Probabilistic Generating Circuits
Probabilistic Generating Circuits
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发表时间：
2021-02
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通讯作者：
Honghua Zhang;Brendan Juba;Guy Van den Broeck
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作者：
Honghua Zhang;Brendan Juba;Guy Van den Broeck
生成在组合和概率理论中广泛使用的函数，将函数值编码为多项式的系数。在本文中，我们探讨了它们作为一种可处理的概率模型的用途，并提出了概率生成电路（PGC）以进行有效表示。 PGC比许多现有的可行概率模型（包括确定点过程（DPP），概率电路（PC）（例如Sum-raprouctuct网络和可拖动图形模型），PGC的表现力更高。我们认为，PGC不仅是一个统一现有模型截然不同的理论框架，而且在对现实数据进行建模方面表现出巨大的潜力。我们展示了一类简单的PGC，这些PGC并未通过PC和DPP的简单组合来微不足道，并在密度估计基准的套件上获得竞争性能。我们还强调了PGCS与强烈雷利分布理论的联系。
Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.