Learning with Biased Complementary Labels

Abstract

In this paper, we study the classi cation 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 andȲ be the true and complementary labels, respectively. We rst model the annotation of complementary labels via transition probabilities P (Ȳ = i|Y = j), i = j ∈ {1, · · · , c}, where c is the number of classes. Previous methods implicitly assume that P (Ȳ = 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 Figure 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 di erent. 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 classi ers to learn with biased complementary labels. (3) It theoretically ensures that the classi er 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.

Generative-Discriminative Complementary Learning

“…Existing Discriminative Complementary Learning (DCL) methods modified the ordinary classification loss function to the complementary classification loss¯ to provide a consistent estimation of f . Various loss functions have been considered in the literature, such as one-vs-all ramp/sigmoid loss (Ishida et al 2017), pair-comparison ramp/sigmoid loss (Ishida et al 2017), and cross-entropy loss (Yu et al 2018).…”

“…In this paper, we consider a recently proposed weaklysupervised classification scenario, i.e., learning from complementary labels (Ishida et al 2017;Yu et al 2018). Unlike an ordinary label, a complementary label specifies a class that an input instance does not belong to.…”

“…However, this method only allows classification loss functions with certain non-convex binary losses for one-versus-all and pairwise comparison. Later, (Yu et al 2018) proposed to use the forward loss correction technique (Patrini et al 2017) that learns the conditional, P Y |X , from complementary labels, where X denote the input features and Y denote labels. (Ishida et al 2018) derived an unbiased estimator of the true classification risk with arbitrary loss functions from complementarily-labeled data.…”

“…In this section, we first introduce the concept of learning from so-called complementary labels. Then, we discuss a state-of-the-art discriminative complementary learning approach, (Yu et al 2018), which is the most relevant to our method.…”

Multi-Modal Multi-Scale Deep Learning for Large-Scale Image Annotation

“…Liu et al [39] use importance reweighting to modify any loss function for classification with noisy labels, and extend the random classification noise to a bounded case [40]. Moreover, Yu et al [41] prove that biased complementary labels can enhance multi-class classification. These methods have been successfully applied in binary classification and multi-class classification, which may lead to improvements when extended to our large-scale image annotation where each image is annotated with one or more tags and labels (but out of the scope of this paper).…”