MRPinterpolation: a Markov reward process-based approach to spatial interpolation
The interpolation of spatial data can be of tremendous value in various applications, such as forecasting weather from only a few measurements of meteorological data. Existing methods for spatial interpolation, such as variants of Kriging and spatial autoregressive models, tend to suffer from (a) a trade-off between modelling local or global spatial interaction, (b) not accounting for multiple trajectories between two points, and (c) the assumption of stationarity and/or isotropy. Addressing these issues, we propose the use of Markov reward processes (MRPs) as a spatial interpolation method, and introduce two variants thereof: (i) a static discount MRP (SD-MRP) and (ii) a transferable weight prediction MRP (WP-MRP). Both these interpolation variants operate locally, while implicitly accounting for global spatial relationships in the entire system through recursion. Additionally, MRP interpolation does not assume stationarity, and WP-MRP is robust to anisotropy.
MRP interpolation research code (January 2021) [zip, 361KB]
Code used for research and publication purposes, including algorithm implementations and experimental setups.
The experimental evaluation of MRPinterpolation made use of the following data sources:
- Map data, sourced from OpenStreetMap and Geofabrik
- GDP data, sourced from World Bank
- South Korean COVID-19 trajectories, sourced from Dacon
Any software available on this page is licenced under the GPL-3.0 license.
- Laurens Arp (supervisors: Dr. Mitra Baratchi & Prof.dr. Holger H. Hoos)
A Markov Reward Process-Based Approach to Spatial Interpolation.Master's Thesis in Computer Science at Leiden Institute of Advanced Computer Science, Leiden University, 2020.