论文标题
支持矢量机的自适应学习率，用于固有维度低的数据
Adaptive Learning Rates for Support Vector Machines Working on Data with Low Intrinsic Dimension
论文作者
论文摘要
在数据中，我们使用高斯内核来提高了支持向量机器的回归和分类速率，因为数据具有一些由盒子计数尺寸描述的低维内在结构。根据一些标准的规律性假设，我们证明了学习率，其中，环境空间的维度被数据生成分布的支持的盒子计数维度所取代。在回归情况下，我们的速率在某些情况下是最佳选择对数因素的最佳速率，而在分类情况下，我们的速率是最小值的最佳选择，以达到我们假设的一定范围内的对数因素，而其他最佳速率的形式则是最佳选择。此外，我们表明，以数据依赖性方式选择SVM的超参数的培训验证方法可以适应相同的速率，这是对数据生成分布的任何知识。
We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under some standard regularity assumptions for regression and classification we prove learning rates, in which the dimension of the ambient space is replaced by the box-counting dimension of the support of the data generating distribution. In the regression case our rates are in some cases minimax optimal up to logarithmic factors, whereas in the classification case our rates are minimax optimal up to logarithmic factors in a certain range of our assumptions and otherwise of the form of the best known rates. Furthermore, we show that a training validation approach for choosing the hyperparameters of an SVM in a data dependent way achieves the same rates adaptively, that is without any knowledge on the data generating distribution.
