Value propagation-based spatio-temporal interpolation inspired by Markov reward processes
user-6073b1344c775e0497f43bf9(2021)
摘要
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.
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关键词
markov reward processes,value,propagation-based,spatio-temporal
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