By sampling from the latent space of an autoencoder and decoding the latent
space samples to the original data space, any autoencoder can simply be turned
into a generative model. For this to work, it is necessary to model the
autoencoder's latent space with a distribution from which samples can be
obtained. Several simple possibilities (kernel density estimates, Gaussian
distribution) and more sophisticated ones (Gaussian mixture models, copula
models, normalization flows) can be thought of and have been tried recently.
This study aims to discuss, assess, and compare various techniques that can be
used to capture the latent space so that an autoencoder can become a generative
model while striving for simplicity. Among them, a new copula-based method, the
Empirical Beta Copula Autoencoder, is considered. Furthermore, we provide
insights into further aspects of these methods, such as targeted sampling or
synthesizing new data with specific features.

通过从自动编码器的潜空间进行采样并将样本解码到原始数据空间，可以将任何自动编码器简单地转变为生成模型。本研究旨在讨论、评估和比较可以用于捕捉潜空间的各种技术，以使自动编码器成为生成模型，同时追求简单性。其中，考虑了一种基于 copula 的新方法，即经验 Beta Copula 自动编码器。此外，我们还提供了关于这些方法进一步方面的见解，例如有针对性的采样或合成具有特定特征的新数据。

学习非参数高维生成模型：经验贝塔 - 科普拉自动编码器

Learning Nonparametric High-Dimensional Generative Models: The  Empirical-Beta-Copula Autoencoder

Critical infrastructures like water treatment facilities and power plants
depend on industrial control systems (ICS) for monitoring and control, making
them vulnerable to cyber attacks and system malfunctions. Traditional ICS
anomaly detection methods lack transparency and interpretability, which make it
difficult for practitioners to understand and trust the results. This paper
proposes a two-phase dual Copula-based Outlier Detection (COPOD) method that
addresses these challenges. The first phase removes unwanted outliers using an
empirical cumulative distribution algorithm, and the second phase develops two
parallel COPOD models based on the output data of phase 1. The method is based
on empirical distribution functions, parameter-free, and provides
interpretability by quantifying each feature's contribution to an anomaly. The
method is also computationally and memory-efficient, suitable for low- and
high-dimensional datasets. Experimental results demonstrate superior
performance in terms of F1-score and recall on three open-source ICS datasets,
enabling real-time ICS anomaly detection.

本文提出了一种基于 Copula 的二阶段异常检测方法，以解决传统方法在透明度、可解释性和性能等方面存在的挑战，并在三个开源的 ICS 数据集中进行了实验验证，表现出优异的检测性能和计算效率，适合于低和高维度数据集的实时 ICS 异常检测。