A directed-divergence function of type β

Rathie, Pushpa N.; Kannappan, Palaniappan

doi:10.1016/s0019-9958(72)90260-4

Cited by 78 publications

(27 citation statements)

References 2 publications

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“…Havrda and Chavrát (1967) defined a quantity they called the directed divergence of order between p and q, and variants of this divergence, which are equivalent up to a scale factor, were discussed by Rathie and Kannappan (1972), Cressie and Read (1984), and Haussler and Opper (1997). Cressie and Read referred to this quantity as the power divergence, and that is the term adopted here for the following reason: the power divergence (as originally introduced by Havrda and Chavrát 1967) is defined for all ∈ by…”

Section: Generalized Measures Of Entropy and Divergencementioning

confidence: 99%

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Scoring Rules, Generalized Entropy, and Utility Maximization

Jose

Nau

Winkler

2008

Operations Research

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Information measures arise in many disciplines, including forecasting (where scoring rules are used to provide incentives for probability estimation), signal processing (where information gain is measured in physical units of relative entropy), decision analysis (where new information can lead to improved decisions), and finance (where investors optimize portfolios based on their private information and risk preferences). In this paper, we generalize the two most commonly used parametric families of scoring rules and demonstrate their relation to well-known generalized entropies and utility functions, shedding new light on the characteristics of alternative scoring rules as well as duality relationships between utility maximization and entropy minimization. In particular, we show that weighted forms of the pseudospherical and power scoring rules correspond exactly to measures of relative entropy (divergence) with convenient properties, and they also correspond exactly to the solutions of expected utility maximization problems in which a risk-averse decision maker whose utility function belongs to the linear-risk-tolerance family interacts with a risk-neutral betting opponent or a complete market for contingent claims in either a one-period or a two-period setting. When the market is incomplete, the corresponding problems of maximizing linear-risk-tolerance utility with the risk-tolerance coefficient are the duals of the problems of minimizing the pseudospherical or power divergence of order between the decision maker's subjective probability distribution and the set of risk-neutral distributions that support asset prices.

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Section: Generalized Measures Of Entropy and Divergencementioning

confidence: 99%

“…Second, it satisfies the following pseudorecursivity property with respect to the splitting of events (Rathie andKannappan 1972, Cressie andRead 1984): …”

Section: Generalized Measures Of Entropy and Divergencementioning

confidence: 99%

Scoring Rules, Generalized Entropy, and Utility Maximization

Jose

Nau

Winkler

2008

Operations Research

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“…It has been used to summarize monitored traffic in a fixed memory, and to provide scalable input for time series analysis. Authors in [8] propose the use of CUmulative SUM (CUSUM) over the sketch for network anomaly detection. Furthermore, they propose a new mechanism for Sketch inversion and malicious flows identification.…”

Section: Related Workmentioning

confidence: 99%

“…The Power Divergence has been first defined in [7] and equivalent variants (up to a scale factor ) of this divergence are discussed in [35], [36]. The divergence measure is therefore the decision measure that generalizes the Kullback-Leibler measure and Hellinger distance to a broad class of divergence of order .…”

Section: Power Divergence (Pd)mentioning

confidence: 99%

Comparison Between Divergence Measures for Anomaly Detection of Mobile Agents in IP Networks

Tajer¹,

Adda²,

Aziz³

2017

IJWMN

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“…Power Divergences are generalizations of this decision measure and are associated with strictly convex functions. The Power Divergence has been first defined in [4] and equivalent variants (up to a scale factor β) of this divergence are discussed in [11]. The divergence measure is therefore the decision measure that generalizes KL, HD and χ 2 divergence to a broad class of divergence of order β.…”

Section: Proposed Approachmentioning

confidence: 99%

Flooding attacks detection in backbone traffic using power divergence

Makke

Salem

Assaad

et al. 2012

Proceedings of the 7th ACM Workshop on Performance Monitoring and Measurement of Heterogeneous Wireless and Wired Networks

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Flooding attacks detection in traffic of backbone networks requires generally the analysis of a huge amount of data with high accuracy and low complexity. In this paper, we propose a new scheme to detect flooding attacks in high speed networks. The proposed mechanism is based on the application of Power Divergence measures over Sketch data structure. Sketch is used for random aggregation of traffic, and Power Divergence is applied to detect deviations between current and established probability distributions of network traffic. We focus on tuning the parameter of Power Divergence to optimize the performance. We evaluate our approach using real Internet traffic traces, obtained from MAWI transPacific wide transit link between USA and Japan. Our results show that the proposed approach outperforms existing solutions in terms of detection accuracy and false alarm ratio.

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A directed-divergence function of type β

Cited by 78 publications

References 2 publications

Scoring Rules, Generalized Entropy, and Utility Maximization

Scoring Rules, Generalized Entropy, and Utility Maximization

Comparison Between Divergence Measures for Anomaly Detection of Mobile Agents in IP Networks

Flooding attacks detection in backbone traffic using power divergence

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