Black hole algorithm as a heuristic approach for rare event classification problem

The logistic regression is generally preferred when there is no big difference in the occurrence frequencies of two possible results for the considered event. However, for the events occurring rarely such as wars, economic crisis and natural disasters, namely having relatively small occurrence frequency when compared to the general events, the logistic regression gives biased parameter estimations. Therefore, the logistic regression underestimates the occurrence probability of the rare events. In this study, a modification of the black hole algorithm (BHA) is proposed as an alternative to the classical logistic regression method in order to obtain more reliable and unbiased rare event parameter estimates. To examine the performance of the proposed approach, we calculate bias and root mean square errors based on Monte Carlo (MC) simulations. We used logistic regression to generate data for the rare event in the simulations and gave values to the beta(0) parameter to obtain different rarity levels. The performance of the methods was examined in different scenarios using comprehensive MC simulations under different conditions for the rarity level and number of subjects. In addition, real-life data was used to examine the classification performance of the proposed approach and the precision, sensitivity and specificity values of the two methods were compared. As a result, we obtained that the proposed BHA gives less biased predictions than logistic regression in simulation and real-life data and has higher classification performance. Additionally, rareness levels have a significant impact on the parameter estimates of the methods.