chapter  8
18 Pages

Detecting Ineffective Features for Nonparametric Regression

WithKris De Brabanter, Paola Gloria Ferrario, László Györfi

Kris De Brabanter Department of Statistics and Department of Computer Science, Iowa State University

Paola Gloria Ferrario Institut für Medizinische Biometrie und Statistik, Universität zu Lübeck

László Györfi Department of Computer Science and Information Theory, Budapest University of Technology and Economics

8.1 Estimate the Minimum Mean Squared Error . . . . . . . . . . . . . . . . . . . . 178 8.2 Tests for the Regression Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 8.3 A New Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.4 Estimation of the Bayes Error Probability . . . . . . . . . . . . . . . . . . . . . . 188 8.5 Tests for the Classification Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

In the nonparametric regression setting, we investigate the hypothesis that some components of the covariate (feature) vector are ineffective. Identifying them would enable us to reduce the dimension of the feature vector, without increasing the minimum mean squared error.