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.
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