On characterizing optimal Wasserstein GAN solutions for non-Gaussian data
On characterizing optimal Wasserstein GAN solutions for non-Gaussian data
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DOI：
10.1109/isit54713.2023.10206785
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Yujia Huang;Shih-Chun Lin;Yu-Chih Huang;Kuan-Hui Lyu;Hsin-Hua Shen;Wan-Yi Lin
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文献类型：
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作者：
Yujia Huang;Shih-Chun Lin;Yu-Chih Huang;Kuan-Hui Lyu;Hsin-Hua Shen;Wan-Yi Lin
生成对抗网络（GAN）旨在通过参数化神经网络（NN）来近似未知分布。虽然GAN已广泛应用于强化和半监督学习以及计算机视觉任务，但选择其参数通常需要进行详尽的搜索，并且只有少数选择方法可以被证明是理论上最优的。最有前途的GAN变体之一是Wasserstein GAN（WGAN）。WGAN最优参数的先前工作仅限于线性二次高斯（LQG）设置，其中NN是线性的，数据是高斯的。在本文中，我们专注于最佳WGAN参数的LQG设置以外的特征。我们推导出具有非线性sigmoid和ReLU激活函数的一维WGAN的封闭形式的最佳参数。还讨论了高维WGAN的扩展。实验结果表明，我们的封闭形式的WGAN参数具有良好的收敛行为与高斯和拉普拉斯分布下的数据。
The generative adversarial network (GAN) aims to approximate an unknown distribution via a parameterized neural network (NN). While GANs have been widely applied in reinforcement and semi-supervised learning as well as computer vision tasks, selecting their parameters often needs an exhaustive search and only a few selection methods can be proved to be theoretically optimal. One of the most promising GAN variants is the Wasserstein GAN (WGAN). Prior work on optimal parameters for WGAN is limited to the linear-quadratic-Gaussian (LQG) setting, where the NN is linear and the data is Gaussian. In this paper, we focus on the characterization of optimal WGAN parameters beyond the LQG setting. We derive closed-form optimal parameters for one-dimensional WGANs with non-linear sigmoid and ReLU activation functions. Extensions to high-dimensional WGANs are also discussed. Empirical studies show that our closed-form WGAN parameters have good convergence behavior with data under both Gaussian and Laplace distributions.