Polynomial kernels are among the most popular kernels in machine learning, since their feature maps model the interactions between the dimensions of the input data. However, these features correspond to tensor products of the input with itself, which makes their dimension grow exponentially with the polynomial degree. We address this issue by proposing Complexto-Real (CtR) sketches for tensor products that can be used as random feature approximations of polynomial kernels. These sketches leverage intermediate complex random projections, leading to better theoretical guarantees and potentially much lower variances than analogs using real projections. Our sketches are simple to construct and their final output is real-valued, which makes their downstream use straightforward. Finally, we show that they achieve state-of-the-art performance in terms of accuracy and speed.

翻译：机器学习中最受欢迎的内核是多式内核,因为它们的特征地图模型是输入数据各维之间的相互作用。 但是,这些特征与输入本身的微粒产品相对应,使得其尺寸随多式度而成,成倍增长。我们提出可用作多式内核随机特征近似的振动产品的复合内核草图(CtR)来解决这个问题。这些草图利用中间复杂的随机预测,导致更好的理论保障和可能比使用真实预测的模拟值低得多的差异。我们的草图简单易建,其最终产出是真实估价的,从而使其下游用途直截了当。最后,我们展示了这些产品在准确性和速度方面达到最新水平的性能。