Copulaboost: additive modeling with copula-based model components
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We propose a type of generalised additive models with of model components based on pair-copula constructions, with prediction as a main aim. The model components are designed such that our model may capture potentially complex interaction effects in the relationship between the response covariates. In addition, our model does not require discretisation of continuous covariates, and is therefore suitable for problems with many such covariates. Further, we have designed a fitting algorithm inspired by gradient boosting, as well as efficient procedures for model selection and evaluation of the model components, through constraints on the model space and approximations, that speed up time-costly computations. In addition to being absolutely necessary for our model to be a realistic alternative in higher dimensions, these techniques may also be useful as a basis for designing efficient models selection algorithms for other types of copula regression models. We have explored the characteristics of our method in a simulation study, in particular comparing it to natural alternatives, such as logic regression, classic boosting models and penalised logistic regression. We have also illustrated our approach on the Wisconsin breast cancer dataset and on the Boston housing dataset. The results show that our method has a prediction performance that is either better than or comparable to the other methods, even when the proportion of discrete covariates is high.
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