Despite the remarkable empirical successes of Generative Adversarial Networks
(GANs), the theoretical guarantees for their statistical accuracy remain rather
pessimistic. In particular, the data distributions on which GANs are applied,
such as natural images, are often hypothesized to have an intrinsic
low-dimensional structure in a typically high-dimensional feature space, but
this is often not reflected in the derived rates in the state-of-the-art
analyses. In this paper, we attempt to bridge the gap between the theory and
practice of GANs and their bidirectional variant, Bi-directional GANs (BiGANs),
by deriving statistical guarantees on the estimated densities in terms of the
intrinsic dimension of the data and the latent space. We analytically show that
if one has access to $n$ samples from the unknown target distribution and the
network architectures are properly chosen, the expected Wasserstein-1 distance
of the estimates from the target scales as $O\left( n^{-1/d_\mu } \right)$ for
GANs and $O\left( n^{-1/(d_\mu+\ell)} \right)$ for BiGANs, where $d_\mu$ and
$\ell$ are the upper Wasserstein-1 dimension of the data-distribution and
latent-space dimension, respectively. The theoretical analyses not only suggest
that these methods successfully avoid the curse of dimensionality, in the sense
that the exponent of $n$ in the error rates does not depend on the data
dimension but also serve to bridge the gap between the theoretical analyses of
GANs and the known sharp rates from optimal transport literature. Additionally,
we demonstrate that GANs can effectively achieve the minimax optimal rate even
for non-smooth underlying distributions, with the use of larger generator
networks.

尽管生成对抗网络（GANs）在实证方面取得了显著的成功，但其统计准确性的理论保证仍然相对悲观。本论文试图在理论和 GANs 以及双向 GANs（BiGANs）的实践之间架起桥梁，通过推导出关于估计密度的统计保证，以数据的固有维度和潜在空间为基础。

关于生成对抗模型在低内在数据维度下的统计特性

On the Statistical Properties of Generative Adversarial Models for Low  Intrinsic Data Dimension

Anomaly detection is a significant and hence well-studied problem. However,
developing effective anomaly detection methods for complex and high-dimensional
data remains a challenge. As Generative Adversarial Networks (GANs) are able to
model the complex high-dimensional distributions of real-world data, they offer
a promising approach to address this challenge. In this work, we propose an
anomaly detection method, Adversarially Learned Anomaly Detection (ALAD) based
on bi-directional GANs, that derives adversarially learned features for the
anomaly detection task. ALAD then uses reconstruction errors based on these
adversarially learned features to determine if a data sample is anomalous. ALAD
builds on recent advances to ensure data-space and latent-space
cycle-consistencies and stabilize GAN training, which results in significantly
improved anomaly detection performance. ALAD achieves state-of-the-art
performance on a range of image and tabular datasets while being several
hundred-fold faster at test time than the only published GAN-based method.

本文提出一种基于双向 GAN 的异常检测方法 ALAD，通过对偶学习特征并利用这些特征的重构误差来确定数据样本是否异常，从而在一系列图像和表格数据集上取得了最先进的性能。