ADMM-SOFTMAX : An ADMM Approach for Multinomial Logistic Regression [article]

Samy Wu Fung, Sanna Tyrväinen, Lars Ruthotto, Eldad Haber
2019 arXiv   pre-print
We present ADMM-Softmax, an alternating direction method of multipliers (ADMM) for solving multinomial logistic regression (MLR) problems. Our method is geared toward supervised classification tasks with many examples and features. It decouples the nonlinear optimization problem in MLR into three steps that can be solved efficiently. In particular, each iteration of ADMM-Softmax consists of a linear least-squares problem, a set of independent small-scale smooth, convex problems, and a trivial
more » ... al variable update. Solution of the least-squares problem can be be accelerated by pre-computing a factorization or preconditioner, and the separability in the smooth, convex problem can be easily parallelized across examples. For two image classification problems, we demonstrate that ADMM-Softmax leads to improved generalization compared to a Newton-Krylov, a quasi Newton, and a stochastic gradient descent method.
arXiv:1901.09450v2 fatcat:lj2stje43fgwjipfhueerbdxhi