  This work provides simple algorithms for multi-class (and multi-label)
prediction in settings where both the number of examples n and the data
dimension d are relatively large. These robust and parameter free algorithms
are essentially iterative least-squares updates and very versatile both in
theory and in practice. On the theoretical front, we present several variants
with convergence guarantees. Owing to their effective use of second-order
structure, these algorithms are substantially better than first-order methods
in many practical scenarios. On the empirical side, we present a scalable
stagewise variant of our approach, which achieves dramatic computational
speedups over popular optimization packages such as Liblinear and Vowpal Wabbit
on standard datasets (MNIST and CIFAR-10), while attaining state-of-the-art
accuracies.
