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Benoît Malézieux

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3 papers

2 author rows

ICML Conference 2023 Conference Paper

Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals

Clément Bonet
Benoît Malézieux
Alain Rakotomamonjy
Lucas Drumetz
Thomas Moreau 0001
Matthieu Kowalski
Nicolas Courty

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires the usage of Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices, and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this discrepancy to brain-age prediction from MEG data, and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications.

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NeurIPS Conference 2022 Conference Paper

Benchopt: Reproducible, efficient and collaborative optimization benchmarks

Thomas Moreau
Mathurin Massias
Alexandre Gramfort
Pierre Ablin
Pierre-Antoine Bannier
Benjamin Charlier
Mathieu Dagréou
Tom Dupre la Tour

Numerical validation is at the core of machine learning research as it allows us to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automatize, publish and reproduce optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard ML tasks: $\ell_2$-regularized logistic regression, Lasso and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details.

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ICLR Conference 2022 Conference Paper

Understanding approximate and unrolled dictionary learning for pattern recovery

Benoît Malézieux
Thomas Moreau 0001
Matthieu Kowalski

Dictionary learning consists of finding a sparse representation from noisy data and is a common way to encode data-driven prior knowledge on signals. Alternating minimization (AM) is standard for the underlying optimization, where gradient descent steps alternate with sparse coding procedures. The major drawback of this method is its prohibitive computational cost, making it unpractical on large real-world data sets. This work studies an approximate formulation of dictionary learning based on unrolling and compares it to alternating minimization to find the best trade-off between speed and precision. We analyze the asymptotic behavior and convergence rate of gradients estimates in both methods. We show that unrolling performs better on the support of the inner problem solution and during the first iterations. Finally, we apply unrolling on pattern learning in magnetoencephalography (MEG) with the help of a stochastic algorithm and compare the performance to a state-of-the-art method.

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