Job opportunities
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Type de contrat
Contexte
<p>The aim of this internship is to investigate the inference of graphs to describe the behavior of dynamical systems (e.g., time-series from climate database).</p>
<p><strong>Subject:</strong> State-space models (SSMs) are common tools in time-series analysis for inference and prediction in dynamical systems. SSMs are versatile probabilistic models that allow for Bayesian inference by describing a (generally Markovian) latent process. However, the parameters of that latent process are often unknown and must be estimated. In [1,2], we have proposed an innovative approach to perform the parameters inference as sparse graphs. The approach, based on an Expectation-Maximization mechanism and advanced non-smooth optimization tools, provides promising results, and benefits from sound convergence guarantees. However, it is limited to the class of linear Gaussian SSMs with first-order Markovian dependancies. In this internship, we plan to explore extensions of the existing models, to cope with more complex situations (e.g., polynomial models, higher-order Markovian latent processes, non-Gaussian noise). <br /><br /></p>
<p>[1] V. Elvira and E. Chouzenoux. Graphical Inference in Linear-Gaussian State-Space Models. IEEE Transactions on Signal Processing, vol. 70, pp. 4757-4771, Sep. 2022<br />[2] E. Chouzenoux and V. Elvira. Sparse Graphical Linear Dynamical Systems, Journal of Machine Learning Research, vol. 25, no. 223, pp. 1-53, 2024</p>
<p><strong>Subject:</strong> State-space models (SSMs) are common tools in time-series analysis for inference and prediction in dynamical systems. SSMs are versatile probabilistic models that allow for Bayesian inference by describing a (generally Markovian) latent process. However, the parameters of that latent process are often unknown and must be estimated. In [1,2], we have proposed an innovative approach to perform the parameters inference as sparse graphs. The approach, based on an Expectation-Maximization mechanism and advanced non-smooth optimization tools, provides promising results, and benefits from sound convergence guarantees. However, it is limited to the class of linear Gaussian SSMs with first-order Markovian dependancies. In this internship, we plan to explore extensions of the existing models, to cope with more complex situations (e.g., polynomial models, higher-order Markovian latent processes, non-Gaussian noise). <br /><br /></p>
<p>[1] V. Elvira and E. Chouzenoux. Graphical Inference in Linear-Gaussian State-Space Models. IEEE Transactions on Signal Processing, vol. 70, pp. 4757-4771, Sep. 2022<br />[2] E. Chouzenoux and V. Elvira. Sparse Graphical Linear Dynamical Systems, Journal of Machine Learning Research, vol. 25, no. 223, pp. 1-53, 2024</p>
Mission confié
<p><strong>Missions:</strong> The recruited student will first perform a bibliography study on graph dynamical models, and familarize with the existing Python codes of the team.Then, in a second step, the student will propose an extended version of the existing method, implement it, and study its performance on synthetic datasets.</p>
<p><strong>Environment:</strong> The intern will be supervised by Emilie Chouzenoux (Head of OPIS team, Inria Saclay) and Victor Elvira (Professor, School of Mathematics, Univ. Edinburgh, UK). The intern student will join the Inria Saclay team OPIS (https://opis-inria.eu/). He/she will be located in the Centre de la Vision Numérique, in CentraleSupélec campus, Saclay, France. He/she will enjoy an international and creative environment where research seminars and reading groups take place very often. Informatic material expenses will be covered within the limits of the scale in force.</p>
<p><strong>Organization:</strong> The proposed offer is dedicated to internship of Master 2 / Engineering students. The starting/end dates are flexible, with a minimum duration of 5 months.</p>
<p><strong>Environment:</strong> The intern will be supervised by Emilie Chouzenoux (Head of OPIS team, Inria Saclay) and Victor Elvira (Professor, School of Mathematics, Univ. Edinburgh, UK). The intern student will join the Inria Saclay team OPIS (https://opis-inria.eu/). He/she will be located in the Centre de la Vision Numérique, in CentraleSupélec campus, Saclay, France. He/she will enjoy an international and creative environment where research seminars and reading groups take place very often. Informatic material expenses will be covered within the limits of the scale in force.</p>
<p><strong>Organization:</strong> The proposed offer is dedicated to internship of Master 2 / Engineering students. The starting/end dates are flexible, with a minimum duration of 5 months.</p>
Principales activités
<p><strong>Main activities</strong> :</p>
<p>Programming in Python or Matlab environment</p>
<p>Bibliographical study</p>
<p>Optimization problem formulation and resolution</p>
<p>Convergence Analysis</p>
<p>Scientific meetings</p>
<p>Writing of scientific reports</p>
<p>Programming in Python or Matlab environment</p>
<p>Bibliographical study</p>
<p>Optimization problem formulation and resolution</p>
<p>Convergence Analysis</p>
<p>Scientific meetings</p>
<p>Writing of scientific reports</p>
Compétences
<p><strong>Languages</strong> : The candidate must be fluent in english and/or french languages.</p>
Référence
2025-09669
Domaine d'activité