Past exam of the advanced topics in statistical machine learning course of the University of Oxford / 2025 / 2 / a / i

In this setting a positive-semidefinite kernel is an inner-product similarity: there exist a real Hilbert space $\mathcal{H}$ and a feature map $\phi :\mathcal{X}\to \mathcal{H}$ such thatThe feature map may be infinite-dimensional. Equivalently, $k$ is symmetric and every finite kernel matrix is a positive semidefinite matrix. The equivalence follows by forming the canonical feature space of a positive-semidefinite kernel and taking its Hilbert space completion.