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Sublinear Partition Estimation

The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is problematic as real-world problem sets continue to grow in categorical types, such as in visual object recognition or discriminative language modeling. We propose three approaches for sublinear estimation of the partition function, based on approximate nearest neighbor search and kernel feature maps and compare the performance of the proposed approaches empirically.