# Active Learning for Regression based on Wasserstein distance and GroupSort Neural Networks

arXiv: https://arxiv.org/abs/2403.15108 · HTML: https://mlsanity.com/paper/2403.15108/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 22 Mar 2024.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Effective Data Augmentation With Diffusion Models](https://mlsanity.com/paper/2302.07944/) (2023)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Deep Active Learning: Unified and Principled Method for Query and Training](https://mlsanity.com/paper/1911.09162/) (2019)
- [Some Theoretical Properties of GANs](https://mlsanity.com/paper/1803.07819/) (2018)
- [Approximating Lipschitz continuous functions with GroupSort neural networks](https://mlsanity.com/paper/2006.05254/) (2020)
- [Active Learning for Regression Using Greedy Sampling](https://mlsanity.com/paper/1808.04245/) (2018)
- [Active Learning for Regression by Inverse Distance Weighting](https://mlsanity.com/paper/2204.07177/) (2022)
- [Pool-Based Unsupervised Active Learning for Regression Using Iterative Representativeness-Diversity Maximization (iRDM)](https://mlsanity.com/paper/2003.07658/) (2020)
- [Optimal 1-Wasserstein Distance for WGANs](https://mlsanity.com/paper/2201.02824/) (2022)

## Abstract (arXiv)

This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The Wasserstein distance is computed using GroupSort Neural Networks. The use of such networks provides theoretical foundations giving a way to quantify errors with explicit bounds for their size and depth. This solution is combined with another uncertainty-based approach that is more outlier-tolerant to complete the query strategy. Finally, this method is compared with other classical and recent solutions. The study empirically shows the pertinence of such a representativity-uncertainty approach, which provides good estimation all along the query procedure. Moreover, the Wasserstein active regression often achieves more precise estimations and tends to improve accuracy faster than other models.