# Density-Aware Farthest Point Sampling

arXiv: https://arxiv.org/abs/2509.13213 · HTML: https://mlsanity.com/paper/2509.13213/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 50 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [LAVA: Data Valuation without Pre-Specified Learning Algorithms](https://mlsanity.com/paper/2305.00054/) (2023)
- [Fast and Eager k-Medoids Clustering: O(k) Runtime Improvement of the PAM, CLARA, and CLARANS Algorithms](https://mlsanity.com/paper/2008.05171/) (2020)
- [Coresets for Robust Training of Neural Networks against Noisy Labels](https://mlsanity.com/paper/2011.07451/) (2020)
- [An Experimental Design Framework for Label-Efficient Supervised Finetuning of Large Language Models](https://mlsanity.com/paper/2401.06692/) (2024)
- [Data Twinning](https://mlsanity.com/paper/2110.02927/) (2021)
- [On minimizing the training set fill distance in machine learning regression](https://mlsanity.com/paper/2307.10988/) (2023)

## Built on by (most cited first, 1 of 1)

- [The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology](https://mlsanity.com/paper/2610.05441/) (2026)

## Abstract (arXiv)

We focus on training machine learning regression models in scenarios where the availability of labeled training data is limited due to computational constraints or high labeling costs. Thus, selecting suitable training sets from unlabeled data is essential for balancing performance and efficiency. For the selection of the training data, we focus on passive and model-agnostic sampling methods that only consider the data feature representations. We derive an upper bound for the expected prediction error of Lipschitz continuous regression models that linearly depends on the weighted fill distance of the training set: a quantity we can estimate simply by considering the data features. We introduce ''Density-Aware Farthest Point Sampling'' (DA-FPS), a novel sampling method. We prove that DA-FPS provides approximate minimizers for a data-driven estimation of the weighted fill distance, thereby aiming at minimizing our derived bound. We conduct experiments using two regression models across three datasets. The results demonstrate that DA-FPS significantly reduces the mean absolute prediction error compared to other sampling strategies.