We consider the two-group classification problem and propose a kernel classifier based on the optimal scoring framework. Unlike previous approaches, we provide theoretical guarantees on the expected risk consistency of the method. We also allow for feature selection by imposing structured sparsity using weighted kernels. We propose fully-automated methods for selection of all tuning parameters, and in particular adapt kernel shrinkage ideas for ridge parameter selection. Numerical studies demonstrate the superior classification performance of the proposed approach compared to existing nonparametric classifiers.
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Flexible Variable Selection for Recovering Sparsity in Nonadditive Nonparametric Models
Variable selection for recovering sparsity in nonadditive and nonparametric models with high-dimensional variables has been challenging. This problem becomes even more difficult due to complications in modeling unknown interaction terms among high-dimensional variables. There is currently no variable selection method to overcome these limitations. Hence, in this article we propose a variable selection approach that is developed by connecting a kernel machine with the nonparametric regression model. The advantages of our approach are that it can: (i) recover the sparsity; (ii) automatically model unknown and complicated interactions; (iii) connect with several existing approaches including linear nonnegative garrote and multiple kernel learning; and (iv) provide flexibility for both additive and nonadditive nonparametric models. Our approach can be viewed as a nonlinear version of a nonnegative garrote method. We model the smoothing function by a Least Squares Kernel Machine (LSKM) and construct the nonnegative garrote objective function as the function of the sparse scale parameters of kernel machine to recover sparsity of input variables whose relevances to the response are measured by the scale parameters. We also provide the asymptotic properties of our approach. We show that sparsistency is satisfied with consistent initial kernel function coefficients under certain conditions. An efficient coordinate descent/backfitting algorithm is developed. A resampling procedure for our variable selection methodology is also proposed to improve the power.
more » « less- NSF-PAR ID:
- 10485120
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 72
- Issue:
- 4
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 1155-1163
- Size(s):
- p. 1155-1163
- Sponsoring Org:
- National Science Foundation
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