estimators with faster convergence. We show that MCDE equipped with these new estimators achieves higher statistical power. Second, we generalize MCDE to GMCDE (Generalized Monte Carlo Dependency Estimation) to quantify dependencies among multivariate random variables. We show that GMCDE inherits all the desirable properties of MCDE and demonstrate its superiority against the state-of-the-art dependency measures with experiments.