We propose a comprehensive sample-based method for assessing the quality of
generative models. The proposed approach enables the estimation of the
probability that two sets of samples are drawn from the same distribution,
providing a statistically rigorous method for assessing the performance of a
single generative model or the comparison of multiple competing models trained
on the same dataset. This comparison can be conducted by dividing the space
into non-overlapping regions and comparing the number of data samples in each
region. The method only requires samples from the generative model and the test
data. It is capable of functioning directly on high-dimensional data, obviating
the need for dimensionality reduction. Significantly, the proposed method does
not depend on assumptions regarding the density of the true distribution, and
it does not rely on training or fitting any auxiliary models. Instead, it
focuses on approximating the integral of the density (probability mass) across
various sub-regions within the data space.

我们提出了一种综合的基于样本的方法来评估生成模型的质量。该方法能够估计从同一分布中抽取两组样本的概率，从而为评估单个生成模型或比较在相同数据集上训练的多个竞争模型的性能提供了统计学上严谨的方法。该方法能够直接在高维数据上进行操作，无需降维，且不依赖于对真实分布密度的假设，也不依赖于训练或拟合任何辅助模型，而是专注于近似计算数据空间中各个子区域的密度（概率质量）的积分。

PQMass：使用概率质量估计评估生成模型质量

PQMass: Probabilistic Assessment of the Quality of Generative Models  using Probability Mass Estimation

The dramatic increase of autonomous systems subject to variable environments
has given rise to the pressing need to consider risk in both the synthesis and
verification of policies for these systems. This paper aims to address a few
problems regarding risk-aware verification and policy synthesis, by first
developing a sample-based method to bound the risk measure evaluation of a
random variable whose distribution is unknown. These bounds permit us to
generate high-confidence verification statements for a large class of robotic
systems. Second, we develop a sample-based method to determine solutions to
non-convex optimization problems that outperform a large fraction of the
decision space of possible solutions. Both sample-based approaches then permit
us to rapidly synthesize risk-aware policies that are guaranteed to achieve a
minimum level of system performance. To showcase our approach in simulation, we
verify a cooperative multi-agent system and develop a risk-aware controller
that outperforms the system's baseline controller. We also mention how our
approach can be extended to account for any $g$-entropic risk measure - the
subset of coherent risk measures on which we focus.

本文提出了一种基于样本的方法来解决固有于自主系统中变化环境的风险问题，能够生成高置信度的验证声明和快速合成保证实现最低系统性能的风险感知策略，并在仿真中验证了一种多主体协作系统和其风险感知控制器的优越性能。