The art of BART: On flexibility of Bayesian forests
Bibliographic record
Abstract
Considerable effort has been directed to developing asymptotically minimax procedures in problems of recovering functions and densities. These methods often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances theoretical understanding of Bayesian forests (including BART) under substantially relaxed smoothness assumptions. In particular, we provide a comprehensive study of asymptotic optimality and posterior contraction of Bayesian forests when the regression function has anisotropic smoothness that possibly varies over the function domain. We introduce a new class of sparse piecewise heterogeneous anisotropic Holder functions and derive their minimax rate of estimation in high-dimensional scenarios under the $L_2$ loss. Next, we find that the default Bayesian CART prior, coupled with a subset selection prior for sparse estimation in high-dimensional scenarios, adapts to unknown heterogeneous smoothness and sparsity. These results show that Bayesian forests are uniquely suited for more general estimation problems which would render other default machine learning tools, such as Gaussian processes, suboptimal. Beyond nonparametric regression, we also show that Bayesian forests can be successfully applied to many other problems including density estimation and binary classification.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.020 | 0.074 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".