We study the consistency of surrogate risks for robust binary classification.

Neural Information Processing Systems http://nips.cc/

We study the consistency of surrogate risks for robust binary classification.

We study the consistency of surrogate risks for robust binary classification.

Existing similarity-based weakly supervised learning approaches often rely on precise similarity annotations between data pairs, which may inadvertently expose sensitive label information and raise privacy risks. To mitigate this issue, we propose Uncertain Similarity and Unlabeled Learning (USimUL), a novel framework where each similarity pair is embedded with an uncertainty component to reduce label leakage. In this paper, we propose an unbiased risk estimator that learns from uncertain similarity and unlabeled data. Additionally, we theoretically prove that the estimator achieves statistically optimal parametric convergence rates. Extensive experiments on both benchmark and real-world datasets show that our method achieves superior classification performance compared to conventional similarity-based approaches. Our source code is available at the anonymous link: https://anonymous.4open.science/r/USimUL-B337

A central concern in classification is the vulnerability of machine learning models to adversarial attacks. Adversarial training is one of the most popular techniques for training robust classifiers, which involves minimizing an adversarial surrogate risk. Recent work characterized when a minimizing sequence of an adversarial surrogate risk is also a minimizing sequence of the adversarial classification risk for binary classification-- a property known as adversarial consistency . However, these results do not address the rate at which the adversarial classification risk converges to its optimal value for such a sequence of functions that minimize the adversarial surrogate. This paper provides surrogate risk bounds that quantify that convergence rate. Additionally, we derive distribution-dependent surrogate risk bounds in the standard (non-adversarial) learning setting, that may be of independent interest.

Collecting labeled data is costly and thus a critical bottleneck in real-world classification tasks. To mitigate this problem, we propose a novel setting, namely learning from complementary labels for multi-class classification. A complementary label specifies a class that a pattern does not belong to. Collecting complementary labels would be less laborious than collecting ordinary labels, since users do not have to carefully choose the correct class from a long list of candidate classes. However, complementary labels are less informative than ordinary labels and thus a suitable approach is needed to better learn from them. In this paper, we show that an unbiased estimator to the classification risk can be obtained only from complementarily labeled data, if a loss function satisfies a particular symmetric condition. We derive estimation error bounds for the proposed method and prove that the optimal parametric convergence rate is achieved. We further show that learning from complementary labels can be easily combined with learning from ordinary labels (i.e., ordinary supervised learning), providing a highly practical implementation of the proposed method. Finally, we experimentally demonstrate the usefulness of the proposed methods.