从签名张量学习路径
Learning Paths from Signature Tensors
AI总结：
本文通过张量分解、代数几何和数值优化方法，研究了张量的矩阵共轭问题，并针对随机分析中的逆问题，提出从第三阶签名张量恢复路径的方法，建立了路径的可识别性结果。
摘要：
矩阵共轭自然地扩展到张量的设置中。我们应用张量分解、代数几何和数值优化的方法来处理这一群作用。给定一个张量在另一个张量的轨道上，我们计算一个矩阵将其转换为另一个。我们的主要应用是一个来自随机分析的逆问题：从第三阶签名张量恢复路径。我们为分段线性路径、多项式路径和通用字典建立了精确和数值的可识别性结果。数值优化应用于从不精确数据中恢复。我们还计算了具有给定签名张量的最短路径。
英文摘要：
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a matrix which transforms one to the other. Our primary application is an inverse problem from stochastic analysis: the recovery of paths from their third order signature tensors. We establish identifiability results, both exact and numerical, for piecewise linear paths, polynomial paths, and generic dictionaries. Numerical optimization is applied for recovery from inexact data. We also compute the shortest path with a given signature tensor.
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。
