Kernels over Sets of Finite Sets using RKHS Embeddings, with Application to Bayesian (Combinatorial) Optimization

9 Oct 2019Poompol BuathongDavid GinsbourgerTipaluck Krityakierne

We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space embeddings, namely the ``Double Sum'' (DS) kernels recently considered in Bayesian set optimization, and a class introduced here called ``Deep Embedding'' (DE) kernels that essentially consists in applying a radial kernel on Hilbert space on top of the canonical distance induced by another kernel such as a DS kernel... (read more)

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