关于单调概率电路与平方概率电路之间关系的研究
On the Relationship Between Monotone and Squared Probabilistic Circuits
AI总结：
本文证明单调电路与平方概率电路在表达能力上不可比较，并提出Inception PCs统一两者，采用复数参数，在表格和图像数据集上优于二者。
摘要：
概率电路是将函数表示为加权求和与乘积的计算图的一种统一表示。其主要应用在于概率建模，其中具有非负权重的电路（单调电路）可用于表示和学习密度/质量函数，并支持可处理的边际推理。近期，有研究提出将密度表示为电路函数的平方（平方电路）；这允许使用负权重同时保持可处理性，并且在表达能力上可能比单调电路呈指数级更高效。不幸的是，我们证明反向情况也成立，这意味着单调电路和平方电路在一般情况下是不可比较的。这引发了一个问题：我们能否调和这两种建模方法，并实际上对它们进行改进。我们给出了肯定回答，提出了一种新型电路——Inception PCs，它自然地涵盖了单调电路和平方电路作为特例，并采用复数参数。实验上，我们验证了Inception PCs在一系列表格和图像数据集上可以胜过单调电路和平方电路。
英文摘要：
Probabilistic circuits are a unifying representation of functions as computation graphs of weighted sums and products. Their primary application is in probabilistic modeling, where circuits with non-negative weights (monotone circuits) can be used to represent and learn density/mass functions, with tractable marginal inference. Recently, it was proposed to instead represent densities as the square of the circuit function (squared circuits); this allows the use of negative weights while retaining tractability, and can be exponentially more expressive efficient than monotone circuits. Unfortunately, we show the reverse also holds, meaning that monotone circuits and squared circuits are incomparable in general. This raises the question of whether we can reconcile, and indeed improve upon the two modeling approaches. We answer in the positive by proposing Inception PCs, a novel type of circuit that naturally encompasses both monotone circuits and squared circuits as special cases, and employs complex parameters. Empirically, we validate that Inception PCs can outperform both monotone and squared circuits on a range of tabular and image datasets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
