Learning and Testing Submodular Functions Grigory Yaroslavtsev Slides at

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Presentation transcript:

Learning and Testing Submodular Functions Grigory Yaroslavtsev Slides at CIS 625: Computational Learning Theory

Submodularity

Approximating everywhere

Approximate learning

Goemans, Harvey, Iwata, Mirrokni Balcan, Harvey Gupta, Hardt, Roth, Ullman Cheraghchi, Klivans, Kothari, Lee Raskhodnikova, Y. Learning TimePoly(|X|) Extra features Under arbitrary distribution Tolerant queries SQ- queries, Agnostic

Learning: Bigger picture XOS = Fractionally subadditive Subadditive Submodular Gross substitutes OXS [Badanidiyuru, Dobzinski, Fu, Kleinberg, Nisan, Roughgarden,SODA’12] Additive (linear) Coverage (valuations)

Discrete convexity

Monotone submodular Submodular

Discrete monotone submodularity

Representation by a formula

Discrete submodularity

Proof

Coverage by monotone lower bounds

Learning pB-formulas and k-DNF

Learning Fourier coefficients

Property testing

Testing by implicit learning

Previous work on testing submodularity

Directions

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