PhD Position F/M [Campagne CORDI-S] - Computational Algebra and Statistical Learning Theory

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Type de contrat : CDD

Niveau de diplôme exigé : Bac + 5 ou équivalent

Fonction : Doctorant

Contexte et atouts du poste

The selected candidate will do her/his research at the OURAGAN team which is a joint team
of Inria Paris and IMJ-PRG Sorbonne Université. She/he will be located at Sorbonne University and she/he will work with Elias Tsigaridas. 

Mission confiée

Singular Learning Theory (SLT) is a framework in statistical learning theory that focuses on analyzing and understanding (parametric)probability models, such as mixture models, hidden Markov models, and neural networks,
in the case where the parameter space has singularities. It expands traditional learning models that function under the assumption that the learning process is smoothly parametrizable. The goal of SLT is to improve the accuracy of the prediction of statistical learning.

To address the presense of singularities in the parameter space Watanabe introduced an approach based on the resolution of singularities; based on the famous work of Hironaka. Nevertheless, we still lack a complete and efficient approach for SLT based on this approach.

Principales activités

We are looking for a PhD student to work on algorithms in Singular Learning Theory in the case where the we can
define (or approximate with guarantees) the functions that define the singularities of the parametric spaces
by polynomials. The emphasis will be on efficient algorithms for the resolution of singulatities in small dimension, e.g., 2 or 3. We will also investigate how recent techniques for sampling from (convex) bodies, relying continuous random walk, can help in this direction.

Compétences

The candidate is expected to hold a research master (or equivalent qualification) in mathematics, applied mathematics or computer science.

Avantages

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking
  • Flexible organization of working hours (after 12 months of employment) 
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training

Rémunération

Monthly gross salary : 2100 € during the first and second years. 2180 € the last year.