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arXiv 2302.06188cs.AI
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通过结构感知增强基于SMT的加权模型积分

Enhancing SMT-based Weighted Model Integration by Structure Awareness

University of Trento(特伦托大学);DISI, University of Trento(特伦托大学DISI(信息工程与计算机科学系))

Giuseppe Spallitta, Gabriele Masina, Paolo Morettin, Andrea Passerini, Roberto Sebastiani

AI总结:

本文提出一种结构感知的基于SMT的加权模型积分算法,通过结合SMT枚举与问题结构编码避免冗余模型生成,并兼容精确与近似积分技术,显著提升了混合领域概率推理的可扩展性。

摘要:

为概率推理开发高效的精确与近似算法是人工智能研究的长期目标。尽管在处理纯离散或纯连续领域方面已取得实质性进展,但将已开发的解决方案用于处理以离散变量、连续变量及其关系为特征的混合领域却极为困难。加权模型积分(Weighted Model Integration, WMI)近年来作为一种用于混合领域概率推理的统一形式化方法而出现。尽管近期已有大量工作,但让WMI算法能够随混合问题的复杂度而扩展仍然是一项挑战。在本文中,我们指出了现有最先进解决方案的一些重大局限,并开发了一种算法,该算法将基于SMT的枚举(一种形式验证中的高效技术)与对问题结构的有效编码相结合。这使得我们的算法能够避免生成冗余模型,从而大幅节省计算开销。此外,我们展示了基于SMT的方法如何能够无缝地处理不同的积分技术,包括精确方法和近似方法,从而显著扩展了WMI技术能够处理的问题集合。在合成数据集和真实世界数据集上的广泛实验评估证实了所提解决方案相对于现有替代方案的显著优势。该技术的应用潜力还在一个旨在验证概率程序公平性的原型任务上得到了进一步展示。

英文摘要:

The development of efficient exact and approximate algorithms for probabilistic inference is a long-standing goal of artificial intelligence research. Whereas substantial progress has been made in dealing with purely discrete or purely continuous domains, adapting the developed solutions to tackle hybrid domains, characterised by discrete and continuous variables and their relationships, is highly non-trivial. Weighted Model Integration (WMI) recently emerged as a unifying formalism for probabilistic inference in hybrid domains. Despite a considerable amount of recent work, allowing WMI algorithms to scale with the complexity of the hybrid problem is still a challenge. In this paper we highlight some substantial limitations of existing state-of-the-art solutions, and develop an algorithm that combines SMT-based enumeration, an efficient technique in formal verification, with an effective encoding of the problem structure. This allows our algorithm to avoid generating redundant models, resulting in drastic computational savings. Additionally, we show how SMT-based approaches can seamlessly deal with different integration techniques, both exact and approximate, significantly expanding the set of problems that can be tackled by WMI technology. An extensive experimental evaluation on both synthetic and real-world datasets confirms the substantial advantage of the proposed solution over existing alternatives. The application potential of this technology is further showcased on a prototypical task aimed at verifying the fairness of probabilistic programs.

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。

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