On the coercivity condition in the learning of interacting particle systems

• URL: http://arxiv.org/abs/2011.10480v2
• Date: Thu, 21 Oct 2021 05:51:24 GMT
• Title: On the coercivity condition in the learning of interacting particle systems
• Authors: Zhongyang Li and Fei Lu
• Abstract summary: Coercivity condition is equivalent to the strictly positive definiteness of an integral kernel arising in the learning. We show that for a class of interaction functions such that the system is ergodic, the integral kernel is strictly positive definite, and hence the coercivity condition holds true.
• Score: 7.089219223012485
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the learning of systems of interacting particles or agents, coercivity condition ensures identifiability of the interaction functions, providing the foundation of learning by nonparametric regression. The coercivity condition is equivalent to the strictly positive definiteness of an integral kernel arising in the learning. We show that for a class of interaction functions such that the system is ergodic, the integral kernel is strictly positive definite, and hence the coercivity condition holds true.

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