A General Class of Coefficients of Divergence of One Distribution from Another

Ali, Shozab S; Silvey, S. D.

doi:10.1111/j.2517-6161.1966.tb00626.x

Cited by 837 publications

(768 citation statements)

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“…3. More generally, investigate the convergence rate of the CE algorithm with some other special cases of the Ali-Silvey distance (Ali and Silvey 1966). 4.…”

Section: Resultsmentioning

confidence: 99%

A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem

2009

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In this paper, we propose a new hybrid algorithm for the Hamiltonian cycle problem by synthesizing the Cross Entropy method and Markov decision processes. In particular, this new algorithm assigns a random length to each arc and alters the Hamiltonian cycle problem to the travelling salesman problem. Thus, there is now a probability corresponding to each arc that denotes the probability of the event "this arc is located on the shortest tour." Those probabilities are then updated as in cross entropy method and used to set a suitable linear programming model. If the solution of the latter yields any tour, the graph is Hamiltonian. Numerical results reveal that when the size of graph is small, say less than 50 nodes, there is a high chance the algorithm will be terminated in its cross entropy component by simply generating a Hamiltonian cycle, randomly. However, for larger graphs, in most of the tests the algorithm terminated in its optimization component (by solving the proposed linear program).

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“…3. More generally, investigate the convergence rate of the CE algorithm with some other special cases of the Ali-Silvey distance (Ali and Silvey 1966). 4.…”

Section: Resultsmentioning

confidence: 99%

A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem

2009

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“…The most important attempt to define a broad class of divergence measures between two probability measures or between the respective Radon-Nikodym derivatives was made by Csiszár (1963Csiszár ( , 1967 and independently by Ali and Silvey (1966). Following these authors, if P and Q are two probability measures on the measurable space (X , A) and μ is a σ -finite measure on the same measurable space, such that P μ and Q μ, then for p and q the respective Radon-Nikodym derivatives, p = d P dμ and q = d Q dμ , a broad class of divergence measures between P and Q, or between p and q, is defined by the following integral,…”

Section: Introductionmentioning

confidence: 99%

On local divergences between two probability measures

Avlogiaris

Micheas

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2015

Metrika

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A broad class of local divergences between two probability measures or between the respective probability distributions is proposed in this paper. The introduced local divergences are based on the classic Csiszár φ-divergence and they provide with a pseudo-distance between two distributions on a specific area of their common domain. The range of values of the introduced class of local divergences is derived and explicit expressions of the proposed local divergences are also derived when the underlined distributions are members of the exponential family of distributions or they are described by multivariate normal models. An application is presented to illustrate the behavior of local divergences.

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“…Other measures of divergence are possible, including the general class of f -divergences (Ali and Silvey 1966;Csiszár 1967). Such class contains as a particular case the family of α-divergences (see, for example, Amari 1990), which in turn contains (the square of) the Hellinger distance as well as the Kullback-Leibler discrepancy.…”

Section: Utility Functionmentioning

confidence: 99%