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Non-competitive VM – Parting Shots . Where do we go from here? . Life isn’t always progressive . Product purchase, technology/innovation adoption, political campaigns are reasonably approximated by progressive models.
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Non-competitive VM – Parting Shots Where do we go from here?
Life isn’t always progressive • Product purchase, technology/innovation adoption, political campaigns are reasonably approximated by progressive models. • However, subscription of services (ISP, mobility, apps) is often non-progressive: subscribers may switch in and out. How do you model and what do you optimize?
Spread isn’t the only thing that matters • (Expected) revenue, or better yet profit is what a business cares about. • Influence doesn’t always imply adoption. • What if we wanted to minimize the seeding expenses to achieve a given target spread? • What if we wanted to achieve a given target spread under a given seeding expense budget in the quickest possible time?
Other Perspectives on Influence Propagation • Minimizing Budget: Given a target expected spread, find the smallest seed set that achieves the target. • Minimizing Propagation Time: Given a target expected spread and a budget on #seeds, find the best seed set under budget that achieves the target in the least possible time.
Minimizing Seeds • Greedy-MinTss provides -approximation to the optimum, while suffering from a shortfall of from the target. • Better approx. unlikely to exist unless . • Formally proved for real-valued submodular set cover.
Minimizing Propagation Time • Unless , there does not exist a PTIME algorithm for MINTIME that guarantees (for any α ≥ 1): • a (α, γ)-approximation, such that |S| ≤ k, R = α・and ) ≥ γ ・ η where γ = (1 − 1/e + δ) OR • a (α, β)-approximation, such that |S| ≤ β・k, R =α・ and (S) ≥ η where β = (1 − δ) lnη, for any fixed δ > 0.
Minimizing Propagation Time • However, if we can tolerate a coverage (i.e., spread) shortfall of and a budget boost of , then Greedy achieves these objectives within the min. possible propagation time.
Summary • Spread, revenue, profit, adoption – hard to optimize on two levels. • In addition to n/w structure, influence probs matter and need to be learned properly from data. • Greedy + MC simulation + CELF++ -- guaranteed approx. but doesn’t scale. • Replacing simulation by SimPath/PMIA etc. dramatic speedup with little loss of accuracy on various data sets. • Credit distribution model allows to predict spread from data directly. • MINTSS, MINTIME – very hard problems in general. Potential for further research. • Non-progressive – some recent progress! • Competition under non-progressive models – largely unexplored territory.
