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Predictive models by consensual aggregation and applications

Abstract : Three important projects are studied in this thesis. The first project is "KFC : a clusterwise supervised learning procedure based on aggregation of distances". It is a three-step procedure for constructing prediction in supervised statistical learning problems. KFC stands for K-means/Fit/Combining. Several performances of the method are illustrated in this part on several synthetic and real energy data. The second project is "A kernel-based consensual aggregation method for regression", which is inspired by the numerical experiments of the previous project. The method is a generalization of consensual aggregation method introduced by Biau et al. (2016) to regular kernel-based setting. The consistency inheritance property of the method is derived, and is confirmed through many numerical experiments on simulated and real datasets. Lastly, the third project is a study of consensual aggregation method on randomly projected high-dimensional features of predictions. The aggregation scheme is composed of two steps: the high-dimensional features of predictions are randomly projected into a small subspace in the first step, then the aggregation method is applied on the projected features in the second step. We numerically show that the consensual aggregation method upholds its performance on very large and highly correlated features of predictions. Moreover, we theoretically show that the performance of the method is almost preserved in much smaller subspaces of projection, with high probability. This shows the robustness of the method in a sense that several types of predictive models can be plainly constructed and directly combined without model selection or cross-validation technique.
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Submitted on : Monday, November 14, 2022 - 10:11:44 AM
Last modification on : Tuesday, November 15, 2022 - 3:55:48 AM

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  • HAL Id : tel-03850725, version 1

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Sothea Has. Predictive models by consensual aggregation and applications. Machine Learning [stat.ML]. Sorbonne Université, 2022. English. ⟨NNT : 2022SORUS229⟩. ⟨tel-03850725⟩

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