Zachary Jones, PhD student at Platon Team.
Title: Random Fourier Features for Hyperkernel learning
Kernel choice and calibration remain an important aspect of machine learning and statistical applications. Defining the space of kernel functions as a reproducing kernel Hilbert space, creating a hyper reproducing kernel Hilbert space, offers one means of both calibrating and choosing a nonparametric kernel in one step. However, the dimensionality of the hyperkernel Gram matrix makes the technique prohibitively expensive to use.
Random Fourier features allow for the definition of an inexpensive high quality low rank kernel approximation with an efficient form for generating out of sample predictions. In this work, the technique of random fourier features is extended to the hyperkernel case, the learned nonparametric kernels are proven to be valid kernel approximations and tested for quality both through kernel fitness tests and in downstream classification approaches. Furthermore, a lower rank “one-shot” learning approach is introduced. Experiments on UCI datsets show strong results in comparison to standard kernel methods and previous attempts at low rank kernel learning in hyper-RKHS.
