用广义Wasserstein-2距离高效训练神经网络重建含连续与类别变量的随机场模型。
A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks
- 基于广义局部平方Wasserstein-2损失函数训练随机神经网络。
- 在混合变量分布重构与时空数据中的复杂噪声系统学习任务中表现优异。
- 适用于不确定性量化场景，尤其适合处理连续与类别混合变量建模。
本文提出一种新型广义Wasserstein-2距离方法，用于高效训练随机神经网络以重建包含连续与类别成分的随机场模型。我们证明，在非限制性条件下，随机神经网络可在Wasserstein-2距离度量下逼近随机场模型。此外，通过最小化所提出的广义局部平方Wasserstein-2损失函数，该网络可高效训练。我们在多种不确定性量化任务中验证了该方法的有效性，包括分类、混合随机变量分布重构，以及从时空数据中学习复杂的噪声动力系统。
原文摘要 · Abstract (English)
In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical components. We prove that a stochastic neural network can approximate random field models under a Wasserstein-2 distance metric under nonrestrictive conditions. Furthermore, this stochastic neural network can be efficiently trained by minimizing our proposed generalized local squared Wasserstein-2 loss function. We showcase the effectiveness of our proposed approach in various uncertainty quantification tasks, including classification, reconstructing the distribution of mixed random variables, and learning complex noisy dynamical systems from spatiotemporal data.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。