A Distributed Approach for Learning Spatial Heterogeneity

Speaker: Zhengyuan Zhu, Iowa State University

Abstract: Spatial regression is widely used for modeling the relationship between a spatial dependent variable and explanatory covariates. In many applications there is spatial heterogeneity in such relationships, i.e., the regression coefficients may vary across space. It is a fundamental and challenging problem to detect the systematic variation in the model and determine which locations share common regression coefficients and where the boundary is. In this talk, we introduce a Spatial Heterogeneity Automatic Detection and Estimation (SHADE) procedure for automatically and simultaneously subgrouping and estimating covariate effects for spatial regression models, and present a distributed spanning-tree-based fused-lasso regression (DTFLR) approach to learn spatial heterogeneity in the distributed network systems, where the data are locally collected and held by nodes. To solve the problem parallelly, we design a distributed generalized alternating direction method of multiplier algorithm, which has a simple node-based implementation scheme and enjoys a linear convergence rate. Theoretical and numerical results as well as real-world data analysis will be presented to show that our approach outperforms existing works in terms of estimation accuracy, computation speed, and communication costs.