A Comparison of Numerical Optimizers for Logistic Regression

Logistic regression is a workhorse of statistics and is closely related to methods used in Machine Learning, including the Perceptron and the Support Vector Machine. This note compares eight different algorithms for computing the maximum a-posteriori parameter estimate. A full derivation of each algorithm is given. In particular, a new derivation of Iterative Scaling is given which applies more generally than the conventional one. A new derivation is also given for the Modified Iterative Scaling algorithm of Collins et al (2002). Most of the algorithms operate in the primal space, but can also work in dual space. All algorithms are compared in terms of computational complexity by experiments on large data sets. The fastest algorithms turn out to be conjugate gradient ascent and quasi-Newton algorithms, which far outstrip Iterative Scaling and its variants.