Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry

@article{Klus2021SymmetricAA,
  title={Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry},
  author={Stefan Klus and Patrick Gel{\ss} and Feliks N{\"u}ske and Frank No'e},
  journal={Machine Learning: Science and Technology},
  year={2021},
  volume={2}
}
We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties. In particular, we compute the feature space dimensions of the resulting polynomial kernels, prove that the reproducing kernel Hilbert spaces induced by symmetric and antisymmetric Gaussian kernels are dense in the space of symmetric and antisymmetric functions, and propose a Slater determinant representation of the antisymmetric Gaussian kernel, which allows for… 
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