Gradient Boosting for Spatial Regression Models with Autoregressive Disturbances

• URL: http://arxiv.org/abs/2506.13682v1
• Date: Mon, 16 Jun 2025 16:40:47 GMT
• Title: Gradient Boosting for Spatial Regression Models with Autoregressive Disturbances
• Authors: Michael Balzer,
• Abstract summary: A novel model-based gradient boosting algorithm is proposed for spatial regression models with autoregressive disturbances.<n>The algorithm provides an alternative estimation procedure which is feasible even in high-dimensional settings.<n>A case study is presented where the life expectancy in German districts is modeled incorporating a potential spatial dependence structure.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 have been introduced. In this article, a novel model-based gradient boosting algorithm for spatial regression models with autoregressive disturbances is proposed. Due to the modular nature, the approach provides an alternative estimation procedure which is feasible even in high-dimensional settings where established quasi-maximum likelihood or generalized method of moments estimators do not yield unique solutions. The approach additionally enables data-driven variable and model selection in low- as well as high-dimensional settings. Since the bias-variance trade-off is also controlled in the algorithm, implicit regularization is imposed which improves prediction accuracy on out-of-sample spatial data. Detailed simulation studies regarding the performance of estimation, prediction and variable selection in low- and high-dimensional settings confirm proper functionality of the proposed methodology. To illustrative the functionality of the model-based gradient boosting algorithm, a case study is presented where the life expectancy in German districts is modeled incorporating a potential spatial dependence structure.

Related papers

• Feature-free regression kriging [4.270650728191168]
  This study proposes a Feature-Free Regression Kriging (FFRK) method to construct a regression-based trend surface without requiring external explanatory variables.<n>We conducted experiments on the spatial distribution prediction of three heavy metals in a mining area in Australia.<n>This approach effectively addresses spatial nonstationarity while reducing the cost of acquiring explanatory variables, improving both prediction accuracy and ability.
  arXiv  Detail & Related papers  (2025-07-10T02:34:07Z)
• On conditional diffusion models for PDE simulations [53.01911265639582]
  We study score-based diffusion models for forecasting and assimilation of sparse observations. We propose an autoregressive sampling approach that significantly improves performance in forecasting. We also propose a new training strategy for conditional score-based models that achieves stable performance over a range of history lengths.
  arXiv  Detail & Related papers  (2024-10-21T18:31:04Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Probabilistic Reduced-Dimensional Vector Autoregressive Modeling with Oblique Projections [0.7614628596146602]
  We propose a reduced-dimensional vector autoregressive model to extract low-dimensional dynamics from noisy data. An optimal oblique decomposition is derived for the best predictability regarding prediction error covariance. The superior performance and efficiency of the proposed approach are demonstrated using data sets from a synthesized Lorenz system and an industrial process from Eastman Chemical.
  arXiv  Detail & Related papers  (2024-01-14T05:38:10Z)
• Generative Modeling with Phase Stochastic Bridges [49.4474628881673]
  Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. We introduce a novel generative modeling framework grounded in textbfphase space dynamics Our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.
  arXiv  Detail & Related papers  (2023-10-11T18:38:28Z)
• BARTSIMP: flexible spatial covariate modeling and prediction using Bayesian additive regression trees [0.0]
  In this paper, we investigate the combination of a Gaussian process spatial model with a Bayesian Additive Regression Tree (BART) model.<n>The computational burden of the approach is reduced by combining Markov chain Monte Carlo with the Integrated Nested Laplace Approximation (INLA) technique.<n>We then use the model to predict anthropometric responses in Kenya, with the data collected via a complex sampling design.
  arXiv  Detail & Related papers  (2023-09-23T05:35:17Z)
• Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimation [45.9982965995401]
  We present Surjective Sequential Neural Likelihood estimation, a novel member in the family of methods for simulation-based inference ( SBI)<n>SSNL fits a dimensionality-reducing surjective normalizing flow model and uses it as a surrogate likelihood function, which allows for computational inference via Markov chain Monte Carlo or variational Bayes methods.<n>We evaluate SSNL on a wide variety of experiments, including two challenging real-world examples from the astrophysics and neuroscience literatures, and show that it either outperforms or is on par with state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-08-02T10:02:38Z)
• Reconstructing Spatiotemporal Data with C-VAEs [49.1574468325115]
  Conditional continuous representation of moving regions is commonly used. In this work, we explore the capabilities of Conditional Varitemporal Autoencoder (C-VAE) models to generate realistic representations of regions' evolution.
  arXiv  Detail & Related papers  (2023-07-12T15:34:10Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Adaptive LASSO estimation for functional hidden dynamic geostatistical model [69.10717733870575]
  We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hiddenstatistical models (f-HD) The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (GMSOLAS) penalty function, wherein the weights are obtained by the unpenalised f-HD maximum-likelihood estimators.
  arXiv  Detail & Related papers  (2022-08-10T19:17:45Z)
• Bayesian Spatial Predictive Synthesis [8.66529877559667]
  spatial dependence is a prevalent and critical issue in spatial data analysis and prediction.<n>We propose a novel Bayesian ensemble methodology that captures spatially-varying model uncertainty.<n>We show that our method provides a finite sample theoretical guarantee for its predictive performance.
  arXiv  Detail & Related papers  (2022-03-10T07:16:29Z)
• Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework [0.0]
  A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes.
  arXiv  Detail & Related papers  (2021-09-09T17:46:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.