  We present a machine learning (ML) method for predicting electronic structure
correlation energies using Hartree-Fock input.The total correlation energy is
expressed in terms of individual and pair contributions from occupied molecular
orbitals, and Gaussian process regression is used to predict these
contributions from a feature set that is based on molecular orbital properties,
such as Fock, Coulomb, and exchange matrix elements. With the aim of maximizing
transferability across chemical systems and compactness of the feature set, we
avoid the usual specification of ML features in terms of atom- or
geometry-specific information, such atom/element-types, bond-types, or local
molecular structure. ML predictions of MP2 and CCSD energies are presented for
a range of systems, demonstrating that the method maintains accuracy while
providing transferability both within and across chemical families; this
includes predictions for molecules with atom-types and elements that are not
included in the training set. The method holds promise both in its current form
and as a proof-of-principle for the use of ML in the design of generalized
density-matrix functionals.
