핵심 개념
Proposing principled Gaussian processes for modeling functions defined over the edge set of a simplicial 2-complex, enabling direct and independent learning for different Hodge components of edge functions.
초록
Gaussian processes are proposed for modeling functions on the edge set of a simplicial 2-complex, focusing on edge-based dynamical processes in complex networks.
The Hodge decomposition theorem is utilized to define divergence-free and curl-free edge Gaussian processes, combined into Hodge-compositional edge GPs.
Applications in foreign currency exchange, ocean currents, and water supply networks showcase the practical potential of these GPs.
Experimental results demonstrate the superiority of Hodge-compositional edge GPs in capturing the structure of edge functions and improving predictive performance.
통계
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인용구
"We propose principled Gaussian processes for modeling functions defined over the edge set of a simplicial 2-complex."
"These GPs facilitate direct and independent learning for the different Hodge components of edge functions."