  We consider the prediction of a basic thermodynamic property---hydration free
energies---across a large subset of the chemical space of small organic
molecules. Our in silico study is based on computer simulations at the
atomistic level with implicit solvent. We report on a kernel-based machine
learning approach that is inspired by recent work in learning electronic
properties, but differs in key aspects: The representation is averaged over
several conformers to account for the statistical ensemble. We also include an
atomic-decomposition ansatz, which we show offers significant added
transferability compared to molecular learning. Finally, we explore the
existence of severe biases from databases of experimental compounds. By
performing a combination of dimensionality reduction and cross-learning models,
we show that the rate of learning depends significantly on the breadth and
variety of the training dataset. Our study highlights the dangers of fitting
machine-learning models to databases of narrow chemical range.
