# Local Adaptivity of Gradient Boosting in Histogram Transform Ensemble Learning

arXiv: https://arxiv.org/abs/2112.02589 · HTML: https://mlsanity.com/paper/2112.02589/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 59 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Randomization as Regularization: A Degrees of Freedom Explanation for Random Forest Success](https://mlsanity.com/paper/1911.00190/) (2019)
- [Minimax optimal rates for Mondrian trees and forests](https://mlsanity.com/paper/1803.05784/) (2018)
- [A Unified Framework for Random Forest Prediction Error Estimation](https://mlsanity.com/paper/1912.07435/) (2019)
- [RaSE: Random Subspace Ensemble Classification](https://mlsanity.com/paper/2006.08855/) (2020)
- [GBHT: Gradient Boosting Histogram Transform for Density Estimation](https://mlsanity.com/paper/2106.05738/) (2021)
- [Histogram Transform Ensembles for Large-scale Regression](https://mlsanity.com/paper/1912.04738/) (2019)

## Abstract (arXiv)

In this paper, we propose a gradient boosting algorithm called textitadaptive boosting histogram transform (textitABHT) for regression to illustrate the local adaptivity of gradient boosting algorithms in histogram transform ensemble learning. From the theoretical perspective, when the target function lies in a locally H"older continuous space, we show that our ABHT can filter out the regions with different orders of smoothness. Consequently, we are able to prove that the upper bound of the convergence rates of ABHT is strictly smaller than the lower bound of textitparallel ensemble histogram transform (textitPEHT). In the experiments, both synthetic and real-world data experiments empirically validate the theoretical results, which demonstrates the advantageous performance and local adaptivity of our ABHT.