Conditional Density Estimation via Weighted Logistic Regressions
This work addresses the need for more informative conditional density estimation in statistics and machine learning, offering a computationally efficient parametric approach.
The paper tackles the problem of estimating conditional density functions to capture complex distributional features like multi-modality, asymmetry, or heteroskedasticity, proposing a novel parametric method that connects general density to inhomogeneous Poisson process likelihoods and achieves computational efficiency via weighted logistic regressions with block-wise alternating maximization and local case-control sampling.
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.