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Random Forests as Statistical Procedures: Design, Variance, and Dependence
We develop a finite-sample, design-based theory for random forests in which each tree is a randomized conditional predictor acting on fixed covariates and the forest is their Monte Carlo average. An exact variance identity separates Monte Carlo error from a covariance floor that persists under infinite aggregation. The floor arises through two mechanisms: observation reuse, where the same training outcomes receive weight across multiple trees, and partition alignment, where independently generated trees discover similar conditional prediction rules. We prove the floor is strictly positive under minimal conditions and show that alignment persists even when sample splitting eliminates observation overlap entirely. We introduce procedure-aligned synthetic resampling (PASR) to estimate the covariance floor, decomposing the total prediction uncertainty of a deployed forest into interpretable components. For continuous outcomes, resulting prediction intervals achieve nominal coverage with a theoretically guaranteed conservative bias direction. For classification forests, the PASR estimator is asymptotically unbiased, providing the first pointwise confidence intervals for predicted conditional probabilities from a deployed forest. Nominal coverage is maintained across a range of design configurations for both outcome types, including high-dimensional settings. The underlying theory extends to any tree-based ensemble with an exchangeable tree-generating mechanism.
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Model Agnostic Supervised Local Explanations
Gregory Plumb, Denali Molitor, Ameet S. Talwalkar
Model interpretability is an increasingly important component of practical machine learning. Some ofthemost common forms ofinterpretability systems are example-based, local, and global explanations. One of the main challenges in interpretability isdesigning explanation systems thatcancapture aspects ofeach of these explanation types, in order to develop a more thorough understanding of the model. We address this challenge in a novel model called MAPLE that useslocallinearmodeling techniques alongwithadualinterpretation ofrandom forests (both as a supervised neighborhood approach and as a feature selection method).
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c460dc0f18fc309ac07306a4a55d2fd6-Paper.pdf
However,twokeydrawbacks of RPS-l2 are thatthey(i)leadtodisagreement between theoriginally trained networkandthe RPS-l2 regularized network modification and (ii) often yield a static ranking of training data fortest points inthesame class, independent ofthetest point being classified. Inspired by the RPS-l2 approach, we propose an alternative method based on a local Jacobian Taylor expansion (LJE).
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