MRPinterpolation: a Markov reward process-based approach to spatial interpolation

Abstract

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.

People

• Laurens Arp
• Mitra Baratchi
• Holger H. Hoos

Software

MRP interpolation research code (January 2021) [zip, 361KB]

Code used for research and publication purposes, including algorithm implementations and experimental setups.

Data

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

License

Any software available on this page is licenced under the GPL-3.0 license.

Papers

• 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.
  [ PDF ∙ BibTeX ]