SHORT BIO

Since November 2022, I am a postdoctoral researcher at Inria Saclay in the Mind team and under the supervision of Alexandre Gramfort.

Previously, I did my PhD in the SONDRA laboratory at CentraleSupélec, University of Paris-Saclay.
My supervisors were Jean-Philippe Ovarlez, Guillaume Ginolhac, Chengfang Ren, Arnaud Breloy and Florent Bouchard.

I previously graduated from University of Technology of Compiègne with a major in Computer Science and a minor in Mathematical modeling.

My research focuses on the estimation of parameters, lying on Riemannian manifolds, of robust and high-dimensional statistical models. I also study the optimal performance achievable by these algorithms using intrinsic Cramér-Rao bounds. I apply these methods as well as Riemannian clustering/classification algorithms on remote sensing images (e.g. SAR and hyperspectral data) and EEG/MEG data.

My curriculum vitae - résumé - is available here: short version, long version (updated in November 2023).


RESEARCH INTERESTS

• Optimization on Riemannian manifolds
• Statistical signal processing
• Statistical estimation, bounds
• Machine learning
• Clustering, classification
• ...

PhD THESIS

Riemannian geometry for statistical estimation and learning: application to remote sensing
Supervisors: J-P. Ovarlez, G. Ginolhac, C. Ren, A. Breloy, F. Bouchard
Jury: A. Giremus, N. Le Bihan, C. Richard, N. Boumal, A. Gramfort
[PDF][slides]


PUBLICATIONS (Google scholar)

© 2023 IEEE.  Personal use of this material is permitted.  Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Book chapter

The Fisher-Rao geometry of CES distributions
F. Bouchard, A. Breloy, A. Collas, A. Renaux, G. Ginolhac
2023 - Springer
[arXiv]

Journals

Harmonizing and aligning M/EEG datasets with covariance-based techniques to enhance predictive regression modeling
A. Mellot, A. Collas, P. L.C. Rodrigues, D. A. Engemann, A. Gramfort
2023 - Imaging Neuroscience MIT Press
[bioRxiv][DOI]

Parametric information geometry with the package Geomstats
A. Le Brigant, J. Deschamps, A. Collas, N. Miolane
2023 - ACM Transactions on Mathematical Software
[arXiv][slides][Github]

Riemannian optimization for non-centered mixture of scaled Gaussian distributions
A. Collas, A. Breloy, C. Ren, G. Ginolhac, J.-P. Ovarlez
2023 - IEEE Transactions on Signal Processing
[arXiv][Github]

Probabilistic PCA from Heteroscedastic Signals: Geometric Framework and Application to Clustering
A. Collas, F. Bouchard, A. Breloy, G. Ginolhac, C. Ren, J.-P. Ovarlez
2021 - IEEE Transactions on Signal Processing
[PDF][DOI]

Robust Low-Rank Change Detection for Multivariate SAR Image Time Series
A. Mian, A. Collas, A. Breloy, G. Ginolhac, J.-P. Ovarlez
2020 - IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
[PDF][DOI]

Conferences

Entropic Wasserstein Component Analysis
A. Collas, T. Vayer, R. Flamary, A. Breloy
2023 - IEEE Machine Learning for Signal Processing (MLSP) - Rome, Italy
[arXiv][slides][poster][Github][POT]

Apprentissage robuste de distance par géométrie riemannienne
A. Collas, A. Breloy, G. Ginolhac, C. Ren, J.-P. Ovarlez
2022 - XXVIIIème Colloque Francophone de Traitement du Signal et des Images GRETSI - Nancy, France
[PDF][slides]

Robust Geometric Metric Learning
A. Collas, A. Breloy, G. Ginolhac, C. Ren, J.-P. Ovarlez
2022 - 30th European Signal Processing Conference (EUSIPCO) - Belgrade, Serbia
Best student paper award
[arXiv][Github][slides][poster]

On The Use of Geodesic Triangles Between Gaussian Distributions for Classification Problems
A. Collas, F. Bouchard, G. Ginolhac, A. Breloy, C. Ren, J.-P. Ovarlez
2022 - IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) - Singapore
[PDF][DOI][slides][poster]

A Tyler-Type Estimator of Location and Scatter Leveraging Riemannian Optimization
A. Collas, F. Bouchard, A. Breloy, C. Ren, G. Ginolhac, J.-P. Ovarlez
2021 - IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) - Toronto, Canada
[PDF][DOI][slides][poster]


TALKS

Parametric information geometry with the package Geomstats
2023 - Mind team - Palaiseau, France
[slides]

Riemannian geometry for statistical estimation and learning: applications to remote sensing and M/EEG
2023 - S3 Seminar - L2S, CentraleSupélec - Gif-sur-Yvette, France
[slides]

Optimal transport and dimension reduction: Entropic Wasserstein Component Analysis
2023 - ELLIS Unconference - HEC - Jouy-en-Josas, France
[slides]

Entropic Wasserstein Component Analysis
2023 - SIMPAS team - Centre de Mathématiques Appliquées de l'Ecole Polytechnique - Palaiseau, France
[slides]

A (very) short presentation of Riemannian optimization using Pymanopt
2023 - Mind team - Palaiseau, France
[slides]

Estimation and classification of location and covariance matrix using Riemannian geometry: application to remote sensing
2023 - Laboratoire Jean Kuntzmann seminar - Grenoble, France
[slides]

On The Use of Geodesic Triangles Between Gaussian Distributions for Classification Problems
2022 - 5th Sondra Workshop - Avignon, France
[slides]

Optimization and statistical learning using Riemannian geometry: application to remote sensing
2022 - DSO National Laboratories - Singapore
[slides]

Optimization and statistical learning using Riemannian geometry and application to remote sensing
2022 - Inria Saclay, Parietal team - Palaiseau, France
[slides]

Robust Clustering for Satellite Images Time-Series
2022 - ONERA, the French Aerospace Lab - Palaiseau, France
[slides]

Probabilistic PCA from Heteroscedastic Signals: Geometric Framework and Application to Clustering
2021 - Statistical Learning for Signal and Image Processing (SLSIP) Workshop. A German-Finnish-French Workshop - Rüdesheim am Rhein, Germany
[slides][website]

Riemannian Geometry to Robust Estimation Covariance matrices with Application to Machine Learning
2021 - LISTIC laboratory - Annecy, France
[slides]


TEACHING

Teaching assistant in signal processing. Graduate studies in Master E3A at Paris-Saclay University in 2020 - 2021. Topics covered: Fourier analysis, linear regression, online estimation, stochastic process, statistical estimation ...