Classification with Asymmetric Label Noise: Consistency and Maximal Denoising (1303.1208v3)

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.

• The paper introduces identifiability conditions via mutual irreducibility that enable effective maximal denoising under asymmetric label noise.
• It recasts noise estimation as a mixture proportion problem and achieves consistent classification through surrogate risk minimization in an RKHS framework.
• Experimental results on benchmark and real-world datasets, including nuclear safeguards, validate the approach’s robustness and practical impact.

Classification with Asymmetric Label Noise: Consistency and Maximal Denoising

The paper addresses the problem of classification in the presence of asymmetric label noise without assuming class separability, independence of noise from true labels, or known noise proportions. The primary objective is to establish necessary and sufficient conditions under which the true class-conditional distributions can be identified from the contaminated distributions.

Key Contributions and Results

1. Identifiability Conditions: The authors introduce conditions under which the class-conditional distributions are identifiable. These conditions relax previous assumptions by allowing for non-separable classes and asymmetric, unknown noise levels. The conditions posited are that a majority of the observed labels are correct and that the true distributions are "mutually irreducible." This concept implies that neither distribution can be expressed as a nontrivial mixture of the other, facilitating maximal denoising.
2. Maximal Denoising and Mixture Proportion Estimation: The paper draws a connection to mixture proportion estimation, highlighting that the problem of determining noise proportions can be recast as estimating the maximal proportion of one distribution in another. The authors provide a novel convergence result for mixture proportion estimation, showing that it assists in the consistent estimation of classification performance using surrogate loss minimization.
3. Experimental Validation: Empirical results on benchmark datasets and a real-world nuclear particle classification problem demonstrate the applicability and effectiveness of their approach. The results validate the proposed methodology's robustness in correctly estimating label noise and improving classification accuracy.
4. Algorithmic Implementation: The paper introduces a discrimination rule based on surrogate risk minimization in a reproducing kernel Hilbert space framework. By estimating the label noise proportions, the algorithm adapts to the noisy data, ensuring universally consistent classification under the proposed conditions.

Implications and Speculations

The theoretical advancements in this paper have significant implications for practical applications in fields where data labeling is inherently noisy. For instance, the methodology could be particularly beneficial in domains like nuclear safeguards, where accurate label estimation is crucial for reliable detection and classification processes. The proposed maximal denoising approach ensures that classifiers trained under noisy conditions align more closely with the ideal classifier based on uncontaminated data, offering insights into underlying class distributions.

From a theoretical standpoint, this work challenges conventional assumptions in the label noise literature and offers a novel lens through which label noise problems can be dissected and understood. The explicit focus on conditions weaker than those typically assumed broadens the applicability of these results to a variety of real-world noisy datasets that were previously constrained by stricter assumptions.

Future Directions in AI

This research opens potential avenues in AI for developing more robust classifiers under noisy labels, thereby extending applicability to semi-supervised and unsupervised contexts. Moreover, the concept of mutual irreducibility could be further explored in the context of ensemble learning or transfer learning, where the fusion and transformation of knowledge are paramount.

Overall, this paper advances the understanding of classification under label noise and proposes methods that can be robustly applied to practical problems, impacting both the theory and applications of machine learning in noisy environments.