Subspace fitting meets regression: The effects of supervision and orthonormality constraints on double descent of generalization errors

Yehuda Dar, Paul Mayer, Lorenzo Luzi, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with varying levels of supervision in the training data (i.e., the proportion of input-output examples of the desired low-dimensional mapping) and orthonormality of the vectors defining the learned operator. This flexible family of problems connects standard, unsupervised subspace fitting that enforces strict orthonormality with a corresponding regression task that is fully supervised and does not constrain the linear operator structure. This class of problems is defined over a supervision-orthonormality plane, where each coordinate induces a problem instance with a unique pair of supervision level and softness of orthonormality constraints. We explore this plane and show that the generalization errors of the corresponding subspace fitting problems follow double descent trends as the settings become more supervised and less orthonormally constrained.

Original languageAmerican English
Title of host publication37th International Conference on Machine Learning, ICML 2020
EditorsHal Daume, Aarti Singh
Pages2344-2353
Number of pages10
ISBN (Electronic)9781713821120
StatePublished - 1 Jan 2020
Externally publishedYes
Event37th International Conference on Machine Learning, ICML 2020 - Virtual, Online
Duration: 13 Jul 202018 Jul 2020

Publication series

Name37th International Conference on Machine Learning, ICML 2020
VolumePartF168147-4

Conference

Conference37th International Conference on Machine Learning, ICML 2020
CityVirtual, Online
Period13/07/2018/07/20

All Science Journal Classification (ASJC) codes

  • Software
  • Human-Computer Interaction
  • Computational Theory and Mathematics

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