论文标题
预测层次支持向量回归的关键层
Predicting the Critical Number of Layers for Hierarchical Support Vector Regression
论文作者
论文摘要
层次支持向量回归（HSVR）模拟来自数据的函数作为SVR模型在一系列尺度范围内的线性组合，从粗糙的比例开始，然后随着层次结构的继续移动到更细的尺度。在HSVR的原始公式中，没有选择模型深度的规则。在本文中，我们在许多模型中观察到训练误差中的相变 - 随着图层的添加，该误差保持相对恒定，直到传递临界标度为止，此时，训练误差接近零，并且对于添加图层而言几乎保持恒定。我们介绍了一种基于数据转换的支持或动态模式分解（DMD）频谱的支持，以预测该临界量表先验的方法。这使我们能够在培训任何模型之前确定所需的层数。
Hierarchical support vector regression (HSVR) models a function from data as a linear combination of SVR models at a range of scales, starting at a coarse scale and moving to finer scales as the hierarchy continues. In the original formulation of HSVR, there were no rules for choosing the depth of the model. In this paper, we observe in a number of models a phase transition in the training error -- the error remains relatively constant as layers are added, until a critical scale is passed, at which point the training error drops close to zero and remains nearly constant for added layers. We introduce a method to predict this critical scale a priori with the prediction based on the support of either a Fourier transform of the data or the Dynamic Mode Decomposition (DMD) spectrum. This allows us to determine the required number of layers prior to training any models.
