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arXiv cs/0305044cs.AI
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用不完整的观测值更新信念

Updating beliefs with incomplete observations

Gert de Cooman, Marco Zaffalon

摘要:

目前,有新的兴趣的问题,提出了谢弗在1985年,更新概率时,观察是不完整的。这是一个基本问题,特别是贝叶斯网络。最近,Grunwald和Halpern已经表明,常用的更新策略在这种情况下失败,除非在非常特殊的假设。在本文中,我们提出了一种新的方法来更新不完整的观测值的概率。我们的方法是故意保守的:我们不对所谓的不完整性机制做任何假设,这种机制将完整与不完整的观察联系起来。我们通过一个空洞的低预见来模拟我们对这种机制的无知,这是一种来自不精确概率理论的工具,我们只使用相干参数来将先验概率转换为后验概率。一般来说,这种新的更新方法会产生较低和较高的后验概率和期望,以及部分确定的决策。这是对不完全性机制的现有无知的逻辑结果。我们应用新的方法来分类的问题,新的证据在概率专家系统,在那里它会导致一个新的,所谓的保守更新规则。在贝叶斯网络使用专家知识构建的特殊情况下,我们提供了一个精确的算法分类的基础上,我们的更新规则,它具有线性时间复杂度的一类网络比多叉树。然后,这个结果被扩展到更一般的信用网络框架,其中计算通常比贝叶斯网络更困难。使用一个例子,我们表明,我们的规则似乎提供了一个坚实的基础,可靠的更新不完整的观察,当没有强有力的假设不完整的机制是合理的。

英文摘要:

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Grunwald and Halpern have shown that commonly used updating strategies fail in this case, except under very special assumptions. In this paper we propose a new method for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no assumptions about the so-called incompleteness mechanism that associates complete with incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and expectations, as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. We apply the new approach to the problem of classification of new evidence in probabilistic expert systems, where it leads to a new, so-called conservative updating rule. In the special case of Bayesian networks constructed using expert knowledge, we provide an exact algorithm for classification based on our updating rule, which has linear-time complexity for a class of networks wider than polytrees. This result is then extended to the more general framework of credal networks, where computations are often much harder than with Bayesian nets. Using an example, we show that our rule appears to provide a solid basis for reliable updating with incomplete observations, when no strong assumptions about the incompleteness mechanism are justified.

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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