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Machine Learning

Statistical Analysis of Machine Learning Algorithms (SAM-lab)

The Project has been co-funded and co-implemented with Yerevan State University.

Principal Investigator: Prof. Arnak Dalalyan

University: ENSAE Paris, France

Research Group: Sona Hunanyan, Arshak Minasyan, Tigran Galstyan, Elen Vardanyan

Contributed researchers։ Henrik Sergoyan, Khachatur Khechoyan, Vahan Arsenyan

Duration: 2020-2024

Status: Complete

Project Importance

The current trend in Artificial Intelligence is to tackle most problems by statistical methods using Machine Learning algorithms. The progress needs to be backed by thorough mathematical analysis to understand the strengths and weaknesses of various methods and prepare solid ground for future innovations. Another trend of recent years is that the strongest students in mathematics and computer science are choosing to specialize in Machine Learning. Master’s programs in Machine Learning/Data Science/Artificial Intelligence are extremely popular all around the world. This is the case in Armenia as well, but the absence of a decent PhD program in this field forces best students to leave the country. One of the aims of this project is to create the possibility of getting a PhD in this field in Armenia.

Results and Achievements

The project focused on 3 main research areas:


  • Robust Estimation of High-Dimensional Parameters: Building upon recent advances in iterative filtering, the team demonstrated that a single estimation method could achieve several critical properties simultaneously: computational tractability, statistical optimality in the sub-Gaussian setting, equivariance under shifts and scaling, and a high breakdown point. A faster method, termediterative spectral dimension reduction, was also introduced, achieving a breakdown point of 0.5—the highest possible—at the expense of a slightly slower convergence rate.

  • Matching Feature Vectors in the Presence of Noise and Outliers: The team thoroughly analyzed and empirically evaluated multiple methods for feature matching, establishing their optimality in terms of detection accuracy and demonstrating it on both synthetic and real-world datasets.

  • Generative Adversarial Modeling (GANs): The research focused on exploring the creative potential of GANs. A rigorous mathematical proof was provided, showing that a GAN can achieve an optimal level of creativity if a smooth left inverse is enforced. Experimental results suggest that this characteristic is inherently encoded in the optimization techniques commonly used in GAN.


Key accomplishments over four years include:

  • 5 Publications: 3 in Q1 journals, 2 in Q4 journals

  • 2 Conference Proceedings: Presented at international AI research events.

  • 5 Courses Delivered: 2 credit-based courses and 3 non-formal lectures, held in Armenia.

  • Successful PhD Graduates: Tigran Galstyan and Arshak Minasyan, key team members, successfully completed their PhD programs during the project, probably becoming the first students known to have defended PhD theses in machine learning in Armenia. Arshak has been appointed Assistant Professor at École Centrale de Paris, one of France's top engineering schools.

  • Research Experience and Career Development: Sona Hunanyan returned to Armenia from Switzerland through this project and has since published two papers at top machine learning conferences, making her a competitive young researcher in Armenia.

  • PhD Program Acceptance: Two other team members, Elen Vardanyan and Vahan Arsenyan, gained their first research experience in machine learning during this project. Both were accepted into fully-funded PhD programs at the Institute Polytechnique de Paris.

  • Fostering the next generation of ML researchers: Team members supervised 5 interns from the American University of Armenia and Yerevan State University.

Courses