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Poland

PhD grants "Characterization of multivariate longitudinal profiles" (SSBCV)

Details

Deadline
Research Field
Formal sciences
Funding Type
Funding
Mobility Incoming
Career Stage
First Stage Researcher (R1) (Up to the point of PhD)

About

  • 36 months doctoral funding (October 2021 to September 2024)
  • Keywords

Statistics, MCMC, Medical imaging, Image processing, Multivariate analysis, Metropolis-Hastings

  • Profile and skills required

The candidate will have a strong mathematical background, with an interest in statistics linked to multivariate analysis, MCMC methods (eg Metropolis-Hastings), and/or an interest in Riemannian geometry, together with data analysis and coding skills.

 

  • Project description

 

Hypothesis – Multivariate, multimodal patient data can be used to create longitudinal profiles that will improve diagnosis precision and earliness.

Background – Brain pathologies are complex processes that have multiple effects on metabolism and on the structure and functioning of the brain. A major difficulty is that they can appear at very different ages, with different evolution patterns, and different evolution speed and symptoms. The evolutionary models that describe their evolution are consequently still largely perfectible. With the development of vectorial biological data such as metabolomics, elastography, tractography or PET imaging, it is possible to work with vector-valued longitudinal data to better characterize these pathologies.

Issue – Learning evolutionary models from longitudinal vector-valued data raise complex methodological issues. Besides variability of measures, one main difficulty is that the pattern and the speed of evolution can vary from one patient to another. Consequently, models based on individual values regression are mostly inadequate to model the disease evolution.

Objectives - In this thesis, we propose to develop a generic statistical framework for the definition and estimation of generative mixt effect models for vector-valued longitudinal data to better characterize the position, trajectory and speed of the pathologies evolution.

Methodology - To achieve these objectives, we will go into a specific mathematical domain : Riemannian geometry. In this domain, trajectories can be represented as parallel curves on high dimensional folded surfaces. In particular, we will work with a class of methods that make few hypothesis on the data and the pathology and for which a key part will consist in defining an appropriate metric on Riemannian surfaces. The developed approaches will be validated on simulated data first, and then on real metabolomic, ultrasonic and IRM data from the team.

  • References

- Durrleman S et al., (2013) Int. J. of Computer Vision, 1 :22-59 ;

 

- Schiratti JB et al., (2017) J. of Machine Learning Research, 18 :4840-4872 ;

- Cavalcanti Y et al., (2019) IEEE TMI, 38 :2231-2241 ;

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