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Computing Maximum Entropy Densities: A Hybrid Approach
Badong Chen, Jinchun Hu, Yu Zhu
Pages - 114 - 122     |    Revised - 30-04-2010     |    Published - 10-06-2010
Volume - 4   Issue - 2    |    Publication Date - May 2010  Table of Contents
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KEYWORDS
Maximum entropy principle (MEP), maximum entropy density (MaxEnt density), Lagrangian multiplier, Newton's method, hybrid algorithm
ABSTRACT
This paper proposes a hybrid method to calculate the maximum entropy (MaxEnt) density subject to known moment constraints, which combines the linear equation (LE) method and Newton¡¯s method together. The new approach is more computationally efficient than ordinary Newton¡¯s method as it usually takes fewer Newton iterations to reach the final solution. Compared with the simple LE method, the hybrid algorithm will produce a more accurate solution. Numerical examples confirm the excellent performance of the proposed method.
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1 Xu, J. (2016). A new method for reliability assessment of structural dynamic systems with random parameters. Structural Safety, 60, 130-143.
2 Krishnan, R., Wu, W., Bodapati, S., & He, L. Accurate Multi-segment Probability Density Estimation Through Moment Matching.
3 Mrabet, E., Guedri, M., Ichchou, M. N., Ghanmi, S., & Soula, M. (2016). A new reliability based optimization of tuned mass damper parameters using energy approach. Journal of Vibration and Control, 1077546316636361.
4 Krishnan, R. (2015). A Moment Matching Based Fitting Algorithm for High Sigma Distribution Modeling.
5 Batou, A. (2014). Dynamique des structures déformables et des solides rigides-Quantification des incertitudes et réduction de modele (Doctoral dissertation, Université Paris-Est).
6 DIRIGER, T. D. H., & RECHERCHES, D. (2014). Dynamique des structures déformables et des solides rigides-Quantification des incertitudes et réduction de modele.
7 Krishnan, R., Wu, W., Gong, F., & He, L. (2013, March). Stochastic behavioral modeling of analog/mixed-signal circuits by maximizing entropy. In Quality Electronic Design (ISQED), 2013 14th International Symposium on (pp. 572-579). IEEE.
8 Batou, A., & Soize, C.(2013).Calculation of Lagrange multipliers in the construction of maximum entropy distributions in high stochastic dimension. SIAM/ASA Journal on Uncertainty Quantification, 1(1), 431-451.
9 Stecker, M. M. (2011).Constrained Signals: A General Theory of Information Content and Detection. Open Signal Processing Journal, 4, 1-18.
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A. Balestrino, A. Caiti, E. Crisostomi, “Efficient numerical approximation of maximum entropy estimates”, International Journal of Control, 79(9): 1145-1155, 2006
A. Zellner, R. A. Highfield, “Calculation of maximum entropy distributions and approximation of marginal posterior distributions”, Journal of Econometrics, 37: 195-209, 1988
D. Erdogmus, K. E. Hild II, Y. N. Rao, J. C. Principe, “Minimax mutual information approach for independent component analysis”, Neural Computation, 16: 1235-1252, 2004
D. Ormoneit, H. White, “An efficient algorithm to compute maximum entropy densities”, Econometrics Reviews, 18(2): 127-140, 1999
E. T. Jaynes, “Information theory and statistical mechanics”, Phys. Rev., 106: 620-630, 1957
J. N. Kapur, H. K. Kesavan, “Entropy Optimization Principles with Applications”, Academic Press, Inc., 1992
L. R. Mead, N. Papanicolaou, “Maximum entropy in the problem of moments”, Journal of Mathematical Physics, 25(8): 2404-2417, 1984
T. M. Cover and J. A. Thomas, “Element of Information Theory”, Chichester: Wiley & Son, Inc., 1991
X. Wu, T. Stengos, “Partially adaptive estimation via the maximum entropy densities”, Econometrics Journal, 8: 352-366, 2005
X. Wu, “Calculation of maximum entropy densities with application to income distribution”, Journal of Econometrics, 115(2): 347-354, 2003
Dr. Badong Chen
Tsinghua University - China
chenbd04@mails.tsinghua.edu.cn
Associate Professor Jinchun Hu
- China
Professor Yu Zhu
Tsinghua University - China