论文信息 - Minimum cross-entropy distributions on Wasserstein balls and their applications

Minimum cross-entropy distributions on Wasserstein balls and their applications

Given a prior probability density p on a compact set K we characterize the probability distribution q∗ δ on K contained in a Wasserstein ball Bδ(μ) centered in a given discrete measure μ for which the relative-entropy H(q, p) achieves its minimum. This characterization gives us an algorithm for computing such distributions efficiently.

Mauricio Velasco | Luis Felipe Vargas | Mauricio Velasco

[1] Evgueni A. Haroutunian,et al. Information Theory and Statistics , 2011, International Encyclopedia of Statistical Science.

[2] Rodney W. Johnson,et al. Axiomatic characterization of the directed divergences and their linear combinations , 1979, IEEE Trans. Inf. Theory.

[3] Rodney W. Johnson,et al. Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy , 1980, IEEE Trans. Inf. Theory.

[4] R. Johnson,et al. Properties of cross-entropy minimization , 1981, IEEE Trans. Inf. Theory.

[5] I. Csiszár. $I$-Divergence Geometry of Probability Distributions and Minimization Problems , 1975 .

[6] Daniel Kuhn,et al. Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations , 2015, Mathematical Programming.

[7] S. Dereich,et al. Constructive quantization: Approximation by empirical measures , 2011, 1108.5346.

[8] A. Hobson. A new theorem of information theory , 1969 .

[9] D. Luenberger. Optimization by Vector Space Methods , 1968 .

[10] Kresimir Mihic,et al. Wasserstein Distance and the Distributionally Robust TSP , 2018, Oper. Res..

[11] K. Lum,et al. To predict and serve? , 2016 .