Application of Partial Least Squares Algorithm Based on Kullback– Leibler Divergence in Intrusion Detection

Yu, Xianping; Chen, Shanxiong; Peng, Xihua; Peng, Maoling

doi:10.1142/9789813146426_0029

Cited by 2 publications

(2 citation statements)

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“…The Kullback-Leibler divergence introduced in [1] is used for quantification of similarity of two probability measures. It plays important role in various domains such as statistical inference (see, e.g., [2,3]), metric learning [4,5], machine learning [6,7], computer vision [8,9], network security [10], feature selection and classification [11][12][13], physics [14], biology [15], medicine [16,17], finance [18], among others. It is worth to emphasize that mutual information, widely used in many research directions (see, e.g., [19][20][21][22][23]), is a special case of the Kullback-Leibler divergence for certain measures.…”

Section: Introductionmentioning

confidence: 99%

Statistical Estimation of the Kullback–Leibler Divergence

Bulinski

Dimitrov

2021

Mathematics

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Asymptotic unbiasedness and L2-consistency are established, under mild conditions, for the estimates of the Kullback–Leibler divergence between two probability measures in Rd, absolutely continuous with respect to (w.r.t.) the Lebesgue measure. These estimates are based on certain k-nearest neighbor statistics for pair of independent identically distributed (i.i.d.) due vector samples. The novelty of results is also in treating mixture models. In particular, they cover mixtures of nondegenerate Gaussian measures. The mentioned asymptotic properties of related estimators for the Shannon entropy and cross-entropy are strengthened. Some applications are indicated.

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Section: Introductionmentioning

confidence: 99%

Statistical Estimation of the Kullback–Leibler Divergence

Bulinski

Dimitrov

2021

Mathematics

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“…The Kullback -Leibler divergence plays important role in various domains such as statistical inference (see, e.g., [25], [28]), machine learning ( [5], [32]), computer vision ( [11], [13]), network security ( [23], [44]), feature selection and classification ( [22], [29], [41]), physics ( [17]), biology ( [9]), finance ( [45]), among others. Recall that this divergence measure between probabilities P and Q on a space (S, B) is defined by way of…”

Section: Introductionmentioning

confidence: 99%

Statistical estimation of the Kullback-Leibler divergence

Bulinski¹,

Denis²

2019

Preprint

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Wide conditions are provided to guarantee asymptotic unbiasedness and L 2 -consistency of the introduced estimates of the Kullback -Leibler divergence for probability measures in R d having densities w.r.t. the Lebesgue measure. These estimates are constructed by means of two independent collections of i.i.d. observations and involve the specified k-nearest neighbor statistics. In particular, the established results are valid for estimates of the Kullback -Leibler divergence between any two Gaussian measures in R d with nondegenerate covariance matrices. As a byproduct we obtain new statements concerning the Kozachenko-Leonenko estimators of the Shannon differential entropy.

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Application of Partial Least Squares Algorithm Based on Kullback– Leibler Divergence in Intrusion Detection

Cited by 2 publications

References 0 publications

Statistical Estimation of the Kullback–Leibler Divergence

Statistical Estimation of the Kullback–Leibler Divergence

Statistical estimation of the Kullback-Leibler divergence

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