# PARIS: Pruning Algorithm via the Representer theorem for Imbalanced Scenarios

arXiv: https://arxiv.org/abs/2512.06950 · HTML: https://mlsanity.com/paper/2512.06950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 7 Dec 2025.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Delving into Deep Imbalanced Regression](https://mlsanity.com/paper/2102.09554/) (2021)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Dataset Pruning: Reducing Training Data by Examining Generalization Influence](https://mlsanity.com/paper/2205.09329/) (2022)
- [Training Gaussian Mixture Models at Scale via Coresets](https://mlsanity.com/paper/1703.08110/) (2017)
- [Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functions](https://mlsanity.com/paper/2007.13481/) (2020)
- [Theoretical and Practical Perspectives on what Influence Functions Do](https://mlsanity.com/paper/2305.16971/) (2023)
- [Revisiting the Fragility of Influence Functions](https://mlsanity.com/paper/2303.12922/) (2023)
- [Quanda: An Interpretability Toolkit for Training Data Attribution Evaluation and Beyond](https://mlsanity.com/paper/2410.07158/) (2024)

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

- [PROSWIN: Probabilistic Solar Wind Speed Forecasting Using Deep Distributional Regression From Solar Images](https://mlsanity.com/paper/2609.26683/) (2026)

## Abstract (arXiv)

The challenge of imbalanced regression arises when standard Empirical Risk Minimization (ERM) biases models toward high-frequency regions of the data distribution, causing severe degradation on rare but high-impact ``tail'' events. Existing strategies uch as loss re-weighting or synthetic over-sampling often introduce noise, distort the underlying distribution, or add substantial algorithmic complexity. We introduce PARIS (Pruning Algorithm via the Representer theorem for Imbalanced Scenarios), a principled framework that mitigates imbalance by optimizing the training set itself. PARIS leverages the representer theorem for neural networks to compute a closed-form representer deletion residual, which quantifies the exact change in validation loss caused by removing a single training point without retraining. Combined with an efficient Cholesky rank-one downdating scheme, PARIS performs fast, iterative pruning that eliminates uninformative or performance-degrading samples. We use a real-world space weather example, where PARIS reduces the training set by up to 75% while preserving or improving overall RMSE, outperforming re-weighting, synthetic oversampling, and boosting baselines. Our results demonstrate that representer-guided dataset pruning is a powerful, interpretable, and computationally efficient approach to rare-event regression.