Unbiased Isotonic Regression Tree for Discovering Hidden Heterogeneity in Monotonicity Constraints

초록

Integrating domain knowledge is increasingly recognized as vital for improving the relevance and reliability of machine learning models. This integration is often implemented through specific types of constraints that reflect real-world conditions or theoretical insights. Within the family of regression trees, the isotonic regression tree is used to incorporate a monotonicity constraint between a predictor and a response variable. However, the isotonic regression tree could be susceptible to split selection bias, as it selects both its split variable and cutpoint simultaneously. This study first explores the possibility of selection bias on split variables in the isotonic regression tree and proposes an unbiased isotonic regression tree that mitigates the issue of the selection bias problem. The results of the simulation and case study demonstrate the effectiveness of the proposed approach and the ability to discover hidden heterogeneous monotonic constraints.

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