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On the Accuracy of Self-Normalized Log-Linear Models
Jacob Andreas · Maxim Rabinovich · Michael Jordan · Dan Klein

Tue Dec 08 04:00 PM -- 08:59 PM (PST) @ 210 C #50

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as ``self-normalization'', which introduces a regularization term in training to penalize log normalizers for deviating from zero. This makes it possible to use unnormalized model scores as approximate probabilities. Empirical evidence suggests that self-normalization is extremely effective, but a theoretical understanding of why it should work, and how generally it can be applied, is largely lacking.We prove upper bounds on the loss in accuracy due to self-normalization, describe classes of input distributionsthat self-normalize easily, and construct explicit examples of high-variance input distributions. Our theoretical results make predictions about the difficulty of fitting self-normalized models to several classes of distributions, and we conclude with empirical validation of these predictions on both real and synthetic datasets.

Author Information

Jacob Andreas (UC Berkeley)
Maxim Rabinovich (UC Berkeley)
Michael Jordan (UC Berkeley)
Dan Klein (UC Berkeley)

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