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High-dimensional classification by sparse logistic regression
- Publication Year :
- 2017
-
Abstract
- We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic bounds for the resulting misclassification excess risk. The bounds can be reduced under the additional low-noise condition. The proposed complexity penalty is remarkably related to the VC-dimension of a set of sparse linear classifiers. Implementation of any complexity penalty-based criterion, however, requires a combinatorial search over all possible models. To find a model selection procedure computationally feasible for high-dimensional data, we extend the Slope estimator for logistic regression and show that under an additional weighted restricted eigenvalue condition it is rate-optimal in the minimax sense.
- Subjects :
- Mathematics - Statistics Theory
Statistics - Machine Learning
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1706.08344
- Document Type :
- Working Paper