Causal inference with Approximate Bayesian Computation for Multivariate Hawkes Processes

Le laboratoire est membre des Fédérations de Recherche CNRS FRUMAM, TERSYS, AGORANTIC.

Il co-organise annuellement deux évènements fédérateurs FRUMAM: le colloquium FRUMAM et les Journées de Systèmes Dynamiques Avignon-Marseille.

Notre laboratoire comporte une vingtaine de membres répartis dans trois équipes de recherche : Equipe d’Analyse non-linéaire et Optimisation, Equipe de Systèmes dynamiques et Géométrie, Equipe de Statistique. 

The main objective of the internship is to recover the interaction graph between the dimensions of the process N , determined by the interaction functions. While some particular families
of Hawkes processes are well studied (most notably, linear processes), and benefit from a wide range of established simulation and inference techniques, much remains unexplored in the more general setting.

In order to recover the interaction graph, we focus on simulation-based techniques (namely Approximate Bayesian Computation). The core idea is to compare observed data from the target process with synthetic trajectories generated by simulations, using parameters sampled from a prior distribution, and to retain those parameters that produce observations sufficiently close to the observed data. An advantage of this family of methods is that they require very little prior
knowledge of the process (like approximating the transition density, or a closed-form likelihood function). A drawback is that they are inherently computationally costly and depend critically
on the choice of similarity measures for comparing different realisations of the stochastic process.

The role of the candidate is to participate in the development of ABC algorithms for non-linear Hawkes processes, with a special attention to the efficiency and reproducibility of the code and simulation methods. They are expected to be working autonomously and be able to
communicate the obtained results in academic context.

• Master 2 level student in applied mathematics, computer science or data science
• Background in point processes or Poisson processes is an asset
• Experience in Monte-Carlo methods or Bayesian inference is a plus
• Proficiency in R ; experience with Rcpp and parallel computing is a plus
• Good working command of English (oral and written), French is a plus