OCDE: Odds Conditional Density Estimator

TL;DR

OCDE introduces a novel approach to conditional density estimation by transforming the problem into odds estimation through a binary classifier, demonstrating competitive performance on simulated and real data.

Contribution

The paper proposes OCDE, a new method that simplifies conditional density estimation by using odds estimation, which is easier to implement and competitive with existing methods.

Findings

OCDE performs well on simulated data.

OCDE is competitive with state-of-the-art methods on real datasets.

Transforming CDE into odds estimation simplifies the problem.

Abstract

Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about the uncertainty of the random variable of interest. In this paper, we propose a new methodology called Odds Conditional Density Estimator (OCDE) to estimate conditional densities in a supervised learning scheme. The main idea is that it is very difficult to estimate $p_{x,y}$ and $p_{x}$ in order to estimate the conditional density $p_{y|x}$, but by introducing an instrumental distribution, we transform the CDE problem into a problem of odds estimation, or similarly, training a binary probabilistic classifier. We demonstrate how OCDE works using simulated data and then test its performance against other known state-of-the-art CDE methods in real data. Overall, OCDE is competitive compared with these methods in real datasets.