Probabilistic Random Forest: A Machine Learning Algorithm for Noisy Data Sets

Machine learning (ML) algorithms have become increasingly important in the analysis of astronomical data. However, because 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 ratios. Astronomical data sets of such high quality are uncommon. In this work, we modify the long-established Random Forest (RF) algorithm to take into account uncertainties in measurements (i.e., features) as well as in 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 into a data set 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 data set with as many as 45% misclassified objects, compared to a clean data set. Apart from improving the prediction accuracy in noisy data sets, the PRF naturally copes with missing values in the data, and outperforms RF when applied to a data set with different noise characteristics in the training and test sets, suggesting that it can be used for transfer learning.