Least Squares Revisited: Scalable Approaches for Multi-class Prediction
This work provides efficient algorithms for multi-class prediction in large-scale machine learning applications, though it appears incremental as it revisits and extends least-squares methods.
The authors tackled the problem of multi-class prediction in high-dimensional settings by developing simple, robust, parameter-free algorithms based on iterative least-squares updates. Their scalable stagewise variant achieved dramatic computational speedups over popular optimization packages like Liblinear and Vowpal Wabbit on MNIST and CIFAR-10 datasets while attaining state-of-the-art accuracies.
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.