Extreme Classification in Log Memory

We present Merged-Averaged Classifiers via Hashing (MACH) for K-classification with ultra-large values of K. Compared to traditional one-vs-all classifiers that require O(Kd) memory and inference cost, MACH only need O(d log K) (d is dimensionality )memory while only requiring O(K log K + d log K) operation for inference. MACH is a generic K-classification algorithm, with provably theoretical guarantees, which requires O(log K) memory without any assumption on the relationship between classes. MACH uses universal hashing to reduce classification with a large number of classes to few independent classification tasks with small (constant) number of classes. We provide theoretical quantification of discriminability-memory tradeoff. With MACH we can train ODP dataset with 100,000 classes and 400,000 features on a single Titan X GPU, with the classification accuracy of 19.28%, which is the best-reported accuracy on this dataset. Before this work, the best performing baseline is a one-vs-all classifier that requires 40 billion parameters (160 GB model size) and achieves 9% accuracy. In contrast, MACH can achieve 9% accuracy with 480x reduction in the model size (of mere 0.3GB). With MACH, we also demonstrate complete training of fine-grained imagenet dataset (compressed size 104GB), with 21,000 classes, on a single GPU. To the best of our knowledge, this is the first work to demonstrate complete training of these extreme-class datasets on a single Titan X

Efficient Loss-Based Decoding on Graphs For Extreme Classification

In extreme classification problems, learning algorithms are required to map instances to labels from an extremely large label set. We build on a recent extreme classification framework with logarithmic time and space, and on a general approach for error correcting output coding (ECOC) with loss-based decoding, and introduce a flexible and efficient approach accompanied by theoretical bounds. Our framework employs output codes induced by graphs, for which we show how to perform efficient loss-based decoding to potentially improve accuracy. In addition, our framework offers a tradeoff between accuracy, model size and prediction time. We show how to find the sweet spot of this tradeoff using only the training data. Our experimental study demonstrates the validity of our assumptions and claims, and shows that our method is competitive with state-of-the-art algorithms