  Kesterite I$_2$-II-IV-V$_4$ semiconductors are promising solar absorbers for
photovoltaics applications. The band gap and it's character, either direct or
indirect, are fundamental properties determining photovoltaic-device
efficiency. We use a combination of accurate first-principles calculations and
machine learning to predict the properties of the band gap for a large number
of kesterite I$_2$-II-IV-V$_4$ semiconductors. In determining the magnitude of
the fundamental gap, we compare results for a number of machine-learning
models, and achieve a root mean squared error as low as 283 meV; the best
results are achieved using support-vector regression with a radial-bias kernel.
This error is well within the uncertainty of even the most advanced
first-principles methods for calculating semiconductor band gaps. Predicting
the direct--indirect property of the band gap is more challenging. After
significant feature engineering, we are able to train a classifier that
predicts the nature of the band gap with an accuracy of 89 \% using logistic
regression. Using these trained models, the band gap properties of 1568
kesterite I$_2$-II-IV-V$_4$ compounds are predicted. We find 717 compounds with
band gaps in the range 0.5 -- 2.5 eV that can potentially act as solar
absorbers, and 242 materials with a band gap in the ``\emph{optimum range}" of
1.2 -- 1.8 eV. The stability of these 242 compounds is assessed by calculating
the Energy Above Hull using the Materials Project database, and the band gaps
are verified using hybrid functional calculations; in the end, we identify 25
compounds that are expected to be synthesizable, and have a band gap in the
range 1.2 -- 1.8 eV -- most of which are previously unexplored. These results
will be useful in the materials engineering of efficient photovoltaic devices.
