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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.

Statistical-Computational Trade-offs in Learning Multi-Index Models via Harmonic Analysis

Hugo Latourelle-Vigeant and Theodor Misiakiewicz

Preprint: arXiv:2602.09959

Summary: We study the problem of learning multi-index models (MIMs), where the label depends on the input only through an unknown low-dimensional projection. Exploiting the equivariance of this problem under the orthogonal group, we obtain a sharp harmonic-analytic characterization of the learning complexity for MIMs with spherically symmetric inputs, refining and generalizing previous Gaussian-specific analyses. We derive statistical and computational lower bounds in the Statistical Query and Low-Degree Polynomial frameworks that decompose across spherical harmonic subspaces. Guided by this structure, we construct spectral algorithms based on harmonic tensor unfolding that sequentially recover the latent directions and nearly achieve these bounds, enabling a range of trade-offs between sample and runtime complexity.

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

Hugo Latourelle-Vigeant and Elliot Paquette

Random Matrices: Theory and Applications

Summary: Developed a theory of the matrix Dyson equation for correlated linearizations, including existence-uniqueness, spectral support bounds, and stability properties. This framework is applied to derive a deterministic equivalent for the empirical test error in random features ridge regression in a proportional high-dimensional regime, conditioned on both training and test data. The results provide a rigorous understanding of generalization in random features models and establish a Gaussian equivalence principle for the test error.

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 an anisotropic global law for pseudo-resolvents with general correlation structures. The thesis develops existence-uniqueness, spectral support, and stability theory for correlated linear pencils, and applies this machinery to obtain an asymptotically exact deterministic expression for the test error of random features ridge regression. This work clarifies the role of implicit regularization in random features models and their connection with kernel methods, without assuming specific data distributions.

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.

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