[scikit-learn] Question about Python's L2-Regularized Logistic Regression

[Kristen M. Altenburger]

Hi All,

I am trying to understand Python’s code [function ‘_fit_liblinear' in https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/svm/base.py] for fitting an L2-logistic regression for a ‘liblinear’ solver. More specifically, my [approximately balanced class] dataset is such that the # of predictors [p=2000] >> # of observations [n=100]. Therefore, I am currently confused that when I increase C [and thus decrease the regularization strength] in fitting the logistic regression model to my training data why I then still obtain high AUC results when the model is then applied to my testing data. Is python internally doing a feature selection when fitting this model for high C values? Or why is it that the almost unregularized model [high C values] versus regularized [cross-validated approach to selecting C] model both result in similar AUC and accuracy results when the model is applied to the testing data? Should I be coding my predictors as +1/-1? 

Any pointers/explanations would be much appreciated!

Thanks,
Kristen