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Summary Ensembles of decision trees are a useful tool for obtaining flexible estimates of regression functions. Examples of these methods include gradient-boosted decision trees, random forests and Bayesian classification and regression trees. Two potential shortcomings of tree ensembles are their lack of smoothness and their vulnerability to the curse of dimensionality. We show that these issues can be overcome by instead considering sparsity inducing soft decision trees in which the decisions are treated as probabilistic. We implement this in the context of the Bayesian additive regression trees framework and illustrate its promising performance through testing on benchmark data sets. We provide strong theoretical support for our methodology by showing that the posterior distribution concentrates at the minimax rate (up to a logarithmic factor) for sparse functions and functions with additive structures in the high dimensional regime where the dimensionality of the covariate space is allowed to grow nearly exponentially in the sample size. Our method also adapts to the unknown smoothness and sparsity levels, and can be implemented by making minimal modifications to existing Bayesian additive regression tree algorithms.
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Interaction Detection with Bayesian Decision Tree Ensembles
Methods based on Bayesian decision tree ensembles have proven valuable in constructing high-quality predictions, and are particularly attractive in certain settings because they encourage low-order interaction effects. Despite adapting to the presence of low-order interactions for prediction purpose, we show that Bayesian decision tree ensembles are generally anti-conservative for the purpose of conducting interaction detection. We address this problem by introducing Dirichlet process forests (DP-Forests), which leverage the presence of low-order interactions by clustering the trees so that trees within the same cluster focus on detecting a specific interaction. We show on both simulated and benchmark data that DP-Forests perform well relative to existing interaction detection techniques for detecting low-order interactions, attaining very low false-positive and false-negative rates while maintaining the same performance for prediction using a comparable computational budget.
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- Award ID(s):
- 1712870
- PAR ID:
- 10097144
- Date Published:
- Journal Name:
- Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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- The DOI is not currently available.
