Conditional density estimation with class probability estimators

Abstract

Many regression schemes deliver a point estimate only, but often it is useful or even essential to quantify the uncertainty inherent in a prediction. If a conditional density estimate is available, then prediction intervals can be derived from it. In this paper we compare three techniques for computing conditional density estimates using a class probability estimator, where this estimator is applied to the discretized target variable and used to derive instance weights for an underlying univariate density estimator; this yields a conditional density estimate. The three density estimators we compare are: a histogram estimator that has been used previously in this context, a normal density estimator, and a kernel estimator. In our experiments, the latter two deliver better performance, both in terms of cross-validated log-likelihood and in terms of quality of the resulting prediction intervals. The empirical coverage of the intervals is close to the desired confidence level in most cases. We also include results for point estimation, as well as a comparison to Gaussian process regression and nonparametric quantile estimation.