Value propagation-based spatio-temporal interpolation inspired by Markov reward processes

Given the common problem of missing data in real-world applications from various fields, such as remote sensing, ecology and meteorology, the interpolation of missing spatial and spatio-temporal data can be of tremendous value. Existing methods for spatial interpolation, most notably Gaussian processes and spatial autoregressive models, tend to suffer from (a) a trade-off between modelling local or global spatial interaction, (b) the assumption there is only one possible path between two points, and (c) the assumption of homogeneity of intermediate locations between points. Addressing these issues, we propose a value propagation method, inspired by Markov reward processes (MRPs), as a spatial interpolation method, and introduce two variants thereof: (i) a static discount (SD-MRP) and (ii) a data-driven weight prediction (WP-MRP) variant. Both these interpolation variants operate locally, while implicitly accounting for global spatial relationships in the entire system through recursion. We evaluated our proposed methods by comparing the mean absolute errors and running times of interpolated grid cells to those of 7 common baselines. Our analysis involved detailed experiments on two synthetic and two real-world datasets over 44 total experimental conditions. Experimental results show the competitive advantage of MRP interpolation on real-world data, as the average performance of SD-MRP on real-world data under all experimental conditions was ranked significantly higher than that of all other methods, followed by WP-MRP. On synthetic data, we show that WP-MRP can perform better than SD-MRP given sufficiently informative features. We further found that, even in cases where our methods had no significant advantage over baselines numerically, our methods preserved the spatial structure of the target grid better than the baselines.