Material Detail

Structured sparsity-inducing norms through submodular functions

Structured sparsity-inducing norms through submodular functions

This video was recorded at 24th Annual Conference on Neural Information Processing Systems (NIPS), Vancouver 2010. Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization problem by replacing the cardinality function by its convex envelope (tightest convex lower bound), in this case the L1-norm. In this paper, we investigate more general set-functions than the cardinality, that may incorporate prior knowledge or structural constraints which are common in many applications: namely, we show that for nondecreasing submodular set-functions, the corresponding convex envelope can be obtained from its Lovasz extension, a common tool in submodular analysis. This defines a family of polyhedral norms, for which we provide generic algorithmic tools (subgradients and proximal operators) and theoretical results (conditions for support recovery or high-dimensional inference). By selecting specific submodular functions, we can give a new interpretation to known norms, such as those based on rank-statistics or grouped norms with potentially overlapping groups; we also define new norms, in particular ones that can be used as non-factorial priors for supervised learning.

Quality

  • User Rating
  • Comments
  • Learning Exercises
  • Bookmark Collections
  • Course ePortfolios
  • Accessibility Info

More about this material

Browse...

Disciplines with similar materials as Structured sparsity-inducing norms through submodular functions

Comments

Log in to participate in the discussions or sign up if you are not already a MERLOT member.