Tight Bounds on Low-Degree Spectral Concentration of Submodular and XOS Functions

@article{Feldman2015TightBO,
  title={Tight Bounds on Low-Degree Spectral Concentration of Submodular and XOS Functions},
  author={Vitaly Feldman and Jan Vondr{\'a}k},
  journal={2015 IEEE 56th Annual Symposium on Foundations of Computer Science},
  year={2015},
  pages={923-942}
}
  • Vitaly Feldman, Jan Vondrák
  • Published 2015
  • Mathematics, Computer Science
  • 2015 IEEE 56th Annual Symposium on Foundations of Computer Science
  • Submodular and fractionally subadditive (or equivalently XOS) functions play a fundamental role in combinatorial optimization, algorithmic game theory and machine learning. Motivated by learnability of these classes of functions from random examples, we consider the question of how well such functions can be approximated by low-degree polynomials in ℓ<sub>2</sub> norm over the uniform distribution. This question is equivalent to understanding the concentration of Fourier weight on low-degree… CONTINUE READING
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