**R. COUILLET**

**Titre de la thèse:**RMT4ML -- Random Matrix Methods for Machine Learning

**Résumé de la thèse:**The BigData challenge induces a need for classical machine learning algorithms to evolve towards large dimensional and more versatile learning engines. Recently, a new direction of research emerging from the field of random matrix theory (so far never used in this context) has opened a path into the understanding and improvement of several families of such techniques for large dimensional datasets (kernel spectral clustering, community detection on graphs, echo-state networks, etc.). The objective of the PhD is to extend those results to the even more fundamental machine learning tools that are support vector machines and semi-supervised learning methods. These challenging questions rely on technical aspects at the crossroads between random matrix theory and quadratic optimization, which are the main expertise of the co-advisors. It is expected that the output of the thesis will foster the new promising area of theoretical large dimensional machine learning.

### Jounals

• **X. Mai**, R. Couillet,“Consistent semi-supervised graph regularization for high dimensional data”, (under review) Journal of Machine Learning Research, 2019.

• **X. Mai**, R. Couillet, “A random matrix analysis and improvement of semi- supervised learning for large dimensional data”, Journal of Machine Learning Research, 2018.

### Conferences

• **X. Mai**, R. Couillet, “Revisiting and improving semi-supervised learning: a large dimensional approach”, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’19), Brighton, UK, 2019.

• **X. Mai**, Z.Liao, R. Couillet, “A large n,p analysis of logistic regression: asymptotic performance and new insights”, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’19), Brighton, UK, 2019.

• **X. Mai**, R. Couillet, “Semi-supervised spectral clustering”, Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 2018.

• R. Couillet, Z. Liao, **X. Mai**, “Classification asymptotics in the random matrix regime”, European Signal Processing Conference (EUSIPCO’18), Rome, Italy, 2018.

• **X. Mai**, R. Couillet, “The counterintuitive mechanism of graph-based semi-supervised learning in the big data regime”, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’17), New Orleans, USA, 2017.