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This paper proposes a method for multi-class classification problems, wherethe number of classes K is large. The method, referred to as Candidates vs.Noises Estimation (CANE), selects a small subset of candidate classes andsamples the remaining classes. We show that CANE is always consistent andcomputationally efficient. Moreover, the resulting estimator has lowstatistical variance approaching that of the maximum likelihood estimator, whenthe observed label belongs to the selected candidates with high probability. Inpractice, we use a tree structure with leaves as classes to promote fast beamsearch for candidate selection. We further apply the CANE method to estimateword probabilities in learning large neural language models. Extensiveexperimental results show that CANE achieves better prediction accuracy overthe Noise-Contrastive Estimation (NCE), its variants and a number of thestate-of-the-art tree classifiers, while it gains significant speedup comparedto standard O(K) methods.

Candidates vs. Noises Estimation for Large Multi-Class Classification Problem