Computationally efficient variational-like approximations of possibilistic inferential models

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning Pub Date : 2025-06-13 DOI:10.1016/j.ijar.2025.109506

Leonardo Cella , Ryan Martin

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引用次数: 0

Abstract

Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite the IM framework's theoretical and foundational advantages, efficient computation is a challenge. This paper presents a simple yet powerful numerical strategy for approximating the IM's possibility contour, or at least its α-cut for a specified

α \in (0, 1)

. Our proposal starts with the specification of a parametric family that, in a certain sense, approximately covers the credal set associated with the IM's possibility measure. Akin to variational inference, we then propose to tune the parameters of that parametric family so that its

100 (1 - α) %

credible set roughly matches the IM contour's α-cut. This parametric α-cut matching strategy implies a full approximation to the IM's possibility contour at a fraction of the computational cost associated with previous strategies.

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计算效率的似变分的可能性推理模型近似

推理模型（IMs）提供可证明的可靠的、数据驱动的、可能性的统计推断。但是，尽管IM框架具有理论和基础优势，但高效计算仍然是一个挑战。本文给出了一种简单而强大的数值策略来逼近IM的可能性轮廓，或者至少是它的α-cut对于指定的α∈(0,1)。我们的建议从参数族的规范开始，在某种意义上，它大致涵盖了与IM的可能性度量相关的凭证集。类似于变分推理，我们建议调整该参数族的参数，使其100(1−α)%可信集大致匹配IM轮廓的α-cut。这种参数α-切匹配策略意味着在与先前策略相关的计算成本的一小部分上完全逼近IM的可能性轮廓。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Approximate Reasoning 工程技术-计算机：人工智能

CiteScore

6.90

自引率

12.80%

发文量

170

审稿时长

67 days

期刊介绍： The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest. Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning. Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.