Learning and Testing Submodular Functions Grigory Yaroslavtsev Columbia University October 26, 2012 With Sofya Raskhodnikova (SODA’13) + Work in progress.

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Presentation transcript:

Learning and Testing Submodular Functions Grigory Yaroslavtsev Columbia University October 26, 2012 With Sofya Raskhodnikova (SODA’13) + Work in progress with Rocco Servedio

Submodularity

Exact learning

Approximate learning

Goemans, Harvey, Iwata, Mirrokni Balcan, Harvey Gupta, Hardt, Roth, Ullman Cheraghchi, Klivans, Kothari, Lee Our result with Sofya 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) Value demand Other positive results: Learning valuation functions [Balcan, Constantin, Iwata, Wang, COLT’12] PMAC-learning (sketching) valuation functions [BDFKNR’12] PMAC learning Lipschitz submodular functions [BH’10] (concentration around average via Talagrand)

Discrete convexity

Monotone submodular Submodular

Discrete monotone submodularity

Representation by a formula

Discrete submodularity

Learning pB-formulas and k-DNF

Property testing

Testing by implicit learning

Previous work on testing submodularity

Thanks!