Kernel median embedding as a functional parameter of the data distribution

抄録

In both supervised and unsupervised learning tasks, embedding the underlying data into a function space using a "kernel mean" has been well-studied, and is known to be an efficient means of characterizing even complex distributions. Here we consider a broad generalization of this notion to countless "functional parameters" of the underlying distribution, and as a concrete example explore what may naturally be called the "kernel median" of the data. In this short paper, we formulate the new parameter class, provide a procedure for obtaining an important special case, with basic convergence guarantees and expressions useful for practical implementation.