Bare in mind that Breiman's polemic was about generative vs discriminative methods. I.e. that we should not start an analysis by thinking about how the data generation can be modelled, but instead we should start with prediction. From that vein came boosted trees, bagging, random forests, xgboost and so on: non generative black box methods.
Still today most of the classical machine learning toolbox is not generative.
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