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Log-linear models are arguably the most successful class of graphical modelsfor large-scale applications because of their simplicity and tractability.Learning and inference with these models require calculating the partitionfunction, which is a major bottleneck and intractable for large state spaces.Importance Sampling (IS) and MCMC-based approaches are lucrative. However, thecondition of having a "good" proposal distribution is often not satisfied inpractice.  In this paper, we add a new dimension to efficient estimation via sampling.We propose a new sampling scheme and an unbiased estimator that estimates thepartition function accurately in sub-linear time. Our samples are generated innear-constant time using locality sensitive hashing (LSH), and so arecorrelated and unnormalized. We demonstrate the effectiveness of our proposedapproach by comparing the accuracy and speed of estimating the partitionfunction against other state-of-the-art estimation techniques including IS andthe efficient variant of Gumbel-Max sampling. With our efficient samplingscheme, we accurately train real-world language models using only 1-2% ofcomputations.

A New Unbiased and Efficient Class of LSH-Based Samplers and Estimators for Partition Function Computation in Log-Linear Models