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arXiv 0712.0130cs.LG
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后验相似与最优相似的关系

On the Relationship between the Posterior and Optimal Similarity

PARC(帕洛阿尔托研究中心)

Thomas M. Breuel

摘要:

对于由联合密度$P(ω,x)$描述的分类问题,$P(ω\eqω'|x,x')$模型("贝叶斯相似性度量“)已被证明是最近邻分类的最佳相似性度量。本文分析论证了该条件分布的几个附加性质。本文首先表明,我们可以重建,直到类标签,类后验分布$P(ω|x)$给定$P(ω\eqω'|x,x')$,给出了恢复类标签的程序,并给出了一个渐近贝叶斯最优分类程序。它还显示,给定这样一个最佳的相似性度量,如何构建一个分类器,优于最近邻分类器,并实现贝叶斯最优分类率。然后,本文分析了贝叶斯相似性的框架中,分类器面临着一些相关的分类任务(多任务学习),并说明重建类后验分布是不可能的一般。最后,本文使用$P(ω\eqω'|x,x')$识别了一类不同的分类问题,并表明使用$P(ω\eqω'|x,x')$来解决这些问题是贝叶斯最优解。

英文摘要:

For a classification problem described by the joint density $P(ω,x)$, models of $P(ω\eqω'|x,x')$ (the ``Bayesian similarity measure'') have been shown to be an optimal similarity measure for nearest neighbor classification. This paper analyzes demonstrates several additional properties of that conditional distribution. The paper first shows that we can reconstruct, up to class labels, the class posterior distribution $P(ω|x)$ given $P(ω\eqω'|x,x')$, gives a procedure for recovering the class labels, and gives an asymptotically Bayes-optimal classification procedure. It also shows, given such an optimal similarity measure, how to construct a classifier that outperforms the nearest neighbor classifier and achieves Bayes-optimal classification rates. The paper then analyzes Bayesian similarity in a framework where a classifier faces a number of related classification tasks (multitask learning) and illustrates that reconstruction of the class posterior distribution is not possible in general. Finally, the paper identifies a distinct class of classification problems using $P(ω\eqω'|x,x')$ and shows that using $P(ω\eqω'|x,x')$ to solve those problems is the Bayes optimal solution.

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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