Kernel mean embedding vs kernel density estimation: A quantum perspective

This short study investigates the link between kernel methods and quantum mechanics. Density operators representing ensembles of pure states of sample wave functions are used in place of probability densities and Kraus operator is used to embed samples. Results show that using density operators associated to different quantum systems along with embedded samples allows to recover kernel density estimation as well as kernel mean embedding equations. Results are illustrated with a simple example using discrete orthogonal wavelet transform.