In this paper, we study the classification problem in which we have access to easily obtainable surrogate for true labels, namely complementary labels, which specify classes that observations do not belong to. Let Y and ( Y ) be the true and complementary labels, respectively. We first model the annotation of complementary labels via transition probabilities (P( Y =i|Y=j), i j 1, ,c ), where c is the number of classes. Previous methods implicitly assume that (P( Y =i|Y=j), i j ), are identical, which is not true in practice because humans are biased toward their own experience. For example, as shown in Fig. 1, if an annotator is more familiar with monkeys than prairie dogs when providing complementary labels for meerkats, she is more likely to employ “monkey” as a complementary label. We therefore reason that the transition probabilities will be different. In this paper, we propose a framework that contributes three main innovations to learning with biased complementary labels: (1) It estimates transition probabilities with no bias. (2) It provides a general method to modify traditional loss functions and extends standard deep neural network classifiers to learn with biased complementary labels. (3) It theoretically ensures that the classifier learned with complementary labels converges to the optimal one learned with true labels. Comprehensive experiments on several benchmark datasets validate the superiority of our method to current state-of-the-art methods.
In the setting of label noise, transition probabilities are introduced to statistically model the generation of noisy labels. In classification and transfer learning, methods @cite_35 @cite_37 @cite_24 @cite_11 employ transition probabilities to modify loss functions such that they can be robust to noisy labels. Similar strategies to modify deep neural networks by adding a transition layer have been proposed in @cite_38 @cite_29 . However, this is the first time that this idea is applied to the new problem of learning with biased complementary labels. Different from label noise, here, all diagonal entries of the transition matrix are zeros and the transition matrix sometimes may be not required to be invertible in empirical.
@cite_35 @cite_37 @cite_38 @cite_29 @cite_24 @cite_11
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In this paper, we theoretically study the problem of binary classification in the presence of random classification noise—the learner, instead of seeing the true labels, sees labels that have independently been flipped with some small probability. Moreover, random label noise is class-conditional— the flip probability depends on the class. We provide two approaches to suitably modify any given surrogate loss function. First, we provide a simple unbiased estimator of any loss, and obtain performance bounds for empirical risk minimization in the presence of iid data with noisy labels. If the loss function satisfies a simple symmetry condition, we show that the method leads to an efficient algorithm for empirical minimization. Second, by leveraging a reduction of risk minimization under noisy labels to classification with weighted 0-1 loss, we suggest the use of a simple weighted surrogate loss, for which we are able to obtain strong empirical risk bounds. This approach has a very remarkable consequence — methods used in practice such as biased SVM and weighted logistic regression are provably noise-tolerant. On a synthetic non-separable dataset, our methods achieve over 88 accuracy even when 40 of the labels are corrupted, and are competitive with respect to recently proposed methods for dealing with label noise in several benchmark datasets. In this paper, we study a classification problem in which sample labels are randomly corrupted. In this scenario, there is an unobservable sample with noise-free labels. However, before being observed, the true labels are independently flipped with a probability @math , and the random label noise can be class-conditional. Here, we address two fundamental problems raised by this scenario. The first is how to best use the abundant surrogate loss functions designed for the traditional classification problem when there is label noise. We prove that any surrogate loss function can be used for classification with noisy labels by using importance reweighting, with consistency assurance that the label noise does not ultimately hinder the search for the optimal classifier of the noise-free sample. The other is the open problem of how to obtain the noise rate @math . We show that the rate is upper bounded by the conditional probability @math of the noisy sample. Consequently, the rate can be estimated, because the upper bound can be easily reached in classification problems. Experimental results on synthetic and real datasets confirm the efficiency of our methods. We present a theoretically grounded approach to train deep neural networks, including recurrent networks, subject to class-dependent label noise. We propose two procedures for loss correction that are agnostic to both application domain and network architecture. They simply amount to at most a matrix inversion and multiplication, provided that we know the probability of each class being corrupted into another. We further show how one can estimate these probabilities, adapting a recent technique for noise estimation to the multi-class setting, and thus providing an end-to-end framework. Extensive experiments on MNIST, IMDB, CIFAR-10, CIFAR-100 and a large scale dataset of clothing images employing a diversity of architectures &#x2014; stacking dense, convolutional, pooling, dropout, batch normalization, word embedding, LSTM and residual layers &#x2014; demonstrate the noise robustness of our proposals. Incidentally, we also prove that, when ReLU is the only non-linearity, the loss curvature is immune to class-dependent label noise. Traditional classification systems rely heavily on sufficient training data with accurate labels. However, the quality of the collected data depends on the labelers, among which inexperienced labelers may exist and produce unexpected labels that may degrade the performance of a learning system. In this paper, we investigate the multiclass classification problem where a certain amount of training examples are randomly labeled. Specifically, we show that this issue can be formulated as a label noise problem. To perform multiclass classification, we employ the widely used importance reweighting strategy to enable the learning on noisy data to more closely reflect the results on noise-free data. We illustrate the applicability of this strategy to any surrogate loss functions and to different classification settings. The proportion of randomly labeled examples is proved to be upper bounded and can be estimated under a mild condition. The convergence analysis ensures the consistency of the learned classifier to the optimal classifier with respect to clean data. Two instantiations of the proposed strategy are also introduced. Experiments on synthetic and real data verify that our approach yields improvements over the traditional classifiers as well as the robust classifiers. Moreover, we empirically demonstrate that the proposed strategy is effective even on asymmetrically noisy data.