Title: A statistical method to detect abrupt changes in trees
Authors: Solene Thepaut - Universite Paris-Sud (France)
Nicolas Verzelen - INRA Montpellier (France)
Guillem Rigaill - INRA (France) [presenting]
Abstract: The problem of detecting multiple changes in the mean of the nodes of a tree is studied. This problem is motivated by an application in ecology, where diversity measurements are made at $n$ points of a river system. The river system is represented as a tree. The goal is to detect sub-trees where the diversity is abnormally high or low. We propose to infer the signal and the position of the changes by minimizing a penalized empirical risk. We propose a penalty satisfying a non-asymptotic oracle inequality. We propose a pruned dynamic programming algorithms to solve this problem. We empirically show that their complexity is on average $O(n^2)$ or less with $n$ the number of nodes of the tree. We tested our approach on simulations and used it on our ecological dataset.