# Bridging Breiman's Brook: From Algorithmic Modeling to Statistical Learning

@article{Mentch2021BridgingBB, title={Bridging Breiman's Brook: From Algorithmic Modeling to Statistical Learning}, author={Lucas Mentch and Giles Hooker}, journal={ArXiv}, year={2021}, volume={abs/2102.12328} }

In 2001, Leo Breiman wrote of a divide between “data modeling” and “algorithmic modeling” cultures. Twenty years later this division feels far more ephemeral, both in terms of assigning individuals to camps, and in terms of intellectual boundaries. We argue that this is largely due to the “data modelers” incorporating algorithmic methods into their toolbox, particularly driven by recent developments in the statistical understanding of Breiman’s own Random Forest methods. While this can be…

## 2 Citations

A cautionary tale on fitting decision trees to data from additive models: generalization lower bounds

- Computer ScienceAISTATS
- 2022

A sharp squared error generalization lower bound is proved for a large class of decision tree algorithms fitted to sparse additive models with C component functions, and a novel connection between decision tree estimation and rate-distortion theory, a sub-field of information theory is established.

Hierarchical Shrinkage: improving the accuracy and interpretability of tree-based methods

- Computer ScienceArXiv
- 2022

Hierarchical Shrinkage (HS), a post-hoc algorithm that does not modify the tree structure, and instead regularizes the tree by shrinking the prediction over each node towards the sample means of its ancestors, is introduced.

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