This letter gives an efficient algorithm for tracking the solution curve of sparse logistic regression with respect to the regularization parameter. The algorithm is based on approximating the logistic regression loss by a piecewise quadratic function, using Rosset and Zhu's path tracking algorithm on the approximate problem, and then applying a correction to get to the true path. Application of the algorithm to text classification and sparse kernel logistic regression shows that the algorithm is efficient.
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Keerthi et al. (2007) studied this question.
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