Many Monte Carlo (MC) and importance sampling (IS) methods use mixture models (MMs) for their simplicity and ability to capture multimodal distributions. Recently, subtractive mixture models (SMMs), i.e. MMs with negative coefficients, have shown greater expressiveness and success in generative modeling. However, their negative parameters complicate sampling, requiring costly auto-regressive techniques or accept-reject algorithms that do not scale in high dimensions. In this work, we use the difference representation of SMMs to construct an unbiased IS estimator ($\Delta\text{Ex}$) that removes the need to sample from the SMM, enabling high-dimensional expectation estimation with SMMs. In our experiments, we show that $\Delta\text{Ex}$ can achieve comparable estimation quality to auto-regressive sampling while being considerably faster in MC estimation. Moreover, we conduct initial experiments with $\Delta\text{Ex}$ using hand-crafted proposals, gaining first insights into how to construct safe proposals for $\Delta\text{Ex}$.

翻译：许多蒙特卡洛（MC）和重要性采样（IS）方法因其简单性和捕捉多模态分布的能力而使用混合模型（MMs）。最近，减性混合模型（SMMs），即具有负系数的混合模型，在生成建模中展现出更强的表达能力和成功应用。然而，其负参数使得采样变得复杂，需要成本高昂的自回归技术或在高维情况下无法扩展的接受-拒绝算法。在本工作中，我们利用SMMs的差分表示构建了一个无偏的重要性采样估计器（$\Delta\text{Ex}$），该估计器无需从SMM中采样，从而实现了使用SMMs进行高维期望估计。在我们的实验中，我们证明$\Delta\text{Ex}$能够达到与自回归采样相当的估计质量，同时在MC估计中显著更快。此外，我们使用手工设计的提议分布对$\Delta\text{Ex}$进行了初步实验，首次获得了关于如何为$\Delta\text{Ex}$构建安全提议分布的见解。