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Individual Shrinkage-Based Fuzzy Variable Selection

Model selection has become a central task in science. The classical model selection such as variable selection in multiple linear regression delivers interpretable models, but its instability is also well known. On the other hand, some shrinkage estimators enjoy the property of stability. To combine these two strengths, we generalize the crisp variable selection by introducing the concept of fuzzy variable selection. After constructing a fuzzy model, we show that the optimal membership function can be estimated by shrinkage. By defining the effective model dimensionality, almost all the classical model selection methods can be extended to our fuzzy scheme. In order to optimize the fuzzy memberships, we also propose a hybrid optimization process, which has both the global and local searching capability. Finally, our numerical study shows its advantages over classical method selection methods.