Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks
This provides a lightweight and easy-to-train method for conditional distribution estimation, which is useful for applications requiring conditional statistics, though it appears incremental as it builds on existing generative and neural network approaches.
The paper tackled the problem of conditional distribution estimation by introducing conditional push-forward neural networks (CPFN), a generative framework that learns a stochastic map for efficient conditional sampling and estimation, achieving performance competitive with or superior to state-of-the-art methods.
We introduce conditional push-forward neural networks (CPFN), a generative framework for conditional distribution estimation. Instead of directly modeling the conditional density $f_{Y|X}$, CPFN learns a stochastic map $\varphi=\varphi(x,u)$ such that $\varphi(x,U)$ and $Y|X=x$ follow approximately the same law, with $U$ a suitable random vector of pre-defined latent variables. This enables efficient conditional sampling and straightforward estimation of conditional statistics through Monte Carlo methods. The model is trained via an objective function derived from a Kullback-Leibler formulation, without requiring invertibility or adversarial training. We establish a near-asymptotic consistency result and demonstrate experimentally that CPFN can achieve performance competitive with, or even superior to, state-of-the-art methods, including kernel estimators, tree-based algorithms, and popular deep learning techniques, all while remaining lightweight and easy to train.