Convex and non-convex approaches for statistical inference with class-conditional noisy labels

Hyebin Song, Ran Dai, Garvesh Raskutti, Rina Foygel Barber

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 lowdimensional 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 √s log 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.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
StatePublished - Aug 2020


  • Class-conditional label noise
  • Generalized linear model
  • Non-convexity
  • PUlearning
  • Regularization

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence
  • Control and Systems Engineering
  • Statistics and Probability


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