Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks

• URL: http://arxiv.org/abs/2511.14455v2
• Date: Thu, 20 Nov 2025 18:06:01 GMT
• Title: Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks
• Authors: Nicola Rares Franco, Lorenzo Tedesco,
• Abstract summary: We introduce conditional push-forward neural networks (CPFN), a generative framework for conditional distribution estimation.<n>CPFN learns a map $varphi=varphi(x,u)$ such that $varphi(x,U)$ and $Y|X=x$ follow approximately the same law.<n>It is trained via an objective function derived from a Kullback-Leibler formulation, without requiring invertibility or adversarial training.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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