A note on concentration of submodular functions
Jan Vondrak
TL;DR
This paper reviews concentration inequalities for submodular functions of independent variables, highlighting their dimension-free nature and implications for standard deviation bounds.
Contribution
It surveys entropy-based concentration bounds for submodular and fractionally subadditive functions, emphasizing their dimension-free properties and improved deviation estimates.
Findings
Dimension-free concentration inequalities for submodular functions
Standard deviation bounds of order √E[f]
Implications for high-dimensional probabilistic analysis
Abstract
We survey a few concentration inequalities for submodular and fractionally subadditive functions of independent random variables, implied by the entropy method for self-bounding functions. The power of these concentration bounds is that they are dimension-free, in particular implying standard deviation O(\sqrt{\E[f]}) rather than O(\sqrt{n}) which can be obtained for any 1-Lipschitz function of n variables.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Approximation and Integration · Complexity and Algorithms in Graphs · Computational Geometry and Mesh Generation