Logistic model tree

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In computer science, a logistic model tree (LMT) is a classification model with an associated supervised training algorithm that combines logistic regression (LR) and decision tree learning.^[1]^[2]

Logistic model trees are based on the earlier idea of a model tree: a decision tree that has linear regression models at its leaves to provide a piecewise linear regression model (where ordinary decision trees with constants at their leaves would produce a piecewise constant model).^[1] In the logistic variant, the LogitBoost algorithm is used to produce an LR model at every node in the tree; the node is then split using the C4.5 criterion. Each LogitBoost invocation is warm-started^[vague] from its results in the parent node. Finally, the tree is pruned.^[3]

The basic LMT induction algorithm uses cross-validation to find a number of LogitBoost iterations that does not overfit the training data. A faster version has been proposed that uses the Akaike information criterion to control LogitBoost stopping.^[3]

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^ ^a ^b Niels Landwehr; Mark Hall; Eibe Frank (2003). Logistic model trees (PDF). ECML PKDD.
^ Landwehr, N.; Hall, M.; Frank, E. (2005). "Logistic Model Trees" (PDF). Machine Learning. 59 (1–2): 161–205. doi:10.1007/s10994-005-0466-3.
^ ^a ^b Sumner, Marc; Eibe Frank; Mark Hall (2005). Speeding up logistic model tree induction (PDF). PKDD. Springer. pp. 675–683.

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