Noisy pairwise comparison feedback has been incorporated to improve the overall query complexity of interactively learning binary classifiers. The positivity comparison oracle is extensively used to provide feedback on which is more likely to be positive in a pair of data points. Because it is impossible to determine accurate labels using this oracle alone without knowing the classification threshold, existing methods still rely on the traditional explicit labeling oracle, which explicitly answers the label given a data point. The current method conducts sorting on all data points and uses explicit labeling oracle to find the classification threshold. However, it has two drawbacks: (1) it needs unnecessary sorting for label inference and (2) it naively adapts quick sort to noisy feedback. In order to avoid these inefficiencies and acquire information of the classification threshold at the same time, we propose a new pairwise comparison oracle concerning uncertainties. This oracle answers which one has higher uncertainty given a pair of data points. We then propose an efficient adaptive labeling algorithm to take advantage of the proposed oracle. In addition, we address the situation where the labeling budget is insufficient compared to the data set size. Furthermore, we confirm the feasibility of the proposed oracle and the performance of the proposed algorithm theoretically and empirically.

The goal of classification with rejection is to avoid risky misclassification in error-critical applications such as medical diagnosis and product inspection. In this paper, based on the relationship between classification with rejection and cost-sensitive classification, we propose a novel method of classification with rejection by learning an ensemble of cost-sensitive classifiers, which satisfies all the following properties: (i) it can avoid estimating class-posterior probabilities, resulting in improved classification accuracy. (ii) it allows a flexible choice of losses including non-convex ones, (iii) it does not require complicated modifications when using different losses, (iv) it is applicable to both binary and multiclass cases, and (v) it is theoretically justifiable for any classification-calibrated loss. Experimental results demonstrate the usefulness of our proposed approach in clean-labeled, noisy-labeled, and positive-unlabeled classification.

Learning from triplet comparison data has been extensively studied in the context of metric learning, where we want to learn a distance metric between two instances, and ordinal embedding, where we want to learn an embedding in a Euclidean space of the given instances that preserve the comparison order as much as possible. Unlike fully labeled data, triplet comparison data can be collected in a more accurate and human-friendly way. Although learning from triplet comparison data has been considered in many applications, an important fundamental question of whether we can learn a classifier only from triplet comparison data without all the labels has remained unanswered. In this letter, we give a positive answer to this important question by proposing an unbiased estimator for the classification risk under the empirical risk minimization framework. Since the proposed method is based on the empirical risk minimization framework, it inherently has the advantage that any surrogate loss function and any model, including neural networks, can be easily applied. Furthermore, we theoretically establish an estimation error bound for the proposed empirical risk minimizer. Finally, we provide experimental results to show that our method empirically works well and outperforms various baseline methods.

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily draw samples. Recently discrete approximation by particles has attracted attention because of its high expression ability. An example is Stein variational gradient descent (SVGD), which iteratively optimizes particles. Although SVGD has been shown to be computationally efficient empirically, its theoretical properties have not been clarified yet and no finite sample bound of the convergence rate is known. Another example is the Stein points (SP) method, which minimizes kernelized Stein discrepancy directly. Althoughafinitesampleboundisassuredtheoretically, SP is computationally inefficient empirically, especially in high-dimensional problems. In this paper, we propose a novel method named maximum mean discrepancy minimization by the Frank-Wolfe algorithm (MMD-FW), which minimizes MMD in a greedy way by the FW algorithm. Our method is computationally efficient empirically and we show that its finite sample convergence bound is in a linear order in finite dimensions.