  Kernel methods are ubiquitous in classical machine learning, and recently
their formal similarity with quantum mechanics has been established. To grasp
the potential advantage of quantum machine learning, it is necessary to
understand the distinction between non-classical kernel functions and classical
kernels. This paper builds on a recently proposed phase space nonclassicality
witness [Bohmann, Agudelo, Phys. Rev. Lett. 124, 133601 (2020)] to derive a
witness for the kernel's quantumness in continuous-variable systems. We discuss
the role of kernel's nonclassicality in data distribution in the feature space
and the effect of imperfect state preparation. Furthermore, we show that the
non-classical kernels lead to the quantum advantage in parameter estimation.
Our work highlights the role of the phase space correlation functions in
understanding the distinction between classical machine learning from quantum
machine learning.
