Updating beliefs with incomplete observations
Updating beliefs with incomplete observations
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DOI：
10.1016/j.artint.2004.05.006
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发表时间：
2004-11-01
影响因子：
14.4
通讯作者：
Zaffalon, M
中科院分区：
文献类型：
--
作者：
de Cooman, G;Zaffalon, M
目前，人们对Shafer在1985年提出的问题重新产生了兴趣，即在观测不完整（或集值）时更新概率。这是一个基本问题，对贝叶斯网络来说尤其重要。最近，Grunwald和Halpern已经证明，除了在非常特殊的假设下，常用的更新策略在这种情况下是失败的。本文提出了一种不完全观测值下概率更新的新方法。我们的方法是故意保守的：我们不假设所谓的不完备机制，即完整与不完整的观察相关联。我们通过一种空洞的低级预测（一种来自不精确概率理论的工具）来模拟我们对这种机制的无知，我们只使用相干论证将先验概率转化为后验概率（更新后验概率）。一般来说，这种更新的新方法产生较低和较高的后验概率和预测（期望），以及部分确定的决策。这是对不完备机制的无知的必然结果。作为一个例子，我们使用新的更新方法来适当地解决“Monty Hall”谜题中明显的悖论。更重要的是，我们将其应用于概率专家系统中新证据的分类问题，在那里它导致了一个新的，所谓的保守更新规则。在使用专家知识构建贝叶斯网络的特殊情况下，我们提供了一种基于我们的更新规则的精确算法来比较类，该规则对于比多树更宽的一类网络具有线性时间复杂度。然后，这个结果被扩展到更一般的凭证网络框架，其中的计算通常比贝叶斯网络要困难得多。通过一个例子，我们展示了我们的规则似乎为不完全观察的可靠更新提供了坚实的基础，当没有关于不完备机制的强假设是合理的。(C) 2004 Elsevier B.V.版权所有
Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or set-valued). 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 (updated) probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and previsions (expectations), as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. As an example, we use the new updating method to properly address the apparent paradox in the 'Monty Hall' puzzle. More importantly, we apply it 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 to compare classes 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. (C) 2004 Elsevier B.V. All rights reserved.