Title: Scalable Expectation Estimation with Subtractive Mixture Models Show Chinese title

Title: 基于减法混合模型的可扩展期望估计

Abstract: 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 $\Delta\text{Ex}$. Show Chinese abstract

Abstract: 许多蒙特卡洛（MC）和重要性采样（IS）方法使用混合模型（MMs）因其简单性和能够捕捉多模态分布的能力。最近，减法混合模型（SMMs），即具有负系数的MMs，在生成建模中表现出更大的表达能力和成功。然而，它们的负参数使得采样变得复杂，需要成本高昂的自回归技术或无法在高维中扩展的接受-拒绝算法。在本工作中，我们利用SMMs的差分表示来构建一个无偏的IS估计器（$\Delta\text{Ex}$），消除了从SMM中采样的需求，使SMMs能够进行高维期望估计。在我们的实验中，我们表明$\Delta\text{Ex}$可以在MC估计中比自回归采样更快，同时达到相当的估计质量。此外，我们使用手工设计的提议对$\Delta\text{Ex}$进行了初步实验，获得了如何为$\Delta\text{Ex}$构建安全提议的初步见解。