In real-world classification problems, pairwise supervision (i.e., a pair of patterns with a binary label indicating whether they belong to the same class or not) can often be obtained at a lower cost than ordinary class labels. Similarity learning is a general framework to utilize such pairwise supervision to elicit useful representations by inferring the relationship between two data points, which encompasses various important preprocessing tasks such as metric learning, kernel learning, graph embedding, and contrastive representation learning. Although elicited representations are expected to perform well in downstream tasks such as classification, little theoretical insight has been given in the literature so far. In this paper, we reveal that a specific formulation of similarity learning is strongly related to the objective of binary classification, which spurs us to learn a binary classifier without ordinary class labels---by fitting the product of real-valued prediction functions of pairwise patterns to their similarity. Our formulation of similarity learning does not only generalize many existing ones, but also admits an excess risk bound showing an explicit connection to classification. Finally, we empirically demonstrate the practical usefulness of the proposed method on benchmark datasets.
We consider the semi-supervised ordinal regression problem, where unlabeled data are given in addition to ordinal labeled data. There are many evaluation metrics in ordinal regression such as the mean absolute error, mean squared error, and mean classification error. Existing work does not take the evaluation metric into account, has a restriction on the model choice, and has no theoretical guarantee. To mitigate these problems, we propose a method based on the empirical risk minimization (ERM) framework that is applicable to optimizing all of the metrics mentioned above. Also, our method has flexible choices of models, surrogate losses, and optimization algorithms. Moreover, our method does not require a restrictive assumption on unlabeled data such as the cluster assumption and manifold assumption. We provide an estimation error bound to show that our learning method is consistent. Finally, we conduct experiments to show the usefulness of our framework.
With the widespread use of machine learning for classification, it becomes increasingly important to be able to use weaker kinds of supervision for tasks in which it is hard to obtain standard labeled data. One such kind of supervision is provided pairwise---in the form of Similar (S) pairs (if two examples belong to the same class) and Dissimilar (D) pairs (if two examples belong to different classes). This kind of supervision is realistic in privacy-sensitive domains. Although this problem has been looked at recently, it is unclear how to learn from such supervision under label noise, which is very common when the supervision is crowd-sourced. In this paper, we close this gap and demonstrate how to learn a classifier from noisy S and D labeled data. We perform a detailed investigation of this problem under two realistic noise models and propose two algorithms to learn from noisy S-D data. We also show important connections between learning from such pairwise supervision data and learning from ordinary class-labeled data. Finally, we perform experiments on synthetic and real world datasets and show our noise-informed algorithms outperform noise-blind baselines in learning from noisy pairwise data.
Clustering using neural networks has recently demon- strated promising performance in machine learning and computer vision applications. However, the performance of current approaches is limited either by unsupervised learn- ing or their dependence on large set of labeled data sam- ples. In this paper, we propose ClusterNet that uses pair- wise semantic constraints from very few labeled data sam- ples (< 5% of total data) and exploits the abundant un- labeled data to drive the clustering approach. We define a new loss function that uses pairwise semantic similarity between objects combined with constrained k-means clus- tering to efficiently utilize both labeled and unlabeled data in the same framework. The proposed network uses con- volution autoencoder to learn a latent representation that groups data into k specified clusters, while also learning the cluster centers simultaneously. We evaluate and com- pare the performance of ClusterNet on several datasets and state of the art deep clustering approaches.
Can we learn a binary classifier from only positive data, without any negative data or unlabeled data? We show that if one can equip positive data with confidence (positive-confidence), one can successfully learn a binary classifier, which we name positive-confidence (Pconf) classification. Our work is related to one-class classification which is aimed at "describing" the positive class by clustering-related methods, but one-class classification does not have the ability to tune hyper-parameters and their aim is not on "discriminating" positive and negative classes. For the Pconf classification problem, we provide a simple empirical risk minimization framework that is model-independent and optimization-independent. We theoretically establish the consistency and an estimation error bound, and demonstrate the usefulness of the proposed method for training deep neural networks through experiments.