Conditional Density Estimation via Weighted Logistic Regressions

TL;DR

This paper introduces a new parametric method for estimating conditional density functions using weighted logistic regressions, leveraging Poisson process models for improved flexibility and computational efficiency.

Contribution

It establishes a novel connection between conditional density estimation and inhomogeneous Poisson processes, enabling efficient maximum likelihood estimation.

Findings

Effective in modeling multi-modal, asymmetric, and heteroskedastic distributions

Computationally efficient due to block-wise alternating maximization and local sampling

Demonstrated through simulation studies

Abstract

Compared to the conditional mean as a simple point estimator, the conditional density function is more informative to describe the distributions with multi-modality, asymmetry or heteroskedasticity. In this paper, we propose a novel parametric conditional density estimation method by showing the connection between the general density and the likelihood function of inhomogeneous Poisson process models. The maximum likelihood estimates can be obtained via weighted logistic regressions, and the computation can be significantly relaxed by combining a block-wise alternating maximization scheme and local case-control sampling. We also provide simulation studies for illustration.