# Convex and Non-convex Approaches for Statistical Inference with Class-Conditional Noisy Labels

arXiv: https://arxiv.org/abs/1910.02348 · HTML: https://mlsanity.com/paper/1910.02348/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2019.

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

- [Leveraging Noisy Manual Labels as Useful Information: An Information Fusion Approach for Enhanced Variable Selection in Penalized Logistic Regression](https://mlsanity.com/paper/2504.16585/) (2025)

## Abstract (arXiv)

We study the problem of estimation and testing in logistic regression with class-conditional noise in the observed labels, which has an important implication in the Positive-Unlabeled (PU) learning setting. With the key observation that the label noise problem belongs to a special sub-class of generalized linear models (GLM), we discuss convex and non-convex approaches that address this problem. A non-convex approach based on the maximum likelihood estimation produces an estimator with several optimal properties, but a convex approach has an obvious advantage in optimization. We demonstrate that in the low-dimensional setting, both estimators are consistent and asymptotically normal, where the asymptotic variance of the non-convex estimator is smaller than the convex counterpart. We also quantify the efficiency gap which provides insight into when the two methods are comparable. In the high-dimensional setting, we show that both estimation procedures achieve ℓ2-consistency at the minimax optimal √slog p/n rates under mild conditions. Finally, we propose an inference procedure using a de-biasing approach. We validate our theoretical findings through simulations and a real-data example.