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Do Linear Regression and Logistic Regression models from sklearn include regularization?

In sklearn they are presented in a different way as you expected. Linear regression is without any regularization term, if you look for a regularized version as the ...
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Gradient tree boosting additive training

do they mean that $\sum\limits_{k=1}^{t-1} \omega(f_k) = constant$? Yes! From the paragraph preceding that: we use an additive strategy: fix what we have learned, and add one new tree at a time. ...
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