输出稀疏性对多标签分类的好处
On the benefits of output sparsity for multi-label classification
摘要：
多标签分类框架，其中每个观察可以与一组标签相关联，近年来引起了极大的关注。现代多标签问题在观测、特征和标签的数量方面通常是大规模的，标签的数量甚至可以与观测的数量相媲美。在这种情况下，已经提出了不同的补救措施来克服维数灾难。在这项工作中，我们的目标是利用输出稀疏性引入一个新的损失，称为稀疏加权汉明损失。这种提议的损失可以被视为经典损失的加权版本，其中活跃和不活跃的标签被单独加权。利用损失函数中稀疏性的影响，我们为经验风险最小化器提供了改进的泛化界，这是一个适合大规模问题的属性。对于这种新的损失，我们得到的收敛率线性的基本输出稀疏，而不是线性的标签的数量。在实践中，最小化相关联的风险可以有效地执行通过使用凸代理和现代凸优化算法。我们在各种真实世界数据集上进行了实验，证明了与非加权技术相比，我们的方法的相关性。
英文摘要：
The multi-label classification framework, where each observation can be associated with a set of labels, has generated a tremendous amount of attention over recent years. The modern multi-label problems are typically large-scale in terms of number of observations, features and labels, and the amount of labels can even be comparable with the amount of observations. In this context, different remedies have been proposed to overcome the curse of dimensionality. In this work, we aim at exploiting the output sparsity by introducing a new loss, called the sparse weighted Hamming loss. This proposed loss can be seen as a weighted version of classical ones, where active and inactive labels are weighted separately. Leveraging the influence of sparsity in the loss function, we provide improved generalization bounds for the empirical risk minimizer, a suitable property for large-scale problems. For this new loss, we derive rates of convergence linear in the underlying output-sparsity rather than linear in the number of labels. In practice, minimizing the associated risk can be performed efficiently by using convex surrogates and modern convex optimization algorithms. We provide experiments on various real-world datasets demonstrating the pertinence of our approach when compared to non-weighted techniques.
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