MCD: Marginal Contrastive Discrimination for conditional density estimation

Abstract: We consider the problem of conditional density estimation, which is a major topic of interest in the fields of statistical and machine learning. Our method, called Marginal Contrastive Discrimination, MCD, reformulates the conditional density function into two factors, the marginal density function of the target variable and a ratio of density functions which can be estimated through binary classification. Like noise-contrastive methods, MCD can leverage state-of-the-art supervised learning techniques to perform conditional density estimation, including neural networks. Our benchmark reveals that our method significantly outperforms in practice existing methods on most density models and regression datasets.