Consensual aggregation of clusters based on Bregman divergences to improve predictive models
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A new procedure to construct predictive models in supervised learning problems by paying attention to the clustering structure of the input data is introduced. We are interested in situations where the input data consists of more than one unknown cluster, and where there exist different underlying models on these clusters. Thus, instead of constructing a single predictive model on the whole dataset, we propose to use a K-means clustering algorithm with different options of Bregman divergences, to recover the clustering structure of the input data. Then one dedicated predictive model is fit per cluster. For each divergence, we construct a simple local predictor on each observed cluster. We obtain one estimator, the collection of the K simple local predictors, per divergence, and we propose to combine them in a smart way based on a consensus idea. Several versions of consensual aggregation in both classification and regression problems are considered. A comparison of the performances of all constructed estimators on different simulated and real data assesses the excellent performance of our method. In a large variety of prediction problems, the consensual aggregation procedure outperforms all the other models.
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