PIANO: A fast parallel iterative algorithm for multinomial and sparse multinomial logistic regression

Multinomial Logistic Regression is a well-studied tool for classification and has been widely used in fields like image processing, computer vision and, bioinformatics, to name few. Under supervised scenario, model learns weight vector differentiate between any two classes by optimizing over the likelihood objective. With advent of big data, inundation data resulted large dimensional also given rise huge number classes, which makes classical methods applicable estimation not computationally viable. To handle this issue, we here propose parallel iterative algorithm: Parallel Iterative Algorithm MultiNomial LOgistic (PIANO) based on Majorization Minimization procedure, can parallely update each element vectors. Further, show that PIANO be easily extended solve Sparse problem - an extensively studied because its attractive feature selection property. In particular, work out extension with ℓ1 ℓ0 regularizations. We prove converges stationary point problems. Simulations were conducted compare existing methods, it was found proposed algorithm performs better than terms speed convergence.