  Understanding the performance of machine learning algorithms is essential for
designing more accurate and efficient statistical models. It is not always
possible to unravel the reasoning of neural networks. Here we propose a method
for calculating machine learning kernels in closed and analytic form by
combining atomic property weighted radial distribution function (AP-RDF)
descriptor with a Gaussian kernel. This allowed us to analyse and improve the
performance of the Bag-of-Bonds descriptor, when the bond type restriction is
included in AP-RDF. The improvement is achieved for the prediction of molecular
atomization energies and is due to the incorporation of a tensor product into
the kernel which captures the multidimensional representation of the AP-RDF. On
the other hand, the numerical version of the AP-RDF is a constant size
descriptor, and it is more computationally efficient than Bag-of-Bonds. We have
also discussed a connection between molecular quantum similarity and machine
learning kernels with first principles kind of descriptors.
