U-Statistics for Importance-Weighted Variational Inference

• URL: http://arxiv.org/abs/2302.13918v1
• Date: Mon, 27 Feb 2023 16:08:43 GMT
• Title: U-Statistics for Importance-Weighted Variational Inference
• Authors: Javier Burroni, Kenta Takatsu, Justin Domke, Daniel Sheldon
• Abstract summary: We propose the use of U-statistics to reduce variance for estimation in importance-weighted variational inference. We find empirically that U-statistic variance reduction can lead to modest to significant improvements in inference performance on a range of models.
• Score: 29.750633016889655
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose the use of U-statistics to reduce variance for gradient estimation in importance-weighted variational inference. The key observation is that, given a base gradient estimator that requires $m > 1$ samples and a total of $n > m$ samples to be used for estimation, lower variance is achieved by averaging the base estimator on overlapping batches of size $m$ than disjoint batches, as currently done. We use classical U-statistic theory to analyze the variance reduction, and propose novel approximations with theoretical guarantees to ensure computational efficiency. We find empirically that U-statistic variance reduction can lead to modest to significant improvements in inference performance on a range of models, with little computational cost.

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