Least Squares Revisited: Scalable Approaches for Multi-class Prediction

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Alekh Agarwal, Sham Kakade, Nikos Karampatziakis, Le Song, Gregory Valiant ;
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):541-549, 2014.

Abstract

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 show how to scale our approach to high dimensional datasets, achieving 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.

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