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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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High-dimensional semi-supervised learning: in search of optimal inference of the mean
Summary A fundamental challenge in semi-supervised learning lies in the observed data’s disproportional size when compared with the size of the data collected with missing outcomes. An implicit understanding is that the dataset with missing outcomes, being significantly larger, ought to improve estimation and inference. However, it is unclear to what extent this is correct. We illustrate one clear benefit: root-$$n$$ inference of the outcome’s mean is possible while only requiring a consistent estimation of the outcome, possibly at a rate slower than root $$n$$. This is achieved by a novel $$k$$-fold, cross-fitted, double robust estimator. We discuss both linear and nonlinear outcomes. Such an estimator is particularly suited for models that naturally do not admit root-$$n$$ consistency, such as high-dimensional, nonparametric or semiparametric models. We apply our methods to estimating heterogeneous treatment effects.
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- Award ID(s):
- 1712481
- PAR ID:
- 10345775
- Date Published:
- Journal Name:
- Biometrika
- Volume:
- 109
- Issue:
- 2
- ISSN:
- 0006-3444
- Page Range / eLocation ID:
- 387 to 403
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/biomet/asab042
