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Boulevard: Regularized Stochastic Gradient Boosted Trees and Their Limiting Distribution
Methodology · Submitted 26 Jun 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim A simulation study and real world examples provide support for both the predictive accuracy of the model and its limiting behavior.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
This paper examines a novel gradient boosting framework for regression. We regularize gradient boosted trees by introducing subsampling and employ a modified shrinkage algorithm so that at every boosting stage the estimate is given by an average of trees. The resulting algorithm, titled Boulevard, is shown to converge as the number of trees grows. We also demonstrate a central limit theorem for this limit, allowing a characterization of uncertainty for predictions. A simulation study and real world examples provide support for both the predictive accuracy of the model and its limiting behavior.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper examines a novel gradient boosting framework for regression. | contribution 0.97 | 0.74 | 0.05 | asserted 0.94 |
| s1 | We regularize gradient boosted trees by introducing subsampling and employ a modified shrinkage algorithm so that at every boosting stage the estimate is given by an average of trees. | method 0.94 | 0.94 | 0.08 | asserted 0.99 |
| s2 | The resulting algorithm, titled Boulevard, is shown to converge as the number of trees grows. | result 0.92 | 0.92 | 0.30 | asserted 1.00 |
| s3 | We also demonstrate a central limit theorem for this limit, allowing a characterization of uncertainty for predictions. | result 0.73 | 0.95 | 0.22 | asserted 1.00 |
| s4 | A simulation study and real world examples provide support for both the predictive accuracy of the model and its limiting behavior. | result 0.78 | 0.95 | 0.21 | asserted 0.99 |
What was examined, and what was not
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The paper
Original abstract
This paper examines a novel gradient boosting framework for regression. We regularize gradient boosted trees by introducing subsampling and employ a modified shrinkage algorithm so that at every boosting stage the estimate is given by an average of trees. The resulting algorithm, titled Boulevard, is shown to converge as the number of trees grows. We also demonstrate a central limit theorem for this limit, allowing a characterization of uncertainty for predictions. A simulation study and real world examples provide support for both the predictive accuracy of the model and its limiting behavior.
Human review
How the literature uses it
6 arXiv papers cite this in 14 sentences
Papers citing it · 12 sentences without a confident label
Cites it as background 2 papers
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There are several theoretical attempts to study SGB convergence, e.g., Boulevard [ref] , AnyBoost [ref] , or gradient boosting in general $L_2$ setting [ref] .
SGLB: Stochastic Gradient Langevin Boosting · Related Work · 0.96
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More sophisticated tree-based ensembles motivated by random forests have been proposed by [ref] , who iteratively grow feature-weighted tree ensembles that perform especially well for discovering interactions, [ref] , who consider a hybrid between random forests and boosting, and [ref] , who do deeper search during splitting to mitigate the greediness of CART.
Local Linear Forests · Related Work · 0.95
What it cites · 3 sentences without a confident label
Compares with 1 paper
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In comparison, [ref] have shown that, in fixed dimension, any tree can be well approximated by a collection of $O(exp(logn)^2)$ hyper rectangles.
Adaptive Concentration of Regression Trees, with Application to Random Forests · Subsampling and Tree Space Capacity · 1.00
Cites as background 2 papers
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Early analyses employed completely randomized trees in which the structure was determined independently of observed responses: see [ref] that, in particular, generate a connection to kernel methods observed in [ref] and [ref] .
The Random Forest Kernel and other kernels for big data from random partitions · Non-adaptivity · 0.81
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Early analyses employed completely randomized trees in which the structure was determined independently of observed responses: see [ref] that, in particular, generate a connection to kernel methods observed in [ref] and [ref] .
Analysis of purely random forests bias · Non-adaptivity · 0.81
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