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The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian…

Applications · Statistics 2020-07-07 Zhihua Ma , Yishu Xue , Guanyu Hu

Researchers in urban and regional studies increasingly deal with spatial data that reflects geographic location and spatial relationships. As a framework for dealing with the unique nature of spatial data, various spatial regression models…

Econometrics · Economics 2025-06-17 Michael Balzer

Local spatial models such as Geographically Weighted Regression (GWR) and Multiscale Geographically Weighted Regression (MGWR) serve as instrumental tools to capture intrinsic contextual effects through the estimates of the local intercepts…

Geographically weighted regression (GWR) is a popular tool for modeling spatial heterogeneity in a regression model. However, the current weighting function used in GWR only considers the geographical distance, while the attribute…

Machine Learning · Computer Science 2023-05-17 Hone-Jay Chu , Po-Hung Chen , Sheng-Mao Chang , Muhammad Zeeshan Ali , Sumriti Ranjan Patra

Linear mixed models are widely used for clustered data, but their reliance on parametric forms limits flexibility in complex and high-dimensional settings. In contrast, gradient boosting methods achieve high predictive accuracy through…

Machine Learning · Statistics 2025-11-04 Mitchell L. Prevett , Francis K. C. Hui , Zhi Yang Tho , A. H. Welsh , Anton H. Westveld

This article focuses on the use of Geographically Weighted Regression (GWR) method to correct air quality low-cost sensors measurements. Those sensors are of major interest in the current era of high-resolution air quality monitoring at…

Applications · Statistics 2026-03-30 Jean-Michel Poggi , Bruno Portier , Emma Thulliez

It is widely known that geographically weighted regression(GWR) is essentially same as varying-coefficient model. In the former research about varying-coefficient model, scholars tend to use multidimensional-kernel-based locally weighted…

Econometrics · Economics 2018-04-13 Zihao Yuan

Spatial statistics is a growing discipline providing important analytical techniques in a wide range of disciplines in the natural and social sciences. In the R package GWmodel, we introduce techniques from a particular branch of spatial…

Applications · Statistics 2014-03-18 Isabella Gollini , Binbin Lu , Martin Charlton , Christopher Brunsdon , Paul Harris

Geographically Weighted Regression (GWR) is a widely recognized technique for modeling spatial heterogeneity. However, it is commonly assumed that the relationships between dependent and independent variables are linear. To overcome this…

Machine Learning · Computer Science 2025-04-08 Jianfei Cao , Dongchao Wang

Inductive bias is a key factor in spatial regression models, determining how well a model can learn from limited data and capture spatial patterns. This work revisits the inductive biases in Geographically Neural Network Weighted Regression…

Machine Learning · Computer Science 2025-07-23 Zhenyuan Chen

Gradient boosting, a method of building additive ensembles from weak learners, has established itself as a practical and theoretically-motivated approach to approximate functions, especially using decision tree weak learners. Comparable…

Machine Learning · Computer Science 2026-03-26 Abhijit Chowdhary , Elizabeth Newman , Deepanshu Verma

Gradient boosting has become a cornerstone of machine learning, enabling base learners such as decision trees to achieve exceptional predictive performance. While existing algorithms primarily handle scalar or Euclidean outputs,…

Machine Learning · Statistics 2025-09-23 Yidong Zhou , Su I Iao , Hans-Georg Müller

Geographically weighted regression (GWR) models handle geographical dependence through a spatially varying coefficient model and have been widely used in applied science, but its general Bayesian extension is unclear because it involves a…

Methodology · Statistics 2026-03-18 Yang Liu , Robert J. B. Goudie

Boosting is a learning scheme that combines weak prediction rules to produce a strong composite estimator, with the underlying intuition that one can obtain accurate prediction rules by combining "rough" ones. Although boosting is proved to…

Machine Learning · Computer Science 2015-05-07 Shaobo Lin , Yao Wang , Lin Xu

In this study, we present a collection of local models, termed geographically weighted (GW) models, that can be found within the GWmodel R package. A GW model suits situations when spatial data are poorly described by the global form, and…

Methodology · Statistics 2013-12-11 Binbin Lu , Paul Harris , Martin Charlton , Chris Brunsdon

Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current…

Methodology · Statistics 2020-11-03 Colin Griesbach , Benjamin Säfken , Elisabeth Waldmann

Gradient boosting algorithms construct a regression predictor using a linear combination of ``base learners''. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with…

Methodology · Statistics 2020-08-11 Xiaomeng Ju , Matías Salibián-Barrera

GWR is a popular approach for investigating the spatial variation in relationships between response and predictor variables, and critically for investigating and understanding process spatial heterogeneity. The geographically weighted (GW)…

Applications · Statistics 2021-09-30 Alexis Comber , Chris Brunsdon , Martin Callaghan , Paul Harris , Binbin Lu , Nick Malleson

Many single-target regression problems require estimates of uncertainty along with the point predictions. Probabilistic regression algorithms are well-suited for these tasks. However, the options are much more limited when the prediction…

Machine Learning · Statistics 2021-06-08 Michael O'Malley , Adam M. Sykulski , Rick Lumpkin , Alejandro Schuler

In this paper, we propose a gradient boosting algorithm for large-scale regression problems called \textit{Gradient Boosted Binary Histogram Ensemble} (GBBHE) based on binary histogram partition and ensemble learning. From the theoretical…

Machine Learning · Statistics 2021-06-04 Hanyuan Hang , Tao Huang , Yuchao Cai , Hanfang Yang , Zhouchen Lin
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