Probabilistic Generating Circuits – Demystified
arxiv(2024)
摘要
Zhang et al. (ICML 2021, PLMR 139, pp. 12447-1245) introduced probabilistic
generating circuits (PGCs) as a probabilistic model to unify probabilistic
circuits (PCs) and determinantal point processes (DPPs). At a first glance,
PGCs store a distribution in a very different way, they compute the probability
generating polynomial instead of the probability mass function and it seems
that this is the main reason why PGCs are more powerful than PCs or DPPs.
However, PGCs also allow for negative weights, whereas classical PCs assume
that all weights are nonnegative. One of the main insights of our paper is that
the negative weights are responsible for the power of PGCs and not the
different representation. PGCs are PCs in disguise, in particular, we show how
to transform any PGC into a PC with negative weights with only polynomial
blowup.
PGCs were defined by Zhang et al. only for binary random variables. As our
second main result, we show that there is a good reason for this: we prove that
PGCs for categorial variables with larger image size do not support tractable
marginalization unless NP = P. On the other hand, we show that we can model
categorial variables with larger image size as PC with negative weights
computing set-multilinear polynomials. These allow for tractable
marginalization. In this sense, PCs with negative weights strictly subsume
PGCs.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要