Applying Mondrian Cross-Conformal Prediction To Estimate Prediction Confidence on Large Imbalanced Bioactivity Data Sets

Conformal prediction has been proposed as a more rigorous way to define prediction confidence compared to other application domain concepts that have earlier been used for QSAR modeling. One main advantage of such a method is that it provides a prediction region potentially with multiple predicted labels, which contrasts to the single valued (regression) or single label (classification) output predictions by standard QSAR modeling algorithms. Standard conformal prediction might not be suitable for imbalanced data sets. Therefore, Mondrian cross-conformal prediction (MCCP) which combines the Mondrian inductive conformal prediction with cross-fold calibration sets has been introduced. In this study, the MCCP method was applied to 18 publicly available data sets that have various imbalance levels varying from 1:10 to 1:1000 (ratio of active/inactive compounds). Our results show that MCCP in general performed well on bioactivity data sets with various imbalance levels. More importantly, the method not only provides confidence of prediction and prediction regions compared to standard machine learning methods but also produces valid predictions for the minority class. In addition, a compound similarity based nonconformity measure was investigated. Our results demonstrate that although it gives valid predictions, its efficiency is much worse than that of model dependent metrics.