# Semi-Supervised Learning with Noisy Proxy Covariates: Generalization Bounds and Distribution Regression

arXiv: https://arxiv.org/abs/2606.00512 · HTML: https://mlsanity.com/paper/2606.00512/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 33 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 6 of 6)

- [DataComp: In search of the next generation of multimodal datasets](https://mlsanity.com/paper/2304.14108/) (2023)
- [Learning Theory for Distribution Regression](https://mlsanity.com/paper/1411.2066/) (2014)
- [Distribution-Free Distribution Regression](https://mlsanity.com/paper/1302.0082/) (2013)
- [Benign Overfitting and Noisy Features](https://mlsanity.com/paper/2008.02901/) (2020)
- [Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning](https://mlsanity.com/paper/2009.04324/) (2020)
- [Learning to Embed Distributions via Maximum Kernel Entropy](https://mlsanity.com/paper/2408.00549/) (2024)

## Abstract (arXiv)

In many modern machine learning pipelines, abundant pretrained representations serve as noisy proxy covariates, while task-specific labels remain scarce. We study semi-supervised regression in this setting, and propose a simple two stage estimator that learns kernel eigenfeatures from all proxy covariates and fits a ridge predictor on labeled data. We derive finite sample bounds showing that fast labeled sample rates are recovered when proxy perturbation is controlled and unlabeled proxy covariates are sufficiently abundant. We also show that distribution regression is a direct special case, with analogous guarantees when the finite bag size is large enough. Experiments show consistent gains over supervised and semi-supervised baselines, especially in low label regimes.