A LRT framework for fast spatial anomaly detection

Given a spatial data set placed on an n x n grid, our goal is to find the rectangular regions within which subsets of the data set exhibit anomalous behavior. We develop algorithms that, given any user-supplied arbitrary likelihood function, conduct a likelihood ratio hypothesis test (LRT) over each rectangular region in the grid, rank all of the rectangles based on the computed LRT statistics, and return the top few most interesting rectangles. To speed this process, we develop methods to prune rectangles without computing their associated LRT statistics.