  Machine learning (ML) algorithms become increasingly important in the
analysis of astronomical data. However, since most ML algorithms are not
designed to take data uncertainties into account, ML based studies are mostly
restricted to data with high signal-to-noise ratio. Astronomical datasets of
such high-quality are uncommon. In this work we modify the long-established
Random Forest (RF) algorithm to take into account uncertainties in the
measurements (i.e., features) as well as in the assigned classes (i.e.,
labels). To do so, the Probabilistic Random Forest (PRF) algorithm treats the
features and labels as probability distribution functions, rather than
deterministic quantities. We perform a variety of experiments where we inject
different types of noise to a dataset, and compare the accuracy of the PRF to
that of RF. The PRF outperforms RF in all cases, with a moderate increase in
running time. We find an improvement in classification accuracy of up to 10% in
the case of noisy features, and up to 30% in the case of noisy labels. The PRF
accuracy decreased by less then 5% for a dataset with as many as 45%
misclassified objects, compared to a clean dataset. Apart from improving the
prediction accuracy in noisy datasets, the PRF naturally copes with missing
values in the data, and outperforms RF when applied to a dataset with different
noise characteristics in the training and test sets, suggesting that it can be
used for Transfer Learning.
