Amplifying Inter-message Distance: On Information Divergence Measures in Big Data
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866911828019249152 |
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| author | She, Rui Liu, Shanyun Fan, Pingyi |
| author_facet | She, Rui Liu, Shanyun Fan, Pingyi |
| contents | Message identification (M-I) divergence is an important measure of the information distance between probability distributions, similar to Kullback-Leibler (K-L) and Renyi divergence. In fact, M-I divergence with a variable parameter can make an effect on characterization of distinction between two distributions. Furthermore, by choosing an appropriate parameter of M-I divergence, it is possible to amplify the information distance between adjacent distributions while maintaining enough gap between two nonadjacent ones. Therefore, M-I divergence can play a vital role in distinguishing distributions more clearly. In this paper, we first define a parametric M-I divergence in the view of information theory and then present its major properties. In addition, we design a M-I divergence estimation algorithm by means of the ensemble estimator of the proposed weight kernel estimators, which can improve the convergence of mean squared error from ${O(\varGamma^{-j/d})}$ to ${O(\varGamma^{-1})}$ $({j\in (0,d]})$. We also discuss the decision with M-I divergence for clustering or classification, and investigate its performance in a statistical sequence model of big data for the outlier detection problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_03690 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Amplifying Inter-message Distance: On Information Divergence Measures in Big Data She, Rui Liu, Shanyun Fan, Pingyi Information Theory Message identification (M-I) divergence is an important measure of the information distance between probability distributions, similar to Kullback-Leibler (K-L) and Renyi divergence. In fact, M-I divergence with a variable parameter can make an effect on characterization of distinction between two distributions. Furthermore, by choosing an appropriate parameter of M-I divergence, it is possible to amplify the information distance between adjacent distributions while maintaining enough gap between two nonadjacent ones. Therefore, M-I divergence can play a vital role in distinguishing distributions more clearly. In this paper, we first define a parametric M-I divergence in the view of information theory and then present its major properties. In addition, we design a M-I divergence estimation algorithm by means of the ensemble estimator of the proposed weight kernel estimators, which can improve the convergence of mean squared error from ${O(\varGamma^{-j/d})}$ to ${O(\varGamma^{-1})}$ $({j\in (0,d]})$. We also discuss the decision with M-I divergence for clustering or classification, and investigate its performance in a statistical sequence model of big data for the outlier detection problem. |
| title | Amplifying Inter-message Distance: On Information Divergence Measures in Big Data |
| topic | Information Theory |
| url | https://arxiv.org/abs/1709.03690 |