## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 10, Number 2 (2016), 2780-2824.

### Classification with asymmetric label noise: Consistency and maximal denoising

Gilles Blanchard, Marek Flaska, Gregory Handy, Sara Pozzi, and Clayton Scott

#### Abstract

In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are “mutually irreducible,” a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions.

Our results are facilitated by a connection to “mixture proportion estimation,” which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence result for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach.

#### Article information

**Source**

Electron. J. Statist., Volume 10, Number 2 (2016), 2780-2824.

**Dates**

Received: August 2015

First available in Project Euclid: 20 September 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1474373835

**Digital Object Identifier**

doi:10.1214/16-EJS1193

**Mathematical Reviews number (MathSciNet)**

MR3549019

**Zentralblatt MATH identifier**

1347.62106

**Subjects**

Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Secondary: 68T10: Pattern recognition, speech recognition {For cluster analysis, see 62H30}

**Keywords**

Classification label noise mixture proportion estimation surrogate loss consistency

#### Citation

Blanchard, Gilles; Flaska, Marek; Handy, Gregory; Pozzi, Sara; Scott, Clayton. Classification with asymmetric label noise: Consistency and maximal denoising. Electron. J. Statist. 10 (2016), no. 2, 2780--2824. doi:10.1214/16-EJS1193. https://projecteuclid.org/euclid.ejs/1474373835