An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications
Hu, Bao-Gang1; Xing, Hong-Jie2
2016-02-01
发表期刊ENTROPY
卷号18期号:2页码:1-19
文章类型Article
摘要In this work, we propose a new approach of deriving the bounds between entropy and error from a joint distribution through an optimization means. The specific case study is given on binary classifications. Two basic types of classification errors are investigated, namely, the Bayesian and non-Bayesian errors. The consideration of non-Bayesian errors is due to the facts that most classifiers result in non-Bayesian solutions. For both types of errors, we derive the closed-form relations between each bound and error components. When Fano's lower bound in a diagram of Error Probability vs. Conditional Entropy is realized based on the approach, its interpretations are enlarged by including non-Bayesian errors and the two situations along with independent properties of the variables. A new upper bound for the Bayesian error is derived with respect to the minimum prior probability, which is generally tighter than Kovalevskij's upper bound.
关键词Entropy Error Probability Bayesian Errors Error Types Upper Bound Lower Bound
WOS标题词Science & Technology ; Physical Sciences
DOI10.3390/e18020059
关键词[WOS]PATTERN-RECOGNITION ; FEATURE-SELECTION ; PROBABILITY ; INFORMATION ; INEQUALITIES ; DECISIONS ; CRITERIA
收录类别SCI
语种英语
项目资助者National Natural Science Foundation of China(61273196 ; 61573348 ; 60903089)
WOS研究方向Physics
WOS类目Physics, Multidisciplinary
WOS记录号WOS:000371827800018
引用统计
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/11372
专题模式识别国家重点实验室_多媒体计算与图形学
作者单位1.Chinese Acad Sci, Inst Automat, NLPR LIAMA, Beijing 100190, Peoples R China
2.Hebei Univ, Coll Math & Informat Sci, Baoding 071002, Peoples R China
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Hu, Bao-Gang,Xing, Hong-Jie. An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications[J]. ENTROPY,2016,18(2):1-19.
APA Hu, Bao-Gang,&Xing, Hong-Jie.(2016).An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications.ENTROPY,18(2),1-19.
MLA Hu, Bao-Gang,et al."An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications".ENTROPY 18.2(2016):1-19.
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