Twoblock clustering trees with coskewness-based dimension reduction: recovering piecewise multivariate linear regimes

2026-07-22

AI Summary

This work proposes the two-block clustering tree (tbtree), a novel deterministic decision tree method tailored for multivariate response data exhibiting piecewise multilinear structures. The approach embeds local multivariate linear models within leaf nodes and guides splits via a two-block dimensionality reduction strategy based on maximizing residual skewness, effectively identifying non-Gaussian clusters. By integrating both sparse and dense dimensionality reduction mechanisms, tbtree achieves strong nonlinear fitting capability while maintaining full interpretability throughout the tree construction process. Empirical evaluations demonstrate that the method accurately recovers the true piecewise linear mechanisms in simulated data and attains predictive performance on real-world datasets comparable to black-box models such as random forests, thereby offering an advantageous balance between interpretability and prediction accuracy.

Abstract

The twoblock clustering tree (\tbtree) is introduced as a highly interpretable regression tree for multivariate responses. Twoblock trees are deterministic decision trees that have local multivariate linear models as their leaves and use dense or sparse twoblock dimension reduction as local leaf models and in the impurity. The resulting models are both computationally efficient and can be highly interpretable. Beyond proposing the decision tree estimator itself, this paper also introduces an estimator for the twoblock dimension reduced space based on maximizing coskewness, which facilitates identification of non-normal clusters in the data. The tree inherently produces a set of local linear models and is therefore apt to recover peicewise linear regimes, which is illustrated in a simulation. However, two real world data examples illustrate that twoblock trees are also capable of modeling more complexly nonlinear dependencies and can perform on par with black box modeling techniques, such as random forests. At each point, both the twoblock models that generate the splits, as well as the ones in the leaves, can be inspected and interpreted.

Problem

• multivariate regression
• piecewise linear regimes
• non-normal clusters
• dimension reduction
• coskewness

Innovation

• twoblock clustering tree
• coskewness-based dimension reduction
• piecewise multivariate linear regimes
• interpretable regression tree
• non-normal cluster identification