Title: Machine learning prediction errors better than DFT accuracy,
Abstract: We investigate the impact of choosing regressors and molecular
representations for the construction of fast machine learning (ML) models of
thirteen electronic ground-state properties of organic molecules. The
performance of each regressor/representation/property combination is assessed
using learning curves which report out-of-sample errors as a function of
training set size with up to $\sim$117k distinct molecules. Molecular
structures and properties at hybrid density functional theory (DFT) level of
theory used for training and testing come from the QM9 database [Ramakrishnan
et al, {\em Scientific Data} {\bf 1} 140022 (2014)] and include dipole moment,
polarizability, HOMO/LUMO energies and gap, electronic spatial extent, zero
point vibrational energy, enthalpies and free energies of atomization, heat
capacity and the highest fundamental vibrational frequency. Various
representations from the literature have been studied (Coulomb matrix, bag of
bonds, BAML and ECFP4, molecular graphs (MG)), as well as newly developed
distribution based variants including histograms of distances (HD), and angles
(HDA/MARAD), and dihedrals (HDAD). Regressors include linear models (Bayesian
ridge regression (BR) and linear regression with elastic net regularization
(EN)), random forest (RF), kernel ridge regression (KRR) and two types of
neural net works, graph convolutions (GC) and gated graph networks (GG). We
present numerical evidence that ML model predictions deviate from DFT less than
DFT deviates from experiment for all properties. Furthermore, our out-of-sample
prediction errors with respect to hybrid DFT reference are on par with, or
close to, chemical accuracy. Our findings suggest that ML models could be more
accurate than hybrid DFT if explicitly electron correlated quantum (or
experimental) data was available.