Section:
New Results
Efficient Primal-Dual Algorithms
for Large-Scale Multiclass Classification.
We develop efficient algorithms to train -regularized linear classifiers with large dimensionality
of the feature space, number of classes , and sample size . Our focus is on
a special class of losses that includes, in particular, the multiclass hinge and logistic losses.
Our approach combines several ideas: (i) passing to the equivalent saddle-point problem
with a quasi-bilinear objective; (ii) applying stochastic mirror descent with a proper choice
of geometry which guarantees a favorable accuracy bound; (iii) devising non-uniform sampling
schemes to approximate the matrix products. In particular, for the multiclass hinge
loss we propose a sublinear algorithm with iterations performed in arithmetic
operations.