The results indicate that mixtures of M\"obius distributions provide interpretable, parsimonious models for the studied steady state density distributions, that match or outperform the alternatives.
Abstract
We consider the problem of learning models of spatial density functions, representing the steady-state density of mobile nodes moving on a two-dimensional terrain. Deriving such models can assist in network design and optimization problems, e.g., by accelerating the computation of the density function during a parameter sweep. We address the question of applicability of off-the-shelf mixture density network models and of, two varieties of, normalizing flows for the description of mobile node density over a disk. We introduce the use of M\"obius distributions to retain symmetric spatial relations. Our results indicate that mixtures of M\"obius distributions provide interpretable, parsimonious models for the studied steady state density distributions, that match or outperform the alternatives.
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