论文标题
分类与过度参数化制度中的回归：损失功能重要吗？
Classification vs regression in overparameterized regimes: Does the loss function matter?
论文作者
论文摘要
我们在过度参数的线性模型中比较了具有高斯特征的分类和回归任务。一方面，我们表明，有足够的过度参数化，所有训练点都是支持向量：最小二乘最小值插值获得的解决方案，通常用于回归，与Hard-Margin Support Support Support Support Support Machine（SVM）产生的解决方案相同，该插值机（SVM）通常可以最大程度地减少用于训练分类器的铰链损耗，该铰链损失最小化。另一方面，我们表明存在通过0-1测试损耗函数评估时这些插值解决方案良好概括的制度，但如果通过正方形损耗函数进行评估，则不会概括，即它们接近无效风险。我们的结果表明，在训练阶段（优化）和测试阶段（概括）中使用的损失函数的作用和特性非常不同。
We compare classification and regression tasks in an overparameterized linear model with Gaussian features. On the one hand, we show that with sufficient overparameterization all training points are support vectors: solutions obtained by least-squares minimum-norm interpolation, typically used for regression, are identical to those produced by the hard-margin support vector machine (SVM) that minimizes the hinge loss, typically used for training classifiers. On the other hand, we show that there exist regimes where these interpolating solutions generalize well when evaluated by the 0-1 test loss function, but do not generalize if evaluated by the square loss function, i.e. they approach the null risk. Our results demonstrate the very different roles and properties of loss functions used at the training phase (optimization) and the testing phase (generalization).
