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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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Dr. Badong Chen
Tsinghua University - China
chenbd04@mails.tsinghua.edu.cn
Associate Professor Jinchun Hu
- China
Professor Yu Zhu
Tsinghua University - China