Identity Testing Under Label Mismatch

Authors Clément L. Canonne , Karl Wimmer

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Author Details

Clément L. Canonne
  • The University of Sydney, Australia
Karl Wimmer
  • Duquesne University, Pittsburgh, PA, USA

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Clément L. Canonne and Karl Wimmer. Identity Testing Under Label Mismatch. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Testing whether the observed data conforms to a purported model (probability distribution) is a basic and fundamental statistical task, and one that is by now well understood. However, the standard formulation, identity testing, fails to capture many settings of interest; in this work, we focus on one such natural setting, identity testing under promise of permutation. In this setting, the unknown distribution is assumed to be equal to the purported one, up to a relabeling (permutation) of the model: however, due to a systematic error in the reporting of the data, this relabeling may not be the identity. The goal is then to test identity under this assumption: equivalently, whether this systematic labeling error led to a data distribution statistically far from the reference model.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Mathematics of computing → Hypothesis testing and confidence interval computation
  • distribution testing
  • property testing
  • permutations
  • lower bounds


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