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A0936
Title: Energy trees: Regression and classification with structured and mixed-type covariates Authors:  Riccardo Giubilei - Luiss Guido Carli (Italy) [presenting]
Tullia Padellini - Bank of Italy (Italy)
Pierpaolo Brutti - University of Rome - Sapienza (Italy)
Abstract: The continuous growth of data complexity requires methods and models that adequately account for non-trivial structures, as any simplification may induce a loss of information. Many analytical tools have been introduced to work with complex data objects in their original form, but they can typically deal with single-type variables only. We introduce Energy Trees as a model for regression and classification where covariates are potentially both structured and of different types. Energy Trees incorporate Energy Statistics to generalize Conditional Trees, from which they inherit statistically sound foundations, interpretability, scale invariance, and lack of distributional assumptions. We consider the cases of functions, graphs, and persistence diagrams as structured covariates, besides showing that the model can be easily adapted to work with almost any other type of variable. Finally, we employ an extensive simulation study and some empirical analyses with human biological data to confirm the desirable properties and the predictive ability of our proposal.