关于相互作用粒子系统学习中的收敛性条件
On the coercivity condition in the learning of interacting particle systems
University of Connecticut（康涅狄格大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
摘要：
在相互作用粒子或主体系统的学习中，广义条件保证了相互作用函数的可辨识性，为非参数回归学习提供了基础。该条件等价于在学习中产生的积分核的严格正定性。我们证明了对于一类相互作用函数，使得系统是遍历的，积分核是严格正定的，因此双态性条件成立。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
