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# Imprecise Extensions of Random Forests and Random Survival Forests

*Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications*, PMLR 103:404-413, 2019.

#### Abstract

Robust weighted aggregation schemes taking into account imprecision of the decision tree estimates in random forests and in random survival forests are proposed in the paper. The first scheme dealing with the random forest improves the classification problem solution. The second scheme dealing with the random survival forest improves the survival analysis task solution. The main idea underlying the proposed modifications is to introduce the tree weights which take simultaneously into account imprecision of estimations as well as aims of the classification and regression problems. The imprecision of the tree estimates is defined by means of imprecise statistical inference models and interval models. Special modifications of loss functions for the classification and regression tasks are proposed in order to simplify minimax and maximin optimization problems for computing optimal weights. Numerical examples illustrate the proposed robust models.