论文标题
用单调gans进行有条件采样：从生成模型到无可能的推断
Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference
论文作者
论文摘要
我们提出了一个新的框架，用于使用块三角传输图的条件采样概率度量。我们在BANACH空间设置中开发了块三角形传输的理论基础，建立了一般条件，在该条件下可以实现条件采样，并在单调块三角形图和最佳传输之间绘制连接。基于该理论，我们引入了一种计算方法，称为单调生成对抗网络（M-GAN），以学习合适的块三角图。我们的算法仅使用来自基本关节概率的样品，因此无可能。使用M-GAN进行的数值实验表明，在合成示例，涉及普通和部分微分方程的贝叶斯逆问题以及概率图像中的贝叶斯逆问题中准确取样。
We present a novel framework for conditional sampling of probability measures, using block triangular transport maps. We develop the theoretical foundations of block triangular transport in a Banach space setting, establishing general conditions under which conditional sampling can be achieved and drawing connections between monotone block triangular maps and optimal transport. Based on this theory, we then introduce a computational approach, called monotone generative adversarial networks (M-GANs), to learn suitable block triangular maps. Our algorithm uses only samples from the underlying joint probability measure and is hence likelihood-free. Numerical experiments with M-GAN demonstrate accurate sampling of conditional measures in synthetic examples, Bayesian inverse problems involving ordinary and partial differential equations, and probabilistic image in-painting.
