DeepAI AI Chat
Log In Sign Up

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

by   Wennan Chang, et al.
Purdue University
Indiana University
Peking University

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.


page 1

page 10


Bayesian Spatial Homogeneity Pursuit Regression for Count Value Data

Spatial regression models are ubiquitous in many different areas such as...

A New Algorithm using Component-wise Adaptive Trimming For Robust Mixture Regression

Mixture regression provides a statistical model for teasing out latent h...

Spatial Resolution Enhancement of Oversampled Images Using Regression Decomposition and Synthesis

A new statistical model designed for regression analysis with a sparse d...

The GWR route map: a guide to the informed application of Geographically Weighted Regression

Geographically Weighted Regression (GWR) is increasingly used in spatial...

Spatially Clustered Regression

Spatial regression or geographically weighted regression models have bee...

Robust Finite Mixture Regression for Heterogeneous Targets

Finite Mixture Regression (FMR) refers to the mixture modeling scheme wh...

Hyper-Spectral Image Analysis with Partially-Latent Regression and Spatial Markov Dependencies

Hyper-spectral data can be analyzed to recover physical properties at la...