Are Anchor Points Really Indispensable in Label-Noise Learning? (1906.00189v2)

Abstract: In label-noise learning, \textit{noise transition matrix}, denoting the probabilities that clean labels flip into noisy labels, plays a central role in building \textit{statistically consistent classifiers}. Existing theories have shown that the transition matrix can be learned by exploiting \textit{anchor points} (i.e., data points that belong to a specific class almost surely). However, when there are no anchor points, the transition matrix will be poorly learned, and those current consistent classifiers will significantly degenerate. In this paper, without employing anchor points, we propose a \textit{transition-revision} ($T$-Revision) method to effectively learn transition matrices, leading to better classifiers. Specifically, to learn a transition matrix, we first initialize it by exploiting data points that are similar to anchor points, having high \textit{noisy class posterior probabilities}. Then, we modify the initialized matrix by adding a \textit{slack variable}, which can be learned and validated together with the classifier by using noisy data. Empirical results on benchmark-simulated and real-world label-noise datasets demonstrate that without using exact anchor points, the proposed method is superior to the state-of-the-art label-noise learning methods.

Insights into Anchor Points and Transition Matrices in Label-Noise Learning

The paper "Are Anchor Points Really Indispensable in Label-Noise Learning?" tackles a critical issue in label-noise learning, particularly the dependency on anchor points for learning noise transition matrices. Unlike prior work that predominantly relies on anchor points—data points that belong to a specific class with near certainty—this paper explores methodologies to learn without such constraints. This holds significant importance in scenarios where anchor points may not be identifiable, or where data distributions simply do not ensure their presence.

Transition Matrices and Consistent Learning

In label-noise learning, the transition matrix, which represents the probabilities of label corruption, is essential for constructing statistically consistent classifiers. Existing approaches utilize anchor points to learn these matrices. However, when such points are absent or incorrectly identified, these methods fail to accurately estimate transition matrices, which in turn degrade classifier performance.

Transition-Revision Methodology

The authors propose a novel Transition-Revision ($T$-Revision) method to circumvent the need for anchor points. This approach starts by approximating anchor points via data points with high noisy class posterior probabilities to initialize the transition matrix. Subsequently, a slack variable is introduced and refined jointly with the classifier using noisy data. This mechanism sidesteps the need for directly inverting the transition matrix, which is typically computationally complex and error-prone.

Empirical Evaluation and Results

The empirical evaluation employs both synthetic noise datasets like MNIST, CIFAR-10, CIFAR-100 and real-world noisy label dataset Clothing1M. Through benchmark datasets, the paper demonstrates that the $T$-Revision approach outperforms state-of-the-art methods that rely on anchor points. Results indicate substantial improvements in classification accuracy when employing $T$-Revision, especially in high noise scenarios.

Significantly, the paper highlights that the proposed method decreases the transition matrix estimation errors—even when traditional anchor points are used for initialization. This improvement is substantial across all datasets, indicating a robust performance of the transition revision mechanism.

Theoretical Implications and Considerations

While much of the paper focuses on empirical methodologies, it also provides theoretical insights into the generalization errors associated with the proposed risk-consistent estimators. These insights are grounded in recent theoretical advances on neural network hypothesis complexities, which provide an acceptable upper bound for generalization errors without relying on inverse transition matrices.

Future Directions

This research opens avenues for further studies in transition matrix estimation and its ramifications in unsupervised or semi-supervised learning environments. Future research could delve into incorporating prior knowledge, such as matrix sparsity, into the $T$-Revision framework to enhance performance further.

Moreover, recursive learning of transition matrices and classifiers or exploring ensemble methods to improve robustness and accuracy may provide fruitful future directions. Another potential exploration is extending the model's applicability in situations where side information or additional context might affect learning under noise conditions.

The $T$-Revision method thus addresses a key gap in the existing literature by enabling effective label-noise learning without the stringent requirement of anchor points, representing a strategic evolution in the landscape of noise-robust classification.