The Kardashian Kernel

We propose a new family of kernels, based on the Kardashian family. We provide theoretical insights. We dance. As an application, we apply the new class of kernels to the problem of doing stuff. Figure 1: A motivation for the Kernel Trick. κ maps the real world of sane people into the subset of (R − Q)∞ spanned by Robert Kardashian, Sr. and Kris Jenner (formerly Kardashian). We would like to avoid having our data appear on Keeping Up with the Kardashians, and so we use the Kardashian Kernel KK to compute an inner product in the Kardashian Space without ever having to go there. Kernel machines are popular because they work well and have fancy math, pleasing practitioners and theoreticians alike. The Kardashians are popular because (TODO). Why not combine them? 1 The Kardashian Kernel Let X be an instance space. The Kardashian Kernel is an inner product operator KK : X × X → R. Applying the Kernel trick [14] we express it as KK(x, x′) = κ(x)κ(x), with κ : X → K. Here K represents a possibly infinitely-dimensional feature space. In Fig. 1, we provide the best (to our knowledge) motivation of the Kernel Trick: by using the Kardashian Kernel, we can leverage the Kardashian Feature space without suffering the Kurse of Dimensionality. This kurse is similar in nature to the better-known Curse of Dimensionality (c.f., [3]); however, the motivation for avoiding such a space is different: here, we wish to avoid having our data be associated with the Kardashian shenanigans.