High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint generation methods have recently enabled efficient learning of L1-regularized support vector machines (SVMs). In this paper, we leverage such methods to obtain an efficient learning algorithm for the recently proposed minimax risk classifiers (MRCs). The proposed iterative algorithm also provides a sequence of worst-case error probabilities and performs feature selection. Experiments on multiple high-dimensional datasets show that the proposed algorithm is efficient in high-dimensional scenarios. In addition, the worst-case error probability provides useful information about the classifier performance, and the features selected by the algorithm are competitive with the state-of-the-art.

翻译：高维数据在医疗保健和基因组学等多个领域中十分常见，其中特征数量可达数万。在此类场景中，大量特征常导致学习效率低下。约束生成方法近期已能支持L1正则化支持向量机的高效学习。本文借助此类方法，为近期提出的极小化极大风险分类器构建高效学习算法。所提出的迭代算法还能生成最坏情况错误概率序列并执行特征选择。在多个高维数据集上的实验表明，该算法在高维场景中具备高效性。此外，最坏情况错误概率能为分类器性能提供有效信息，且算法所选特征与现有最优方法具有竞争力。