This paper proposes a partitioning structure learning method for segmented linear regression trees (SLRT), which assigns linear predictors over the terminal nodes. The recursive partitioning process is driven by an adaptive split selection algorithm that maximizes, at each node, a criterion function based on a conditional Kendall's τ statistic that measures the rank dependence between the regressors and the fitted linear residuals. Theoretical analysis shows that the split selection algorithm permits consistent identification and estimation of the unknown segments. A sufficiently large tree is induced by applying the split selection algorithm recursively. Then the minimal cost-complexity tree pruning procedure is applied to attain the right-sized tree, that ensures (i) the nested structure of pruned subtrees and (ii) consistent estimation to the number of segments. Implanting the SLRT as the built-in base predictor, we obtain the ensemble predictors by random forests (RF) and the proposed weighted random forests (WRF). The practical performance of the SLRT and its ensemble versions are evaluated via numerical simulations and empirical studies. The latter shows their advantageous predictive performance over a set of state-of-the-art tree-based models on well-studied public datasets.

Originality: The paper is fairly original in that it proposes a new tree-splitting criterion that seems to work very well when the leaves are linear models rather than constants. It also provides a novel application of several pieces of previous work, including LASSO and random forests. There are adequate citations of related work. Quality: I did not carefully check the math or read the proofs in the supplemental material, but I did not observe any technical mistakes. There is not much discussion of the limitations of their approach.

The paper proposes and investigates how to learn tree structure for linear regression trees based on a conditional Kendall's tau statistics with theoretical analysis.The ideas were new and generally satisfying to reviewers. While some reviewers would have liked to see even more experiments and experimental comparisons and details, other reviewers felt that the author response about the experiments was satisfying.

This paper proposes a partitioning structure learning method for segmented linear regression trees (SLRT), which assigns linear predictors over the terminal nodes. The recursive partitioning process is driven by an adaptive split selection algorithm that maximizes, at each node, a criterion function based on a conditional Kendall's τ statistic that measures the rank dependence between the regressors and the fit- ted linear residuals. Theoretical analysis shows that the split selection algorithm permits consistent identification and estimation of the unknown segments. A suffi- ciently large tree is induced by applying the split selection algorithm recursively. Then the minimal cost-complexity tree pruning procedure is applied to attain the right-sized tree, that ensures (i) the nested structure of pruned subtrees and (ii) consistent estimation to the number of segments.

This paper proposes a partitioning structure learning method for segmented linear regression trees (SLRT), which assigns linear predictors over the terminal nodes. The recursive partitioning process is driven by an adaptive split selection algorithm that maximizes, at each node, a criterion function based on a conditional Kendall's τ statistic that measures the rank dependence between the regressors and the fit- ted linear residuals. Theoretical analysis shows that the split selection algorithm permits consistent identification and estimation of the unknown segments. A suffi- ciently large tree is induced by applying the split selection algorithm recursively. Then the minimal cost-complexity tree pruning procedure is applied to attain the right-sized tree, that ensures (i) the nested structure of pruned subtrees and (ii) consistent estimation to the number of segments.