# Screening Data Points in Empirical Risk Minimization via Ellipsoidal Regions and Safe Loss Functions

arXiv: https://arxiv.org/abs/1912.02566 · HTML: https://mlsanity.com/paper/1912.02566/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [On Inductive Biases for Machine Learning in Data Constrained Settings](https://mlsanity.com/paper/2302.10692/) (2023)
- [Gap Safe Screening Rules for Fast Training of Robust Support Vector Machines under Feature Noise](https://mlsanity.com/paper/2603.25221/) (2026)

## Abstract (arXiv)

We design simple screening tests to automatically discard data samples in empirical risk minimization without losing optimization guarantees. We derive loss functions that produce dual objectives with a sparse solution. We also show how to regularize convex losses to ensure such a dual sparsity-inducing property, and propose a general method to design screening tests for classification or regression based on ellipsoidal approximations of the optimal set. In addition to producing computational gains, our approach also allows us to compress a dataset into a subset of representative points.