Least Squares Conditional Density Estimation in semi-supervised learning settings

The goal of regression analysis is to estimate the conditional mean of an input-output relation. But if the data has multimodality, highly asymmetric distribution or heteroscedastic noise, then estimating the conditional mean is not sufficient. In these scenarios, the conditional distribution itself needs to be estimated. Recently a method called Least Squares Conditional Density Estimation (LSCDE) has been proposed for estimating conditional density. LSCDE estimates the conditional density by considering it as a ratio of two densities and directly estimating the ratio. This method works quite well but cannot make use of any available unlabeled samples. In this paper, the method LSCDE has been extended to semi-supervised settings so that the unlabeled samples can be used to improve accuracy of estimation.