arXiv Machine Learning By Yuta Shikuri, Hironori Fujisawa

Surrogate Graph Partitioning for Spatial Prediction

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The paper introduces a method called Surrogate Graph Partitioning for Spatial Prediction, which constructs spatial segments by minimizing within-segment prediction variance. The assignment of points to segments is framed as a mixed‑integer quadratic programming problem, but due to its high computational cost, an approximation scheme based on graph partitioning properties is proposed. Experiments show that this approximation efficiently identifies spatial segments.

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arXiv Statistics ML
Oct 9

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

The paper introduces the twoblock clustering tree (TBTREE), a deterministic regression tree designed for multivariate responses that uses local multivariate linear models as leaves and incorporates dense or sparse twoblock dimension reduction both in the leaf models and impurity calculation. TBTREE aims to provide an interpretable, regime‑aligned piecewise‑linear description of data while maintaining predictive performance through a split/leaf decoupling strategy. Additionally, the authors propose a coskewness‑based estimator for the twoblock reduced space to identify non‑normal clusters, demonstrating the method’s ability to recover piecewise linear regimes in simulations and to model complex nonlinear dependencies in real‑world datasets, achieving performance comparable to black‑box techniques such as random forests.

By Sven Serneels