Lassonet: A neural network with feature sparsity

Ismael Lemhadri, Feng Ruan, Louis Abraham, Robert Tibshirani

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


Much work has been done recently to make neural networks more interpretable, and one approach is to arrange for the network to use only a subset of the available features. In linear models, Lasso (or '1-regularized) regression assigns zero weights to the most irrelevant or redundant features, and is widely used in data science. However the Lasso only applies to linear models. Here we introduce LassoNet, a neural network framework with global feature selection. Our approach achieves feature sparsity by adding a skip (residual) layer and allowing a feature to participate in any hidden layer only if its skip-layer representative is active. Unlike other approaches to feature selection for neural nets, our method uses a modified objective function with constraints, and so integrates feature selection with the parameter learning directly. As a result, it delivers an entire regularization path of solutions with a range of feature sparsity. We apply LassoNet to a number of real-data problems and find that it significantly outperforms state-of-the-art methods for feature selection and regression. LassoNet uses projected proximal gradient descent, and generalizes directly to deep networks. It can be implemented by adding just a few lines of code to a standard neural network.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
StatePublished - 2021


  • Feature Selection
  • Neural Networks
  • Proximal Gradient Descent
  • Strong Hierarchy

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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