RINA - Démonstrateur d’utilisation de l’intelligence artificielle pour la gestion opérationnelle des risques naturels gravitaires géologiques | FEREC 2020

47 conditional intensity function λ ? ( t ) without the need of specifying a fixed parametric specification for the dependency structure over the history " Figure B.2: RMTPP from paper [5] , overview on left and zoom on unfold hidden state h j on right Paper O. Takahiro 2019 [8] Specialisation of RNN model proposed by Du et al [5] . source code available "In this approach, an RNN is used to obtain a compact representation of the event history. The conditional intensity function is then modeled as a function of the hidden state of the RNN. Consequently, the RNN based models outperform the parametric models in prediction performance." Paper A. Soen 2020 [9] it give some theoretical results about point process approximation, some reference about RNN models at most, and propose a RNN model call UNIPoint. "A known method for approximating a wide variety of functions is the use of neural networks Hornik et al. (1989); Hornik (1991). Recent work has utilised recurrent neural networks to define point process intensity functions Du et al. (2016); Mei and Eisner (2017); Omi et al. (2019); Shchur et al. (2020). A central concept amongst these models is the usage of a recurrent neural network to encode the past events in a sequence, initially proposed by by the Recurrent Marked Temporal Point Process model Du et al. (2016) " "There are many different types of point processes, and a variety of applications in which they are employed, for example analysing social networks Mishra et al. (2016); Wilhelm et al. (2018). The homogeneous Poisson process is often considered the simplest type of point process, where the number of events over a finite time interval is a random variable with a Poisson distribution Kingman (2005); Daley and Vere-Jones (2007). For the homogeneous Poisson process, the dis- tribution of points is independent of the history and the distribution does not change over time.