[scikit-learn] biased predictions in logistic regression

[Rachel Melamed]

Hi all,
Does anyone have any suggestions for this problem:
http://stackoverflow.com/questions/41125342/sklearn-logistic-regression-gives-biased-results


I am running around 1000 similar logistic regressions, with the same covariates but slightly different data and response variables. All of my response variables have a sparse successes (p(success) < .05 usually).

I noticed that with the regularized regression, the results are consistently biased to predict more "successes" than is observed in the training data. When I relax the regularization, this bias goes away. The bias observed is unacceptable for my use case, but the more-regularized model does seem a bit better.

Below, I plot the results for the 1000 different regressions for 2 different values of C: [results for the different regressions for 2 different values of C] <https://i.stack.imgur.com/1cbrC.png>

I looked at the parameter estimates for one of these regressions: below each point is one parameter. It seems like the intercept (the point on the bottom left) is too high for the C=1 model. [enter image description here] <https://i.stack.imgur.com/NTFOY.png>

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