用生成式神经网络直接学习条件分布，无需复杂训练即可高效采样。
Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks
- 通过随机映射建模条件分布，避免直接估计密度函数。
- 在多个数据集上表现优于或媲美主流方法，且模型轻量易训练。
- 适合需要快速生成条件样本的场景，如不确定性量化与仿真。
我们提出条件推移神经网络（CPFN），一种用于条件分布估计的生成框架。不同于直接建模条件密度 $f_{Y|X}$，CPFN 学习一个随机映射 $φ=φ(x,u)$，使得 $φ(x,U)$ 与 $Y|X=x$ 的分布近似一致，其中 $U$ 是预定义的潜变量随机向量。该方法支持高效的条件采样，并可通过蒙特卡洛方法简便估算条件统计量。模型通过基于相对熵的损失函数进行训练，无需可逆性或对抗训练。我们建立了近渐近一致性理论结果，并实验表明，CPFN 在多个基准上性能可媲美甚至超越现有主流方法，包括核估计、树模型和主流深度学习技术，同时保持轻量与易训练特性。
原文摘要 · Abstract (English)
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 $φ=φ(x,u)$ such that $φ(x,U)$ 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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