标题： 通过隐式模型和最优传输成本最小化进行回归 显示英文标题

标题： Regression via Implicit Models and Optimal Transport Cost Minimization

摘要： 本文解决了回归的经典问题，该问题涉及映射的归纳学习，$y=f(x,z)$表示噪声，$z$表示噪声，$f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$。最近，条件生成对抗网络（CGAN）已被用于回归，并显示出优于其他标准方法如高斯过程回归的优势，因为它能够隐式地建模复杂的噪声形式。然而，当前用于回归的CGAN实现使用了经典的生成器-判别器架构和极小极大优化方法，由于训练不稳定或无法收敛等问题而以难以训练而闻名。在本文中，我们朝着隐式建模噪声的回归模型又迈进了一步，并提出了一种直接优化真实概率分布$p(y|x)$与估计分布$\hat{p}(y|x)$之间的最优传输成本的解决方案，且不会受到与极小极大方法相关的问题的影响。在各种合成和现实世界的数据集上，我们的解决方案取得了最先进的结果。本文的代码可在"https://github.com/gurdaspuriya/ot_regression"获取。 显示英文摘要

摘要： This paper addresses the classic problem of regression, which involves the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$. Recently, Conditional GAN (CGAN) has been applied for regression and has shown to be advantageous over the other standard approaches like Gaussian Process Regression, given its ability to implicitly model complex noise forms. However, the current CGAN implementation for regression uses the classical generator-discriminator architecture with the minimax optimization approach, which is notorious for being difficult to train due to issues like training instability or failure to converge. In this paper, we take another step towards regression models that implicitly model the noise, and propose a solution which directly optimizes the optimal transport cost between the true probability distribution $p(y|x)$ and the estimated distribution $\hat{p}(y|x)$ and does not suffer from the issues associated with the minimax approach. On a variety of synthetic and real-world datasets, our proposed solution achieves state-of-the-art results. The code accompanying this paper is available at "https://github.com/gurdaspuriya/ot_regression".