Parameter Estimation for the Spatial Autoregression Model: A Rigorous Approach

The spatial autoregression (SAR) model is a knowledge discovery technique used for mining massive geo-spatial data in many application domains. Estimation of the parameters of the exact SAR model using Maximum Likelihood (ML) theory is computationally very expensive because of the need to compute the logarithm of the determinant (log-det) of a large matrix in the loglikelihood function. In this paper, we developed a faster, scalable and NOvel pRediction and estimation TecHnique for the exact SpaTial Auto Regression model solution (NORTHSTAR). In this heuristic, the SAR model parameters are first estimated using a computationally more efficient sum-of-squared errors (SSE) term of the log-likelihood function. Next, starting from an initial estimate very close to the optimal estimate, the computationally more expensive log-det term is embedded into the estimation process to save log-det computations. Experimental results show that the NORTHSTAR algorithm outperformed the previous exact SAR model solutions.