Spatially and Robustly Hybrid Mixture Regression Model for Inference of Spatial Dependence

• URL: http://arxiv.org/abs/2109.00539v2
• Date: Fri, 3 Sep 2021 04:32:06 GMT
• Title: Spatially and Robustly Hybrid Mixture Regression Model for Inference of Spatial Dependence
• Authors: Wennan Chang, Pengtao Dang, Changlin Wan, Xiaoyu Lu, Yue Fang, Tong Zhao, Yong Zang, Bo Li, Chi Zhang, Sha Cao
• Abstract summary: We propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial nonstationarity, local homogeneity, and outliers. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method.
• Score: 15.988679065054498
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex spatially dynamic patterns that cannot be captured by constant regression coefficients. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial nonstationarity, local homogeneity, and outlier contaminations. Compared with existing spatial regression models, our proposed model assumes the existence a few distinct regression models that are estimated based on observations that exhibit similar response-predictor relationships. As such, the proposed model not only accounts for nonstationarity in the spatial trend, but also clusters observations into a few distinct and homogenous groups. This provides an advantage on interpretation with a few stationary sub-processes identified that capture the predominant relationships between response and predictor variables. Moreover, the proposed method incorporates robust procedures to handle contaminations from both regression outliers and spatial outliers. By doing so, we robustly segment the spatial domain into distinct local regions with similar regression coefficients, and sporadic locations that are purely outliers. Rigorous statistical hypothesis testing procedure has been designed to test the significance of such segmentation. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method, compared with other robust finite mixture regression, spatial regression and spatial segmentation methods.

Related papers

• Deep Fréchet Regression [4.915744683251151]
  We propose a flexible regression model capable of handling high-dimensional predictors without imposing parametric assumptions. The proposed model outperforms existing methods for non-Euclidean responses.
  arXiv  Detail & Related papers  (2024-07-31T07:54:14Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Conformal inference for regression on Riemannian Manifolds [49.7719149179179]
  We investigate prediction sets for regression scenarios when the response variable, denoted by $Y$, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space. We prove the almost sure convergence of the empirical version of these regions on the manifold to their population counterparts.
  arXiv  Detail & Related papers  (2023-10-12T10:56:25Z)
• BART-SIMP: a novel framework for flexible spatial covariate modeling and prediction using Bayesian additive regression trees [0.0]
  We investigate a novel combination of a Gaussian process spatial model and a Bayesian Additive Regression Tree (BART) model. The computational burden of the approach is reduced by combining Markov chain Monte Carlo with the Integrated Nested Laplace Approximation (INLA) technique. We study the performance of the method via simulations and use the model to predict anthropometric responses, collected via household cluster samples in Kenya.
  arXiv  Detail & Related papers  (2023-09-23T05:35:17Z)
• Errors-in-variables Fr\'echet Regression with Low-rank Covariate Approximation [2.1756081703276]
  Fr'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. Our proposed framework combines the concepts of global Fr'echet regression and principal component regression, aiming to improve the efficiency and accuracy of the regression estimator.
  arXiv  Detail & Related papers  (2023-05-16T08:37:54Z)
• Strong identifiability and parameter learning in regression with heterogeneous response [5.503319042839695]
  We investigate conditions of strong identifiability, rates of convergence for conditional density and parameter estimation, and the Bayesian posterior contraction behavior arising in finite mixture of regression models. We provide simulation studies and data illustrations, which shed some light on the parameter learning behavior found in several popular regression mixture models reported in the literature.
  arXiv  Detail & Related papers  (2022-12-08T05:58:13Z)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• Beyond Instance Discrimination: Relation-aware Contrastive Self-supervised Learning [75.46664770669949]
  We present relation-aware contrastive self-supervised learning (ReCo) to integrate instance relations. Our ReCo consistently gains remarkable performance improvements.
  arXiv  Detail & Related papers  (2022-11-02T03:25:28Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences [77.68028443709338]
  We propose a fully Bayesian formulation of the Epidemic Type Aftershock Sequence (ETAS) model. The occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process.
  arXiv  Detail & Related papers  (2020-02-05T10:11:26Z)

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.