标题： 具有变化点的时间事件强度学习 显示英文标题

标题： Learning the intensity of time events with change-points

摘要： 我们研究了在稀疏分段假设下学习计数过程非齐次强度的问题。 我们引入了一种加权总变差惩罚项，使用数据驱动的权重，这些权重在观测区间上正确地缩放惩罚项。 我们证明，这导致分段先验凸松弛的精确调整，通过陈述具有快速收敛速度的oracle不等式以及改变点检测的一致性，从而证明了这一点。 这为分段问题提供了第一个标准独立同分布信号+白噪声设置之外的理论保证。 我们提出了一种快速算法来解决这个凸优化问题。 数值实验在模拟数据和高频率基因组数据集上验证了我们的方法。 显示英文摘要

摘要： We consider the problem of learning the inhomogeneous intensity of a counting process, under a sparse segmentation assumption. We introduce a weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We prove that this leads to a sharp tuning of the convex relaxation of the segmentation prior, by stating oracle inequalities with fast rates of convergence, and consistency for change-points detection. This provides first theoretical guarantees for segmentation with a convex proxy beyond the standard i.i.d signal + white noise setting. We introduce a fast algorithm to solve this convex problem. Numerical experiments illustrate our approach on simulated and on a high-frequency genomics dataset.