# Optimal Sampling for Generalized Linear Model under Measurement Constraint with Surrogate Variables

arXiv: https://arxiv.org/abs/2501.00972 · HTML: https://mlsanity.com/paper/2501.00972/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 1 Jan 2025.

## Builds on (most cited first, 9 of 9)

- [A Statistical Perspective on Algorithmic Leveraging](https://mlsanity.com/paper/1306.5362/) (2013)
- [Optimal Subsampling for Large Sample Logistic Regression](https://mlsanity.com/paper/1702.01166/) (2017)
- [Semi-supervised Inference for Explained Variance in High-dimensional Linear Regression and Its Applications](https://mlsanity.com/paper/1806.06179/) (2018)
- [Information-Based Optimal Subdata Selection for Big Data Linear Regression](https://mlsanity.com/paper/1710.10382/) (2017)
- [Asymptotic Analysis of Sampling Estimators for Randomized Numerical Linear Algebra Algorithms](https://mlsanity.com/paper/2002.10526/) (2020)
- [Optimal and Safe Estimation for High-Dimensional Semi-Supervised Learning](https://mlsanity.com/paper/2011.14185/) (2020)
- [LowCon: A design-based subsampling approach in a misspecified linear modeL](https://mlsanity.com/paper/2010.12178/) (2020)
- [Raking and Regression Calibration: Methods to Address Bias from Correlated Covariate and Time-to-Event Error](https://mlsanity.com/paper/1905.08330/) (2019)
- [Optimal Sampling for Generalized Linear Models under Measurement Constraints](https://mlsanity.com/paper/1907.07309/) (2019)

## Abstract (arXiv)

Measurement-constrained datasets, often encountered in semi-supervised learning, arise when data labeling is costly, time-intensive, or hindered by confidentiality or ethical concerns, resulting in a scarcity of labeled data. In certain cases, surrogate variables are accessible across the entire dataset and can serve as approximations to the true response variable; however, these surrogates often contain measurement errors and thus cannot be directly used for accurate prediction. We propose an optimal sampling strategy that effectively harnesses the available information from surrogate variables. This approach provides consistent estimators under the assumption of a generalized linear model, achieving theoretically lower asymptotic variance than existing optimal sampling algorithms that do not use surrogate data information. By employing the A-optimality criterion from optimal experimental design, our strategy maximizes statistical efficiency. Numerical studies demonstrate that our approach surpasses existing optimal sampling methods, exhibiting reduced empirical mean squared error and enhanced robustness in algorithmic performance. These findings highlight the practical advantages of our strategy in scenarios where measurement constraints exist and surrogates are available.