Paper:
Asymptotic Behavior of Linear Approximations of Pseudo-Boolean Functions
Guoli Ding*, Robert F. Lax*, Peter Chen**,
and Jianhua Chen**
*Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
**Department of Computer Science, Louisiana State University, Baton Rouge, LA 70803, USA
- [1] A. T. Bharucha-Reid and M. Sambandham, “Random Polynomials,” Academic Press, 1986.
- [2] E. Boros and P. L. Hammer, “Pseudo-Boolean Optimization,” Discrete Appl. Math., 123 (1-3), pp. 155-225, 2002.
- [3] G. Ding, J. Chen, R. Lax, and P. Chen, “Efficient learning of pseudo-boolean functions from limited training data,” Foundations of Intelligent Systems: 15th International Symposium, ISMIS 2005, Lect. Notes in Comp. Sci. 3488 (Springer, 2005), pp. 323-331.
- [4] H. E. Dixon and M. L. Ginsberg, “Inference methods for a pseudo-Boolean satisfiability solver,” Proc. of American Association of AI Conference, 2002.
- [5] P. H. Giang and P. P. Shenoy, “A Qualitative Linear Utility Theory for Spohn’s Theory of Epistemic Beliefs,” Proceedings of Int. Conference on Uncertainty in AI, San Francisco, CA, pp. 220-229, 2000.
- [6] P. L. Hammer and R. Holzman, “Approximations of Pseudo-Boolean Functions; Applications to Game Theory,” ZOR – Methods and Models of Operations Research, 36, pp. 3-21, 1992.
- [7] R. Herbrich and T. Graepel, “Bayes Point Machines,” Journal of Machine Learning Research, 1, pp. 245-279, 2001.
- [8] Y. Jin, “A Comprehensive Survey of Fitness Approximation in Evolutionary Computation,” Soft Computing, 9, pp. 3-12, 2005.
- [9] R. Khardon, D. Roth, and L. G. Valiant, “Relational Learning for NLP using Linear Threshold Elements,” Proceedings of Int. Joint Conference on AI (IJCAI’99), Aug., 1999.
- [10] R. Lax, G. Ding, P. Chen, and J. Chen, “Approximating Pseudo-Boolean Functions on Non-uniform Domains,” Proceedings of IJCAI-05, pp. 1754-1755, 2005.
- [11] L. Liu, C. Shenoy, and P. P. Shenoy, “A Linear Belief Function Approach to Portfolio Evaluation,” Proceedings of Int. Conference on Uncertainty in AI, San Francisco, CA, pp. 370-377, 2003.
- [12] V. M. Manquinho and J. Marques-Silva, “Integration of Lower Bound Estimates in Pseudo-Boolean Optimization,” Proc. of IEEE Int. Conference on Tools with AI, 2004.
- [13] S. Prestwich and C. Quirke, “Boolean and Pseudo-Boolean Models for Scheduling,” Proc. of Second International Workshop on Modeling and Reformulating Constraint Satisfaction Problems, 2003.
- [14] L. A. Zadeh and J. Kacprzyk (Eds.), “Fuzzy Logic for the Management of Uncertainty,” John Wiley & Sons, 1992.
- [15] H. Zhang and J. E. Rowe, “Best Approximations of Fitness Functions of Binary Strings,” Natural Computing, 3, pp. 113-124, 2004.
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