Conditional density estimation is a fundamental task in statistics and machine learning. In many applications, the target variable Y is univariate, while the conditioning set X can be high-dimensional, posing significant challenges for estimation methods. This work focuses specifically on this setting and aims to develop a conditional density estimation method that effectively handles the high dimensionality of X while leveraging the univariate nature of Y. To this end, we propose a novel approach inspired by noise-contrastive methods. Our methodology reformulates the conditional density estimation problem into two simpler sub-tasks: marginal density estimation and binary classification. Our method, called Marginal Contrastive Discrimination (MCD), demonstrates performance that is comparable to, and sometimes surpasses, state-of-the-art conditional density estimation approaches, especially when the dimensionality of the conditioning set is high.
