Maxime van Cutsem

Sylvain Sardy, Maxime van Cutsem, Xiaoyu Ma

The growing environmental footprint of artificial intelligence (AI), especially in terms of storage and computation, calls for more frugal and interpretable models. Sparse models (e.g., linear, neural networks) offer a promising solution by selecting only the most relevant features, reducing complexity, preventing over-fitting and enabling interpretation-marking a step towards truly intelligent AI. The concept of a right amount of sparsity (without too many false positive or too few true positive) is subjective. So we propose a new paradigm previously only observed and mathematically studied for compressed sensing (noiseless linear models): obtaining a phase transition in the probability of retrieving the relevant features. We show in practice how to obtain this phase transition for a class of sparse learners. Our approach is flexible and applicable to complex models ranging from linear to shallow and deep artificial neural networks while supporting various loss functions and sparsity-promoting penalties. It does not rely on cross-validation or on a validation set to select its single regularization parameter. For real-world data, it provides a good balance between predictive accuracy and feature sparsity. A Python package is available at https://github.com/VcMaxouuu/HarderLASSO containing all the simulations and ready-to-use models.

Maxime van Cutsem, Sylvain Sardy

We revisit Cox's proportional hazard models and LASSO in the aim of improving feature selection in survival analysis. Unlike traditional methods relying on cross-validation or BIC, the penalty parameter $λ$ is directly tuned for feature selection and is asymptotically pivotal thanks to taking the square root of Cox's partial likelihood. Substantially improving over both cross-validation LASSO and BIC subset selection, our approach has a phase transition on the probability of retrieving all and only the good features, like in compressed sensing. The method can be employed by linear models but also by artificial neural networks.