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Ph.D. Statistics and Data Science

Yale University

M.Sc. Mathematics and Statistics

McGill University

• Master's Thesis: The matrix Dyson equation for machine learning: Correlated linearizations and the test error in random features regression

B.Sc. Joint Honours Mathematics and Computer Science

McGill University

• Graduated with First Class Joint Honours

Data Science Intern

CDPQ

Internship in data science at CDPQ during the summer of 2024. Part of the NLP team.

The matrix Dyson equation for machine learning: Correlated linearizations and the test error in random features regression

Hugo Latourelle-Vigeant

McGill University

Summary: Extended the matrix Dyson equation framework to derive an anisotropic global law for pseudo-resolvents with general correlation structures. Applied this framework to provide an exact deterministic expression for the empirical test error in random features ridge regression, addressing aspects such as existence-uniqueness, spectral support bounds, and stability properties.

Dyson Equation for Correlated Linearizations and Test Error of Random Features Regression

Hugo Latourelle-Vigeant and Elliot Paquette

Preprint: arXiv:2312.09194v2

Summary: Developed theory for the matrix Dyson equation for correlated linearizations, including existence-uniqueness, spectral support bounds, and stability properties, and applied this to derive a deterministic equivalent for the test error in random features ridge regression.

Matrix Dyson Equation for Correlated Linearizations

The many facets of random matrix theory Workshop at Canadian Mathematical Society Winter Meeting

Summary: Extended the matrix Dyson equation framework for linearizations to derive an anisotropic global law for pseudo-resolvents with general correlation structures, and applied this to derive an exact asymptotic expression for the validation error of random features ridge regression.

Matrix Dyson Equation for Linearizations

Seminar in random matrix theory, machine learning and optimization at McGill University

Summary: Extended the matrix Dyson equation framework to analyze rational expressions in random matrices using a linearization trick, and applied this to study the test error of a random feature model.

GD and Large Linear Regression: Concentration and Asymptotics for a Spiked Model

4th Undergraduate Student Research Conference at McGill University

Summary: Demonstrated that the halting time in large-scale spiked random least squares problems trained with gradient descent exhibits a universality property, independent of input probability distribution, and provided explicit asymptotic results.

Calculus 2 - MATH 141

Teaching Assistant

Convex Optimization - Math 463/563

Graduate Course Assistant

Calculus 2 - MATH 141

Teaching Assistant

Convex Optimization - Math 463/563

Graduate Course Assistant

Numerical Optimization - Math 560

Graduate Course Assistant

Calculus 2 - MATH 141

Teaching Assistant

Numerical Optimization - Math 560

Undergraduate Course Assistant

First-class honours in Mathematics and Computer Science

McGill University

Undergraduate student research award

NSERC

The NSERC Undergraduate Student Research Award is a competitive award granted by the Natural Sciences and Engineering Research Council of Canada (NSERC) on the basis of academic excellence and research potential to support a full-time undergraduate summer research project.

Major entrance scholarship in science

Hydro-Québec

Montreal RMT-ML-OPT seminar at McGill University

OPT Workshop on Optimization for Machine Learning

2nd Workshop on High-dimensional Learning Dynamics (HiLD): The Emergence of Structure and Reasoning

High-dimensional Learning Dynamics Workshop

OPT Workshop on Optimization for Machine Learning

OPT Workshop on Optimization for Machine Learning