Feature selection, L 1 vs. L 2 regularization, and rotational invariance

We consider supervised learning in the presence of very many irrelevant features, and study two different regularization methods for preventing overfitting. Focusing on logistic regression, we show that using L1 regularization of the parameters, the sample complexity (i.e., the number of training examples required to learn "well,") grows only logarithmically in the number of irrelevant features. This logarithmic rate matches the best known bounds for feature selection, and indicates that L1 regularized logistic regression can be effective even if there are exponentially many irrelevant features as there are training examples. We also give a lower-bound showing that any rotationally invariant…

• DA
  Defense Advanced Research Projects Agency