Appendix for Parameter-free HE-friendly Logistic Regression 1 Additional Details on Theoretical Framework Lemma 1

H . Therefore, the result follows. Following the notations and definitions in Mohri et al. [2018], let Notice that the first term of the right-hand side of Eq. (4) is the loss function for the logistic regression In our framework by step 2 and step 3, we tried to mitigate the difference between the two distributions. Using centered inputs as above, regression model without intercept becomes as follows. That is, for k = 1,...,null, ˆ u In the algorithm, the notation of basic operation follows that of Park et al. [2020]. Our effective Ridge regression method can be extended to nonlinear regression by considering linear combination of fixed nonlinear basis functions of the input variables.