  We develop a probabilistic machine learning model and use it to screen for
new hybrid organic-inorganic perovskites (HOIPs) with targeted electronic band
gap. The data set used for this work is highly diverse, containing multiple
atomic structures for each of 192 chemically distinct HOIP formulas. Therefore,
any property prediction on a given formula must be associated with an
irreducible "uncertainty" that comes from its unknown atomic details. As a
result, dozens of new HOIP formulas with band gap falling between 1.25 and 1.50
eV were identified and validated against suitable first-principles
computations. Through this demonstration we show that the probabilistic deep
learning approach is robust, versatile, and can be used to properly quantify
this uncertainty. In conclusion, the probabilistic standpoint and approach
described herein could be widely useful for the very common and inevitable data
uncertainty which is rooted at the incompleteness of information during
experiments and/or computations.
