Uppsala University, Department of Medical Sciences, Academic Hospital, 751 85 Uppsala, Sweden.
Artif Intell Med. 2010 Jun;49(2):93-104. doi: 10.1016/j.artmed.2010.02.004. Epub 2010 Mar 27.
OBJECTIVE: Successful use of classifiers that learn to make decisions from a set of patient examples require robust methods for performance estimation. Recently many promising approaches for determination of an upper bound for the error rate of a single classifier have been reported but the Bayesian credibility interval (CI) obtained from a conventional holdout test still delivers one of the tightest bounds. The conventional Bayesian CI becomes unacceptably large in real world applications where the test set sizes are less than a few hundred. The source of this problem is that fact that the CI is determined exclusively by the result on the test examples. In other words, there is no information at all provided by the uniform prior density distribution employed which reflects complete lack of prior knowledge about the unknown error rate. Therefore, the aim of the study reported here was to study a maximum entropy (ME) based approach to improved prior knowledge and Bayesian CIs, demonstrating its relevance for biomedical research and clinical practice. METHOD AND MATERIAL: It is demonstrated how a refined non-uniform prior density distribution can be obtained by means of the ME principle using empirical results from a few designs and tests using non-overlapping sets of examples. RESULTS: Experimental results show that ME based priors improve the CIs when employed to four quite different simulated and two real world data sets. CONCLUSIONS: An empirically derived ME prior seems promising for improving the Bayesian CI for the unknown error rate of a designed classifier.
目的:成功使用从一组患者示例中学习做出决策的分类器需要稳健的性能估计方法。最近,已经有许多很有前途的方法被报道,用于确定单个分类器的错误率上限,但从传统的留一法测试获得的贝叶斯置信区间(CI)仍然提供了最紧的界限之一。在测试集大小小于几百个的实际应用中,传统的贝叶斯 CI 会变得过大。造成这个问题的原因是,CI 完全由测试示例的结果确定。换句话说,使用的均匀先验密度分布完全没有提供任何信息,这反映了对未知错误率的完全缺乏先验知识。因此,本研究报告的目的是研究基于最大熵(ME)的方法来改进先验知识和贝叶斯 CI,并证明其在生物医学研究和临床实践中的相关性。
方法和材料:演示了如何通过使用几个设计和使用不重叠示例集的测试的经验结果,通过 ME 原理获得更精细的非均匀先验密度分布。
结果:实验结果表明,当应用于四个非常不同的模拟数据集和两个真实世界数据集时,基于 ME 的先验可以改善 CI。
结论:从经验中得出的 ME 先验似乎有希望提高设计分类器的未知错误率的贝叶斯 CI。