Robust Prediction and Outlier Detection for Spatial Datasets

Spatial kriging is a widely used predictive model for spatial datasets. In spatial kriging model, the observations are assumed to be Gaussian for computational convenience. However, its predictive accuracy could be significantly compromised if the observations are contaminated by outliers. This deficiency can be systematically addressed by increasing the robustness of spatial kriging model using heavy tailed distributions, such as the Huber, Laplace, and Student´s t distributions. This paper presents a novel Robust and Reduced Rank Spatial Kriging Model (R³-SKM), which is resilient to the influences of outliers and allows for fast spatial inference. Furthermore, three effective and efficient algorithms are proposed based on R³-SKM framework that can perform robust parameter estimation, spatial prediction, and spatial outlier detection with a linear-order time complexity. Extensive experiments on both simulated and real data sets demonstrated the robustness and efficiency of our proposed techniques.