# Learning Halfspaces with Massart Noise Under Structured Distributions

arXiv: https://arxiv.org/abs/2002.05632 · HTML: https://mlsanity.com/paper/2002.05632/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2020.

## Built on by (most cited first, 30 of 45)

- [Random Feature Amplification: Feature Learning and Generalization in Neural Networks](https://mlsanity.com/paper/2202.07626/) (2022)
- [Learning General Halfspaces with General Massart Noise under the Gaussian Distribution](https://mlsanity.com/paper/2108.08767/) (2021)
- [Learning a Single Neuron with Adversarial Label Noise via Gradient Descent](https://mlsanity.com/paper/2206.08918/) (2022)
- [Self-training Converts Weak Learners to Strong Learners in Mixture Models](https://mlsanity.com/paper/2106.13805/) (2021)
- [Efficient Testable Learning of Halfspaces with Adversarial Label Noise](https://mlsanity.com/paper/2303.05485/) (2023)
- [Improved Algorithms for Efficient Active Learning Halfspaces with Massart and Tsybakov noise](https://mlsanity.com/paper/2102.05312/) (2021)
- [Semi-Random Sparse Recovery in Nearly-Linear Time](https://mlsanity.com/paper/2203.04002/) (2022)
- [An Efficient Tester-Learner for Halfspaces](https://mlsanity.com/paper/2302.14853/) (2023)
- [Provable Generalization of SGD-trained Neural Networks of Any Width in the Presence of Adversarial Label Noise](https://mlsanity.com/paper/2101.01152/) (2021)
- [Tester-Learners for Halfspaces: Universal Algorithms](https://mlsanity.com/paper/2305.11765/) (2023)
- [Forster Decomposition and Learning Halfspaces with Noise](https://mlsanity.com/paper/2107.05582/) (2021)
- [Optimal SQ Lower Bounds for Learning Halfspaces with Massart Noise](https://mlsanity.com/paper/2201.09818/) (2022)
- [Sample-Optimal PAC Learning of Halfspaces with Malicious Noise](https://mlsanity.com/paper/2102.06247/) (2021)
- [List-Decodable Sparse Mean Estimation](https://mlsanity.com/paper/2205.14337/) (2022)
- [Smoothed Analysis for Learning Concepts with Low Intrinsic Dimension](https://mlsanity.com/paper/2407.00966/) (2024)
- [Provable Robustness of Adversarial Training for Learning Halfspaces with Noise](https://mlsanity.com/paper/2104.09437/) (2021)
- [Boosting in the Presence of Massart Noise](https://mlsanity.com/paper/2106.07779/) (2021)
- [ReLU Regression with Massart Noise](https://mlsanity.com/paper/2109.04623/) (2021)
- [Information-Computation Tradeoffs for Learning Margin Halfspaces with Random Classification Noise](https://mlsanity.com/paper/2306.16352/) (2023)
- [Robust Learning of Multi-index Models via Iterative Subspace Approximation](https://mlsanity.com/paper/2502.09525/) (2025)
- [The Power of Iterative Filtering for Supervised Learning with (Heavy) Contamination](https://mlsanity.com/paper/2505.20177/) (2025)
- [Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariates](https://mlsanity.com/paper/2206.07594/) (2022)
- [A Separation in Heavy-Tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplers](https://mlsanity.com/paper/2405.16736/) (2024)
- [A Near-optimal Algorithm for Learning Margin Halfspaces with Massart Noise](https://mlsanity.com/paper/2501.09691/) (2025)
- [SQ Lower Bounds for Learning Single Neurons with Massart Noise](https://mlsanity.com/paper/2210.09949/) (2022)
- [Near-Optimal Bounds for Learning Gaussian Halfspaces with Random Classification Noise](https://mlsanity.com/paper/2307.08438/) (2023)
- [Efficient PAC Learning of Halfspaces with Constant Malicious Noise Rate](https://mlsanity.com/paper/2410.01186/) (2024)
- [Learning Noisy Halfspaces with a Margin: Massart is No Harder than Random](https://mlsanity.com/paper/2501.09851/) (2025)
- [Semi-verified PAC Learning from the Crowd](https://mlsanity.com/paper/2106.07080/) (2021)
- [Outlier Robust and Sparse Estimation of Linear Regression Coefficients](https://mlsanity.com/paper/2208.11592/) (2022)

## Abstract (arXiv)

We study the problem of learning halfspaces with Massart noise in the distribution-specific PAC model. We give the first computationally efficient algorithm for this problem with respect to a broad family of distributions, including log-concave distributions. This resolves an open question posed in a number of prior works. Our approach is extremely simple: We identify a smooth em non-convex surrogate loss with the property that any approximate stationary point of this loss defines a halfspace that is close to the target halfspace. Given this structural result, we can use SGD to solve the underlying learning problem.