  Progress in the application of machine learning (ML) methods to materials
design is hindered by the lack of understanding of the reliability of ML
predictions, in particular for the application of ML to small data sets often
found in materials science. Using ML prediction for transparent conductor oxide
formation energy and band gap, dilute solute diffusion, and perovskite
formation energy, band gap and lattice parameter as examples, we demonstrate
that 1) analysis of ML results by construction of a convex hull in feature
space that encloses accurately predicted systems can be used to identify
regions in feature space for which ML predictions are highly reliable 2)
analysis of the systems enclosed by the convex hull can be used to extract
physical understanding and 3) materials that satisfy all well-known chemical
and physical principles that make a material physically reasonable are likely
to be similar and show strong relationships between the properties of interest
and the standard features used in ML. We also show that similar to the
composition-structure-property relationships, inclusion in the ML training data
set of materials from classes with different chemical properties will not be
beneficial and will slightly decrease the accuracy of ML prediction and that
reliable results likely will be obtained by ML model for narrow classes of
similar materials even in the case where the ML model will show large errors on
the dataset consisting of several classes of materials. Our work suggests that
analysis of the error distributions of ML predictions will be beneficial for
the further development of the application of ML methods in material science.
