In theory, the scale of your inputs are irrelevant to logistic regression.
You can "theoretically" multiply X1 by 1E6 and the estimate for β1 will
adjust accordingly. It will be 1E-6 times smaller than the original β1, due
to the invariance property of MLEs.
However, during the optimization process, the convergence (rate)
depends on the condition number of the training dataset. Scaling
the variables often reduces this condition number, thus improving
the convergence rate.
Without reducing the condition number, some training datasets
mixing the columns with different scales may not be able to converge.
GLMNET and LIBSVM packages perform the scaling to reduce
the condition number, and return the weights in the original scale.
See page 9 in http://cran.r-project.org/web/packages/glmnet/glmnet.pdf
Here, if useFeatureScaling is enabled, we will standardize the training
features by dividing the variance of each column (without subtracting
the mean to densify the sparse vector), and train the model in the
scaled space. Then we transform the coefficients from the scaled space
to the original scale as GLMNET and LIBSVM do.
Currently, it's only enabled in LogisticRegressionWithLBFGS.
Author: DB Tsai <dbtsai@alpinenow.com>
Closes#1897 from dbtsai/dbtsai-feature-scaling and squashes the following commits:
f19fc02 [DB Tsai] Added more comments
1d85289 [DB Tsai] Improve the convergence rate by minimize the condition number in LOR with LBFGS
9622106757