Scalable Look-Ahead Linear Regression Trees

The motivation behind Look-ahead Linear Regression Trees (LLRT) is that out of all the methods proposed to date, there has been no scalable approach to exhaustively evaluate all possible models in the leaf nodes in order to obtain an optimal split. Using several optimizations, LLRT is able to generate and evaluate thousands of linear regression models per second. This allows for a near-exhaustive evaluation of all possible splits in a node, based on the quality of fit of linear regression models in the resulting branches. We decompose the calculation of the Residual Sum of Squares in such a way that a large part of it is pre-computed. The resulting method is highly scalable. We observe it to obtain high predictive accuracy for problems with strong mutual dependencies between attributes. We report on experiments with two simulated and seven real data sets.