Unbiased recursive partitioning: A conditional inference framework

Unbiased recursive partitioning: A conditional inference framework

July 2004 | Hothorn, Torsten; Hornik, Kurt; Zeileis, Achim
This paper introduces an unbiased recursive partitioning framework for regression analysis, which addresses the issues of overfitting and variable selection bias in traditional tree-based models. The method is based on conditional inference procedures and uses permutation tests to ensure unbiased variable selection. The framework allows for the construction of tree-structured regression models that are not biased towards covariates with many possible splits or missing values. It is applicable to a wide range of regression problems, including nominal, ordinal, numeric, censored, and multivariate response variables, as well as arbitrary measurement scales for covariates. The approach involves testing for independence between the response variable and each covariate using permutation tests, and stopping the recursion when no significant association is found. The method is implemented using multiple test procedures and is shown to produce regression models with predictive performance comparable to optimally pruned trees from exhaustive search methods. The framework is demonstrated through various applications, including animal abundance, glaucoma classification, node positive breast cancer, and mammography experience. The paper also discusses the development of the framework, including the use of conditional inference for splitting criteria and handling of missing values. It presents a unified approach for recursive partitioning that embeds tree-structured regression models into a well-defined theory of conditional inference. The methodology is computationally efficient and applicable to a wide range of regression problems, providing an intuitive and statistically sound solution to the overfitting problem. The results show that the partitions and models induced by the framework are structurally different from those obtained by traditional methods, highlighting the importance of unbiased variable selection in tree-structured regression models.This paper introduces an unbiased recursive partitioning framework for regression analysis, which addresses the issues of overfitting and variable selection bias in traditional tree-based models. The method is based on conditional inference procedures and uses permutation tests to ensure unbiased variable selection. The framework allows for the construction of tree-structured regression models that are not biased towards covariates with many possible splits or missing values. It is applicable to a wide range of regression problems, including nominal, ordinal, numeric, censored, and multivariate response variables, as well as arbitrary measurement scales for covariates. The approach involves testing for independence between the response variable and each covariate using permutation tests, and stopping the recursion when no significant association is found. The method is implemented using multiple test procedures and is shown to produce regression models with predictive performance comparable to optimally pruned trees from exhaustive search methods. The framework is demonstrated through various applications, including animal abundance, glaucoma classification, node positive breast cancer, and mammography experience. The paper also discusses the development of the framework, including the use of conditional inference for splitting criteria and handling of missing values. It presents a unified approach for recursive partitioning that embeds tree-structured regression models into a well-defined theory of conditional inference. The methodology is computationally efficient and applicable to a wide range of regression problems, providing an intuitive and statistically sound solution to the overfitting problem. The results show that the partitions and models induced by the framework are structurally different from those obtained by traditional methods, highlighting the importance of unbiased variable selection in tree-structured regression models.
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