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To alleviate the data requirement for training effective binary classifiers in binary classification, many weakly supervised learning settings have been proposed. Among them, some consider using pairwise but not pointwise labels, when pointwise labels are not accessible due to privacy, confidentiality, or security reasons. However, as a pairwise label denotes whether or not two data points share a pointwise label, it cannot be easily collected if either point is equally likely to be positive or negative. Thus, in this paper, we propose a novel setting called pairwise comparison (Pcomp) classification, where we have only pairs of unlabeled data that we know one is more likely to be positive than the other. Firstly, we give a Pcomp data generation process, derive an unbiased risk estimator (URE) with theoretical guarantee, and further improve URE using correction functions. Secondly, we link Pcomp classification to noisy-label learning to develop a progressive URE and improve it by imposing consistency regularization. Finally, we demonstrate by experiments the effectiveness of our methods, which suggests Pcomp is a valuable and practically useful type of pairwise supervision besides the pairwise label.
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We propose a novel parameterized family of Mixed Membership Mallows Models (M4) to account for variability in pairwise comparisons generated by a heterogeneous population of noisy and inconsistent users. M4 models individual preferences as a user-specific probabilistic mixture of shared latent Mallows components. Our key algorithmic insight for estimation is to establish a statistical connection between M4 and topic models by viewing pairwise comparisons as words, and users as documents. This key insight leads us to explore Mallows components with a separable structure and leverage recent advances in separable topic discovery. While separability appears to be overly restrictive, we nevertheless show that it is an inevitable outcome of a relatively small number of latent Mallows components in a world of large number of items. We then develop an algorithm based on robust extreme-point identification of convex polygons to learn the reference rankings, and is provably consistent with polynomial sample complexity guarantees. We demonstrate that our new model is empirically competitive with the current state-of-the-art approaches in predicting real-world preferences.
Recent work by Locatello et al. (2018) has shown that an inductive bias is required to disentangle factors of interest in Variational Autoencoder (VAE). Motivated by a real-world problem, we propose a setting where such bias is introduced by providing pairwise ordinal comparisons between instances, based on the desired factor to be disentangled. For example, a doctor compares pairs of patients based on the level of severity of their illnesses, and the desired factor is a quantitive level of the disease severity. In a real-world application, the pairwise comparisons are usually noisy. Our method, Robust Ordinal VAE (ROVAE), incorporates the noisy pairwise ordinal comparisons in the disentanglement task. We introduce non-negative random variables in ROVAE, such that it can automatically determine whether each pairwise ordinal comparison is trustworthy and ignore the noisy comparisons. Experimental results demonstrate that ROVAE outperforms existing methods and is more robust to noisy pairwise comparisons in both benchmark datasets and a real-world application.
We consider the problem of ranking $n$ players from partial pairwise comparison data under the Bradley-Terry-Luce model. For the first time in the literature, the minimax rate of this ranking problem is derived with respect to the Kendalls tau distance that measures the difference between two rank vectors by counting the number of
The 01 loss is robust to outliers and tolerant to noisy data compared to convex loss functions. We conjecture that the 01 loss may also be more robust to adversarial attacks. To study this empirically we have developed a stochastic coordinate descent algorithm for a linear 01 loss classifier and a single hidden layer 01 loss neural network. Due to the absence of the gradient we iteratively update coordinates on random subsets of the data for fixed epochs. We show our algorithms to be fast and comparable in accuracy to the linear support vector machine and logistic loss single hidden layer network for binary classification on several image benchmarks, thus establishing that our method is on-par in test accuracy with convex losses. We then subject them to accurately trained substitute model black box attacks on the same image benchmarks and find them to be more robust than convex counterparts. On CIFAR10 binary classification task between classes 0 and 1 with adversarial perturbation of 0.0625 we see that the MLP01 network loses 27% in accuracy whereas the MLP-logistic counterpart loses 83%. Similarly on STL10 and ImageNet binary classification between classes 0 and 1 the MLP01 network loses 21% and 20% while MLP-logistic loses 67% and 45% respectively. On MNIST that is a well-separable dataset we find MLP01 comparable to MLP-logistic and show under simulation how and why our 01 loss solver is less robust there. We then propose adversarial training for our linear 01 loss solver that significantly improves its robustness on MNIST and all other datasets and retains clean test accuracy. Finally we show practical applications of our method to deter traffic sign and facial recognition adversarial attacks. We discuss attacks with 01 loss, substitute model accuracy, and several future avenues like multiclass, 01 loss convolutions, and further adversarial training.
As pairwise ranking becomes broadly employed for elections, sports competitions, recommendations, and so on, attackers have strong motivation and incentives to manipulate the ranking list. They could inject malicious comparisons into the training data to fool the victim. Such a technique is called poisoning attack in regression and classification tasks. In this paper, to the best of our knowledge, we initiate the first systematic investigation of data poisoning attacks on pairwise ranking algorithms, which can be formalized as the dynamic and static games between the ranker and the attacker and can be modeled as certain kinds of integer programming problems. To break the computational hurdle of the underlying integer programming problems, we reformulate them into the distributionally robust optimization (DRO) problems, which are computationally tractable. Based on such DRO formulations, we propose two efficient poisoning attack algorithms and establish the associated theoretical guarantees. The effectiveness of the suggested poisoning attack strategies is demonstrated by a series of toy simulations and several real data experiments. These experimental results show that the proposed methods can significantly reduce the performance of the ranker in the sense that the correlation between the true ranking list and the aggregated results can be decreased dramatically.
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