多变量Hawkes过程路径的ERM-Lasso分类算法
ERM-Lasso classification algorithm for Multivariate Hawkes Processes paths
AI总结：
本文提出基于Lasso估计器的ERM-Lasso方法，用于分类多变量Hawkes过程路径，通过稀疏性假设和最小化L2风险实现高维网络下的分类任务。
摘要：
我们关注多变量Hawkes过程（MHP）路径分类问题，其中路径来自多个类别。MHP是一类 versatile 的点过程，用于建模网络中个体间的相互作用。本文通过外生强度向量和邻接矩阵进行分类，其中邻接矩阵编码相互作用强度。观测学习数据由在固定时间区间内的标记重复且独立路径组成。此外，我们考虑高维设置，即网络维度可能较大。因此，我们要求对邻接矩阵施加稀疏性假设。在此背景下，我们提出了一种新方法，首先通过类别进行初始相互作用恢复步骤，随后基于合适的分类准则进行重新拟合。为了恢复邻接矩阵的支持，提出了一种Lasso型估计器，并建立了收敛率。然后，利用估计的支持，基于最小化L2风险构建分类程序。值得注意的是，提供了分类程序的收敛率。使用合成数据的深入测试阶段支持了理论结果。
英文摘要：
We are interested in the problem of classifying Multivariate Hawkes Processes (MHP) paths coming from several classes. MHP form a versatile family of point processes that models interactions between connected individuals within a network. In this paper, the classes are discriminated by the exogenous intensity vector and the adjacency matrix, which encodes the strength of the interactions. The observed learning data consist of labeled repeated and independent paths on a fixed time interval. Besides, we consider the high-dimensional setting, meaning the dimension of the network may be large {\it w.r.t.} the number of observations. We consequently require a sparsity assumption on the adjacency matrix. In this context, we propose a novel methodology with an initial interaction recovery step, by class, followed by a refitting step based on a suitable classification criterion. To recover the support of the adjacency matrix, a Lasso-type estimator is proposed, for which we establish rates of convergence. Then, leveraging the estimated support, we build a classification procedure based on the minimization of a $L_2$-risk. Notably, rates of convergence of our classification procedure are provided. An in-depth testing phase using synthetic data supports both theoretical results.
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。
