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A new extremely simple ensemble-based model with the uniformly generatedaxis-parallel hyper-rectangles as base models (HRBM) is proposed. Two types ofHRBMs are studied: closed rectangles and corners. The main idea behind HRBM isto consider and count training examples inside and outside each rectangle. Itis proposed to incorporate HRBMs into the gradient boosting machine (GBM).Despite simplicity of HRBMs, it turns out that these simple base models allowus to construct effective ensemble-based models and avoid overfitting. A simplemethod for calculating optimal regularization parameters of the ensemble-basedmodel, which can be modified in the explicit way at each iteration of GBM, isconsidered. Moreover, a new regularization called the "step height penalty" isstudied in addition to the standard L1 and L2 regularizations. An extremelysimple approach to the proposed ensemble-based model prediction interpretationby using the well-known method SHAP is proposed. It is shown that GBM with HRBMcan be regarded as a model extending a set of interpretable models forexplaining black-box models. Numerical experiments with real datasetsillustrate the proposed GBM with HRBMs for regression and classificationproblems. Experiments also illustrate computational efficiency of the proposedSHAP modifications. The code of proposed algorithms implementing GBM with HRBMis publicly available.

Interpretable Ensembles of Hyper-Rectangles as Base Models