Beyond the conventional trial-and-error method, machine learning offers a great opportunity to accelerate the discovery of functional materials, but still often suffers from difficulties such as limited materials data and unbalanced distribution of target property. Here, we propose the ab initio Bayesian active learning method that combines active learning and high-throughput ab initio calculations to accelerate prediction of desired functional materials with the ultrahigh efficiency and accuracy. We apply it as an instance to a large family (3,119) of two-dimensional hexagonal binary compounds with unbalanced materials property, and accurately screen out the materials with maximal electric polarization and proper photovoltaic band gaps, respectively, whereas the computational costs are significantly reduced by only calculating a few tenths of possible candidates in comparison to the random search. This approach shows enormous advantages for the cases with unbalanced distributions of target property. It can be readily applied to seek for a broad range of advanced materials.
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