Beyond spatial auto-regressive models: Predicting housing prices with satellite imagery

Abstract

When modeling geo-spatial data, it is critical to capture spatial correlations for achieving high accuracy. Spatial Auto-Regression (SAR) is a common tool used to model such data, where the spatial contiguity matrix (W) encodes thespatial correlations. However, the efficacy of SAR is limited by two factors. First, it depends on the choice of contiguity matrix, which is typically not learnt from data, but instead, is assumed to be known apriori. Second, it assumes that the observations can be explained by linear models. In this paper, we propose a Convolutional Neural Network (CNN) framework to model geo-spatial data (specifically housing prices), to learn the spatial correlations automatically. We show that neighborhood information embedded in satellite imagery can be leveraged to achieve the desired spatial smoothing. An additional upside of our framework is the relaxation of linear assumption on the data. Specific challenges we tackle while implementing our framework include, (i) how much of the neighborhood is relevant while estimating housing prices? (ii) what is the right approach to capture multiple resolutions of satellite imagery? and (iii) what other data-sources can help improve the estimation of spatial correlations? We demonstrate a marked improvement of 57% on top of the SAR baseline through the use of features from deep neural networks for the cities of London, Birmingham and Liverpool.