On Translation Invariant Kernels and Screw Functions
This work offers a theoretical insight into kernel methods in machine learning, but it is incremental as it provides an alternate proof rather than new results.
The paper revisits the connection between Hilbertian metrics and positive definite kernels on the real line, leveraging a known characterization by von Neumann and Schoenberg to provide an alternate proof of Bochner's theorem for translation invariant kernels.
We explore the connection between Hilbertian metrics and positive definite kernels on the real line. In particular, we look at a well-known characterization of translation invariant Hilbertian metrics on the real line by von Neumann and Schoenberg (1941). Using this result we are able to give an alternate proof of Bochner's theorem for translation invariant positive definite kernels on the real line (Rudin, 1962).