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 or remote sensing data. Existing methods for spatial interpolation, such as variants of kriging and spatial autoregressive models, tend to suffer from at least one of the following limitations: (a) the assumption of stationarity, (b) the assumption of isotropy, and (c) the trade-off between modelling local or global spatial interaction. Addressing these issues in this work, we propose the use of Markov reward processes (MRPs) as a spatial interpolation method, and we introduce three variants thereof: (i) a basic static discount MRP (SD-MRP), (ii) an accurate but mostly theoretical optimised MRP (O-MRP), and (iii) a transferable weight prediction MRP (WP-MRP). All variants of MRP interpolation operate locally, while also implicitly accounting for global spatial relationships in the entire system through recursion. Additionally, O-MRP and WP-MRP no longer assume stationarity and are robust to anisotropy. We evaluated our proposed methods by comparing the mean absolute errors of their interpolated grid cells to those of 7 common baselines, selected from models based on spatial autocorrelation, (spatial) regression, and deep learning. We performed detailed evaluations on two publicly available datasets (local GDP values, and COVID-19 patient trajectory data). The results from these experiments clearly show the competitive advantage of MRP interpolation, which achieved significantly lower errors than the existing methods in 23 out of 40 experimental conditions, or 35 out of 40 when including O-MRP.
Code (1)
Tasks
Gaussian ProcessesSpatial InterpolationSimilar Papers 제목 키워드 기반
Generalized Wishart processes for interpolation over diffusion tensor fields
Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive tool for watching the microstructure of fibrous nerve and muscle tissue. From dMRI, it is possible to estimate 2-rank diffusion tensors imaging (DTI) fields, …
Amortized Bayesian Local Interpolation NetworK: Fast covariance parameter estimation for Gaussian Processes
Gaussian processes (GPs) are a ubiquitous tool for geostatistical modeling with high levels of flexibility and interpretability, and the ability to make predictions at unseen spatial locations through a process called Kr…
Computational EfficiencyGaussian Processesparameter estimationInferring Probabilistic Reward Machines from Non-Markovian Reward Processes for Reinforcement Learning
The success of reinforcement learning in typical settings is predicated on Markovian assumptions on the reward signal by which an agent learns optimal policies. In recent years, the use of reward machines has relaxed thi…
Decision Makingreinforcement-learningReinforcement LearningReinforcement Learning (RL)A Markov Variation Approach to Smooth Graph Signal Interpolation
In this paper we present the Markov variation, a smoothness measure which offers a probabilistic interpretation of graph signal smoothness. This measure is then used to develop an optimization framework for graph signal …
Detecting Hidden Triggers: Mapping Non-Markov Reward Functions to Markov
Many Reinforcement Learning algorithms assume a Markov reward function to guarantee optimality. However, not all reward functions are Markov. This paper proposes a framework for mapping non-Markov reward functions into e…