Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive mixture models (SMMs), have been proposed as a potentially more expressive alternative. However, how to effectively use SMMs for VI and IS is still an open question as they do not provide latent variable semantics and therefore cannot use sampling schemes for classical MMs. In this work, we study how to circumvent this issue by designing several expectation estimators for IS and learning schemes for VI with SMMs, and we empirically evaluate them for distribution approximation. Finally, we discuss the additional challenges in estimation stability and learning efficiency that they carry and propose ways to overcome them. Code is available at: https://github.com/april-tools/delta-vi.

翻译：经典混合模型作为变分推理和重要性采样等近似推理场景中广泛使用的易处理拟议案，近年来出现了具有负系数的混合模型——即减法混合模型，它被提出作为更具表达力的替代方案。然而，如何有效将减法混合模型应用于变分推理和重要性采样仍是待解决的问题，因为这类模型缺乏隐变量语义，无法沿用经典混合模型的采样方案。本研究通过设计适用于重要性采样的多种期望估计器及适用于变分推理的减法混合模型学习方案，实证评估了它们在分布近似任务中的表现。最后，我们讨论了这些方法在估计稳定性和学习效率方面面临的额外挑战，并提出了相应的解决方案。代码开源地址：https://github.com/april-tools/delta-vi。