This paper introduces a probabilistic architecture called sum–product graphical model (SPGM). SPGMs represent a class of probability distributions that combines, for the first time, the semantics of probabilistic graphical models (GMs) with the evaluation efficiency of sum–product networks (SPNs): Like SPNs, SPGMs always enable tractable inference using a class of models that incorporate context specific independence. Like GMs, SPGMs provide a high-level model interpretation in terms of conditional independence assumptions and corresponding factorizations. Thus, this approach provides new connections between the fields of SPNs and GMs, and enables a high-level interpretation of the family of distributions encoded by SPNs. We provide two applications of SPGMs in density estimation with empirical results close to or surpassing state-of-the-art models. The theoretical and practical results demonstrate that jointly exploiting properties of SPNs and GMs is an interesting direction of future research.

中文翻译：

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总和积图模型

本文介绍了一种称为 sum–product 图形模型 (SPGM) 的概率架构。SPGMs 代表了一类概率分布，它首次将概率图模型 (GMs) 的语义与和-积网络 (SPNs) 的评估效率相结合：与 SPNs 一样，SPGMs 总是能够使用一类模型进行易处理的推理包含特定于上下文的独立性。与 GM 一样，SPGM 在条件独立假设和相应的因式分解方面提供了高级模型解释。因此，这种方法提供了 SPNs 和 GMs 领域之间的新连接，并能够对由 SPNs 编码的分布族进行高级解释。我们提供了 SPGM 在密度估计中的两种应用，其经验结果接近或超过最先进的模型。理论和实践结果表明，联合开发 SPNs 和 GMs 的特性是未来研究的一个有趣方向。