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

Abstract: Log-linear models are arguably the most successful class of graphical models for large-scale applications because of their simplicity and tractability. Learning and inference with these models require calculating the partition function, which is a major bottleneck and intractable for large state spaces. Importance Sampling (IS) and MCMC-based approaches are lucrative. However, the condition of having a "good" proposal distribution is often not satisfied in practice. 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 the partition function accurately in sub-linear time. Our samples are generated in near-constant time using locality sensitive hashing (LSH), and so are correlated and unnormalized. We demonstrate the effectiveness of our proposed approach by comparing the accuracy and speed of estimating the partition function against other state-of-the-art estimation techniques including IS and the efficient variant of Gumbel-Max sampling. With our efficient sampling scheme, we accurately train real-world LLMs using only 1-2% of computations.