# LowCon: A design-based subsampling approach in a misspecified linear modeL

arXiv: https://arxiv.org/abs/2010.12178 · HTML: https://mlsanity.com/paper/2010.12178/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [Model-free Subsampling Method Based on Uniform Designs](https://mlsanity.com/paper/2209.03617/) (2022)
- [Optimal Sampling Designs for Multi-dimensional Streaming Time Series with Application to Power Grid Sensor Data](https://mlsanity.com/paper/2303.08242/) (2023)
- [Optimal Sampling for Generalized Linear Model under Measurement Constraint with Surrogate Variables](https://mlsanity.com/paper/2501.00972/) (2025)
- [Core-elements Subsampling for Alternating Least Squares](https://mlsanity.com/paper/2509.18024/) (2025)
- [Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification](https://mlsanity.com/paper/2610.19351/) (2026)

## Abstract (arXiv)

We consider a measurement constrained supervised learning problem, that is, (1) full sample of the predictors are given; (2) the response observations are unavailable and expensive to measure. Thus, it is ideal to select a subsample of predictor observations, measure the corresponding responses, and then fit the supervised learning model on the subsample of the predictors and responses. However, model fitting is a trial and error process, and a postulated model for the data could be misspecified. Our empirical studies demonstrate that most of the existing subsampling methods have unsatisfactory performances when the models are misspecified. In this paper, we develop a novel subsampling method, called "LowCon", which outperforms the competing methods when the working linear model is misspecified. Our method uses orthogonal Latin hypercube designs to achieve a robust estimation. We show that the proposed design-based estimator approximately minimizes the so-called "worst-case" bias with respect to many possible misspecification terms. Both the simulated and real-data analyses demonstrate the proposed estimator is more robust than several subsample least squares estimators obtained by state-of-the-art subsampling methods.