Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
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Consider the semi-parametric linear regression model Y=@b^'X+@e, where @e has an unknown distribution F"0. The semi-parametric MLE @b@? of @b under this set-up is called the generalized semi-parametric MLE(GSMLE). Although the GSML estimation of the linear regression model is statistically appealing, it has never been attempted due to difficulties with obtaining the GSML estimates of @b and F until recent work on linear regression for complete data and for right-censored data by Yu and Wong [2003a. Asymptotic properties of the generalized semi-parametric MLE in linear regression. Statistica Sinica 13, 311-326; 2003b. Semi-parametric MLE in simple linear regression analysis with interval-censored data. Commun. Statist.-Simulation Comput. 32, 147-164; 2003c. The semi-parametric MLE in linear regression with right censored data. J. Statist. Comput. Simul. 73, 833-848]. However, after obtaining all candidates, their algorithm simply does an exhaustive search to find the GSML estimators. In this paper, it is shown that Yu and Wong's algorithm leads to the so-called dimension disaster. Based on their idea, a simulated annealing algorithm for finding semi-parametric MLE is proposed along with techniques to reduce computations. Experimental results show that the new algorithm runs much faster for multiple linear regression models while keeping the nice features of Yu and Wong's original one.