Classification of Hawkes processes and application to bats monitoring.
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: stochastic process
Session: IPS 763 - Statistics for Stochastic Processes
Tuesday 7 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
We consider the classification of high-dimension Hawkes processes (size M) from repeated observed paths on a fixed interval. The classes are discriminated by the parameters of the Hawkes process. The challenge is to deal with the high-dimension of the model together with the classification task. To do so, we make the assumption that in each class there is a sparse representation of the model which generates the data. Then, we propose an empirical risk minimization algorithm, based on a first step of support recovery of the adjacency matrix in each class, which describes the interactions between the components of the Hawkes process. We prove first the consistency of the estimated active set through a lasso criterion, and then the consistency of the classification rule. We use this classification algorithm firstly in a one dimensional problem (M=1) for classify commuting and foraging behavior of bats at a site. To this extent, we use echolocation calls data detected by acoustic sensors during a night at this site. As the temporal distribution of calls is a relevant indicator of behavior, it is natural to model the calls sequences by point processes. Given the self-exciting dynamics observed in foraging behavior, we propose to model the calls sequences of bats by Hawkes processes. The results obtained of the real data set are interesting ecologically and the method is a useful tool for ecologists. The high-dimensional framework is going to be use in order to deal with the whole data containing many species of bats and trying to infer competition between them.