# A05 – Combining non parametric statistical and probabilistic approaches for inference on cloud-of-points data

## Objectives

This project combines non-parametric statistical and probabilistic approaches for inference on cloud-of-points data. Such data sets can be modeled as point processes, which can be embedded into Hilbert spaces using appropriate reproducing kernels. The project will investigate convergence rates for the associated non-parametric estimators and will extend available results to probabilistic point process models with interaction, such as Gibbs fields and point processes over path spaces, e.g. "clouds of trajectories".

The intended research programme within this project follows first two major directions:

- Analyze the convergence rate of Reproducing Kernel Hilbert Space methods over a generic metric space and identify the role of key quantities (metric entropy, distribution characteristics of covariate X such as probabilities of small balls)
- Link to point process theory: focus on point processes with generating distributions of Gibbsian type and construct kernels taking into account specific properties. Example: One considers an unknown but fixed Gibbs interaction potential with random activity (corresponding to the reference density of points in the cloud)
- The developed methods will be tested on gaze fixation data (collaboration with Project B05) for discrimination tasks (discriminate type of image being looked at, or image familiarity to participant, from gaze fixation data)

Suitable candidates for the postdoctoral research position are expected to have successfully completed PhD in Probability theory or in Statistics and must have solid knowledge in Machine Learning and/or in Gibbs field Theory.