SDM 2019 Keynote

What Can Networks Do for Campaigns?
Laks V.S. Lakshmanan

Social & Information Networks
SDM, May 2019, Calgary, Canada.

Information Propagation
People are connected and perform actions
nice
read
indeed!
09:3009:00
comment, link,
rate, like,
retweet, post a
message, photo,
or video, etc.
friends,
fans,
followers,
etc. SDM, May 2019, Calgary, Canada.

Outline
•  Some real-life applications
•  Classic Influence Maximization
•  Awareness vs Adoption
•  Competition “revisited”
•  [Incentivized] Social Advertising
•  Social Welfare
•  Summary & Open Challenges

Real-life Applications of Influence
Analysis
•  Viral Marketing
•  adoption of prescription drugs
•  regulatory mechanism for yeast cell cycle
•  voter turnout influence in 2010 US congressional elections
•  influence maximization for social good (HEALER)
•  Gang violence control by Chicago PD using profit
maximization!
•  …

Viral Marketing of Drug
Prescriptions

Propagation of Drug Prescriptions
•  nodes = physicians; links = ties.
•  Question: does contagion work through the network?
•  answer: affirmative.
•  volume of usage (prescription of drug) by peer controls
contagion more than whether peer prescribed drug.
•  genuine social contagion found to be at play, even after
controlling for mass media marketing efforts, and global
network wide changes.
•  targeting sociometric opinion leaders definitely beneficial.
[R. Iyengar, C. Van den Bulte, and T.W. Valente. Opinion Leadership and Social Contagion in New  
Product Diffusion. Marketing Science, 30(2):195–212, 2011.]

Analysis workflow for Saccharomyces cerevisiae.
IM and Yeast Cell Cycle Regulation
[Gibbs DL, Schmulevich I (2017). Solving the inﬂuence maximization problem reveals regulatory
organization of the yeast cell cycle. PLOS Compt.Biol 13(6). e1005591. https://doi.org/10.1371/journal.pcbi.
1005591].

Topology of influential nodes.
[Gibbs DL, Shmulevich I (2017) Solving the inﬂuence maximization problem reveals regulatory organization of the yeast cell cycle.
PLOS Computational Biology 13(6): e1005591. https://doi.org/10.1371/journal.pcbi.1005591]
http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005591
IM and Yeast Cell Cycle Regulation

Yeast Cell Cycle Study Conclusions
•  IM contributes to understanding of yeast cell
cycles.
•  Can we find minimum sets of biological
entities that have the greatest influence in the
network context?
•  they in turn have greatest control on network
è understand link between network
dynamics and disease.

IM for Social Good – The Healer
homeless  
youth
Facebook
application
homeless  
youth
. 
. 
.
DIME
solver
shelter  
official
action
recommendation
feedback
[A. Yadav, H. Chan, A. Jiang, H. Xu, E. Rice, and M. Tambe. Using Social Networks to Aid Homeless Shelters:
Dynamic Influence Maximization Under Uncertainty. Proc. Int. Conf. on Autonomous Agents and Multiagent
Systems (AAMAS), 2016.]  
[A. Yadav, B. Wilder, E. Rice, R. Petering J. Craddock, A.Y. Maxwell, M. Hemler, L.O. Vera, M. Tambe, and D.
Woo. Bridging the Gap Between Theory and Practice in Influence Maximization: Raising Awareness about HIV
among Homeless Youth. IJCAI 2018.]
HEALER PROJECT: http://teamcore.usc.edu/people/amulya/healer/index.html

Classic Influence Maximization

Propagation/Diffusion Models
•  How does influence/information travel?
•  Deterministic versus stochastic models (e.g.,
independent cascade, linear threshold, …)
•  Discrete time versus continuous time models.
•  Phenomena captured: infection, product
adoption, information, opinion, rumor, etc.
[W. Chen, L., and C. Castillo. Information and Influence Propagation in Social Networks. Morgan-Claypool
2013].

Some Basics
•  initial focus on single (product/infection/
rumor) campaign.
inactive active

Independent cascade model
0.1
0.02
0.
3
0.
1
0.
3
0.
3
0.7
0.1
[Kempe et al. KDD 2003].
•  Each edge has
inﬂuence probability .
•  Seeds selected activate
at time
•  At each , each active
node gets one shot at
activating its inactive
neighbor ; succeeds w.p.
and fails w.p.
•  Once active, stay active.
(u,v)
puv
t = 0.
t > 0
u
v
puv (1− puv ).
e.g., infection propagation. SDM, May 2019, Calgary, Canada.

For all discrete time models
•  Let be a set of nodes activated at time 0.
– initial adaptors, “patients zero”, …
•  = expected number of nodes activated
under model M when diffusion saturates. (spread)
•  Key IM problem: choose S to maximize
•  Model parameters: edge weights/probabilities.
•  Problem parameter: budget k.
S
M (S)
M (S)

Influence Maximization
•  Core optimization problem in IM: Given a
diffusion model M, a network G = (V,E),
model parameters, and problem parameters
(budget). Find a seed set under budget
that maximizes
(expected) spread.
S ⇢ V
M (S)

Complexity of IM
•  Theorem: The IM problem is NP-hard for
several major diffusion models under both
discrete time and continuous time.
.

Complexity of Spread Computation
•  Theorem: It is #P-hard to compute the
expected spread of a node set under both IC
and LT models.

Properties of Spread Function
(resp., ) is
monotone: and
submodular:
S ✓ S0
=) (S)  (S0
).
(S) (S, T)
S, S0
⇢ V =)
(S [ S0
) + (S S0
)  (S) + (S0
).
S ⇢ S0
⇢ V, x 2 V S0
=)
(x|S0
)  (x|s), where
(x|S) := (S [ {x}) (S).
⌘
marginal gain.

Approximation of Submodular
Function Maximization
•  Theorem: Let be a monotone
submodular function, with Let
and resp. be the greedy and optimal solutions.
Then
f : 2V
! R 0
f(;) = 0. SGrd
S⇤
f(SGrd
) (1
1
e
)f(S⇤
).
[Nemhauser et al. An analysis of the approximations for maximizing submodular
set functions. Math. Prog., 14:265–294, 1978.]

Approximation of Submodular
Function Maximization
Theorem: Let be a monotone
submodular function, with Let and
resp. be the greedy and optimal solutions. Then
•  Theorem: The spread function is monotone
and submodular under various major diffusion
models.
(.)
[D. Kempe, J. Kleinberg, and E. Tardos. On maximizing the spread of inﬂuence through a  
network. KDD 2003.]

Baseline Approximation Algorithm
Monte Carlo simulations for estimating
expected spread.
Lazy Forward optimization to save useless
updates.
Greedy still extremely slow on large networks.
[J. Leskovec, A. Krause, C. Guestarin, C. Faloutsos, J. VanBriesen, and  
N. Glance. Cost-effective outbreak detection in networks. KDD, pp. 420–429, 2007].
[D. Kempe, J. Kleinberg, and E. Tardos. Maximizing the spread  
of inﬂuence through a social network. KDD 2003].

Reverse Influence Sampling
•  A series of algorithms that guarantee a
-approximation to the optimal
expected spread.
•  Key : use random reverse reachable sets
(rr-sets) to gauge quality of (candidate) seeds.
(1
1
e
✏)
<latexit sha1_base64="AW/ZWNJ71ORm2nTuWljbif+hLkI=">AAACAXicbVBNS8NAEN34WetX1IvgZbEI9dCSVEGPBS8eK9gPaErZbCft0s0m7G6EEuLFv+LFgyJe/Rfe/Ddu2xy09cHA470ZZub5MWdKO863tbK6tr6xWdgqbu/s7u3bB4ctFSWSQpNGPJIdnyjgTEBTM82hE0sgoc+h7Y9vpn77AaRikbjXkxh6IRkKFjBKtJH69nHZrXiBJDR1sxSyigexYjwS53275FSdGfAycXNSQjkaffvLG0Q0CUFoyolSXdeJdS8lUjPKISt6iYKY0DEZQtdQQUJQvXT2QYbPjDLAQSRNCY1n6u+JlIRKTULfdIZEj9SiNxX/87qJDq57KRNxokHQ+aIg4VhHeBoHHjAJVPOJIYRKZm7FdERMHtqEVjQhuIsvL5NWrepeVGt3l6V6PY+jgE7QKSojF12hOrpFDdREFD2iZ/SK3qwn68V6tz7mrStWPnOE/sD6/AGGeJZN</latexit>
[C. Borgs, M. Brautbar, J. Chayes, and Maximizing Social Influence in Nearly Optimal Time. SODA 2014]

Reverse Reachable Sets (RR-Sets)
A

B

C
E

D

0.4

0.3

0.6

0.5

0.2

0.3
0.4

•  rr-set = sample subgraph of G.
•  example of rr-set generation under IC model.

start from a
random node
A

B

C
E

D

0.4

0.3

0.6

0.5

0.2

0.3
0.4

RR-‐set
=
{A}


start from a
random node
A

B

C
E

D

0.4

0.3

0.6

0.5

0.2

0.3
0.4

sample its  
incoming edges
RR-‐set
=
{A}


start from a
random node
A

B

C
E

D

0.4

0.3

0.6

0.5

0.2

0.3
0.4

sample its  
incoming edges
RR-‐set
=
{A}

add the sampled
neighbors

start from a
random node
A

B

C
E

D

0.4

0.3

0.6

0.5

0.2

0.3
0.4

sample its  
incoming edges
RR-‐set
=
{A,
C}

add the sampled
neighbors

start from a
random node
A

B

C
E

D

0.4

0.3

0.6

0.5

0.2

0.3
0.4

sample its/their  
incoming edges
RR-‐set
=
{A,
C}

add the sampled
neighbors

start from a
random node
A

B

C
E

D

0.4

0.3

0.6

0.5

0.2

0.3
0.4

incoming edges
RR-‐set
=
{A,
C,
B,
E}

add the sampled
neighbors

•  An RR-set is a subgraph sample of 𝐺
•  Generation of RR-sets under the IC model:
start from a
random node
A

B

C
E

D

0.4

0.3

0.6

0.5

0.2

0.3
0.4

incoming edges
RR-‐set
=
{A,
C,
B,
E}

add the sampled
neighbors
•  Intuition:
–  An rr-set is a sample set of nodes that can
influence node A

Influence Estimation with RR-Sets
•  Theorem: Pr[S overlaps a random rr-set] =
1/n * expected spread of S.
•  Family of approx. algorithms: TIM, IMM, Stop-
and-Stare.
[Tang et al., “Influence Maximization: Near-Optimal Time Complexity Meets Practical Efficiency”, SIGMOD 2014]
[Tang et al., “Influence Maximization in Near-Linear Time: A Martingale Approach”, SIGMOD 2015]
[Chen et al. An issue in the Martingale Analysis of the Influence Maximization Algorithm IMM. arXiv 2018].
[Nguyen et al., “Stop-and-Stare: Optimal Sampling Algorithms for Viral Marketing in Billion-scale Networks”,
SIGMOD 2016] à arXiv
[K. Huang, S. Wang, G. Bevilacqua, X. Xiao, and L. Revisiting the Stop-and-Stare Algorithms for Influence
Maximization, PVLDB 2017]

Is there anything more to
campaigns?

Awareness vs Adoption

Awareness vs. Adoption
•  Influenced è Adopt?
•  Classical models:
– Assume influenced è adopt.
– Profit captured by proxy: expected
spread!
•  Need models and algorithms for VM
taking these distinctions into account.
[S. Bhagat, A. Goyal, and L. Maximizing product adoption in social networks. WSDM 2012]

Influence ⇏ Adoption
•  Observation: Only a subset of
influenced users actually adopt the
marketed product
Inﬂuenced Adopt
q  Awareness/information spreads in an
epidemic-like manner while adoption
depends on factors such as product quality
and price
[S. Kalish. A new product adoption model with price, advertising, and uncertainty.  
Management Science, 31(12), 1985].

LT-C – LT Model with Colors
•  Model Parameters
–  A is the set of active friends
–  fv(A) is the activation function
–  ru,i is the (predicted) rating for product i given by user u
–  αv is the probability of user v adopting the product
–  βv is the probability of user v promoting the product
Inactive
Tattle
Adopt
Active
Inhibit
Promote
fv(A)
1 fv(A)
↵v
1 ↵v
1 v
v
User
v
Active
Friends
fv(A) =
P
u2A wu,v(ru,i rmin)
rmax rmin

Maximizing Product Adoption
•  Problem: Given a social network and product actions,
find k users, targeting whom the expected number of
adopters is maximized.
•  Problem is NP-hard.
•  Spread function is monotone and submodular è
-approximation algorithm.
•  Separation of awareness from adoption improves
accuracy of prediction of adoption on real datasets.
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Competition “Revisited”

Previously in Competitive IM
•  Mainly follower’s perspective: given
state (say of seed selection) of previous
companies (agents/players):
–  what’s the best strategy for the “follower” to maximize its
spread in the face of the competition?
–  What’s the best strategy for the follower to maximize its
blocked influence against opponent?
•  Most competitive IM algorithms not
scalable or assume unfettered access to
the n/w for all players.

But …
•  Campaign runners don’t necessarily have unfettered
access to the network!
•  There is an owner of the network.
•  Campaigns need owner’s permission.
•  May need to pay the owner.

A New Business Model – Introducing
…
Network owner
Provides VM service.
How should the host select/allocate seeds?
I need 100 seeds
I need 250 seeds
Competition starts after host
selects/allocates seeds.
[W. Lu, F. Bonchi, A. Goyal, and L. The bang for the buck: … host perspective. KDD 2013].

Business Model (contd.)
• 


Why fairness?
Possible scenario:
Fitbit Versa
30 seeds
Spread 240
Garmin Forerunner 935
50 seeds
Spread 1000
For comparable products, if the b4b is substantially different,
dissatisfied company(ies) may take their VM business elsewhere!

What should we optimize?
•  Obvious candidate:
•  Proposition:
•  è allocations differ only in degree of fairness, gauged
using bang for buck (b4b) :=
•  Theorem: Fair Seed Allocation using min-max fairness
is NP-hard.
•  Needy Greedy Algorithm for fair seed allocation.
all(S) :=
X
i
i
(S), where S = (S1, . . . , SK).
<latexit sha1_base64="jOCptERYpjnHMg9vqZu/6YECpmY=">AAACSXicbZDNSxtBGMZn40c1VRv12MtLQyGChN1YaCkVhF6EXpQ0KmTTdXbybjI4s7PMzFrDsv9eL9689X/oxUOL9NRJsogffWDg4fm9LzPzxJngxvr+T6+2sLi0/GJltf5ybX3jVWNz68SoXDPsMSWUPoupQcFT7FluBZ5lGqmMBZ7GF5+n/PQSteEq/WonGQ4kHaU84YxaF0WN89DwkaRRQYUoW0UYJ9Atd+DjPoQmlxGHOf/G79kuhDJWVwV8H6NGKKECsA+tbhQ4LIbKml3oRl922hA1mn7bnwmem6AyTVLpKGrchEPFcompZYIa0w/8zA4Kqi1nAst6mBvMKLugI+w7m1KJZlDMmijhrUuGkCjtTmphlj7cKKg0ZiJjNympHZunbBr+j/Vzm3wYFDzNcospm1+U5AKsgmmtMOQamRUTZyjT3L0V2Jhqyqwrv+5KCJ5++bk56bSDvXbn+F3z4FNVxwp5Td6QFgnIe3JADskR6RFGfpBf5Df54117t96d93c+WvOqnW3ySLWFf881ryE=</latexit>
all(S) = LT (
[
i
Si).
<latexit sha1_base64="RXRDzikcM5dua+W26JWF4I1T/UM=">AAACHnicbVDLSsNAFJ3UV62vqEs3g0VoNyGpii4UCm5cuKj0JTQhTKaTdujkwcxEKCFf4sZfceNCEcGV/o3TNoK2HrhwOOde7r3HixkV0jS/tMLS8srqWnG9tLG5tb2j7+51RJRwTNo4YhG/85AgjIakLalk5C7mBAUeI11vdDXxu/eECxqFLTmOiROgQUh9ipFUkquf2oIOAuSmiLGsktqeD5tZFV7CH/2mlVVsjw5wErsUNl1aNSB09bJpmFPARWLlpAxyNFz9w+5HOAlIKDFDQvQsM5ZOirikmJGsZCeCxAiP0ID0FA1RQISTTt/L4JFS+tCPuKpQwqn6eyJFgRDjwFOdAZJDMe9NxP+8XiL9cyelYZxIEuLZIj9hUEZwkhXsU06wZGNFEOZU3QrxEHGEpUq0pEKw5l9eJJ2aYR0btduTcv0ij6MIDsAhqAALnIE6uAYN0AYYPIAn8AJetUftWXvT3metBS2f2Qd/oH1+A/k3oRE=</latexit>
i
(S)
bi
.
<latexit sha1_base64="QNo2yhMtfzyvCaFoSK0xiIoytb8=">AAACCHicbVDLSsNAFJ3UV62vqEsXDhahbkJSBV24KLhxWdE+oIlhMp20Q2eSMDMRSsjSjb/ixoUibv0Ed/6N0zYLbT1w4XDOvdx7T5AwKpVtfxulpeWV1bXyemVjc2t7x9zda8s4FZi0cMxi0Q2QJIxGpKWoYqSbCIJ4wEgnGF1N/M4DEZLG0Z0aJ8TjaBDRkGKktOSbh24oEM5cSQcc3dNa5gYhvM1P8izwaW5B36zalj0FXCROQaqgQNM3v9x+jFNOIoUZkrLn2InyMiQUxYzkFTeVJEF4hAakp2mEOJFeNn0kh8da6cMwFroiBafq74kMcSnHPNCdHKmhnPcm4n9eL1XhhZfRKEkVifBsUZgyqGI4SQX2qSBYsbEmCAuqb4V4iHQySmdX0SE48y8vknbdck6t+s1ZtXFZxFEGB+AI1IADzkEDXIMmaAEMHsEzeAVvxpPxYrwbH7PWklHM7IM/MD5/ABB5mVM=</latexit>
[W. Lu, F. Bonchi, A. Goyal, and L. The bang for the buck: … host perspective. KDD 2013].

Social Advertising

Social Advertising
•  Similar to organic posts from friends
in a social network
•  Contain an advertising message:
text, image or video
•  Can propagate to friends via social
actions: “likes”, “shares”
•  Each click to a promoted post
produces social proof to friends,
increasing their chances to click
Promoted Posts

Business Model
promoted posts via  
social feeds
$Bi<latexit sha1_base64="xpsNJ2f1ME0brEj3LTdJjPUgNIw=">AAAB7HicbVA9SwNBEJ3zM8avqKXNYhSswl0UtLAI2lhG8JJAcoS9zV6yZG/v2J0TQshvsLFQxNYfZOe/cZNcoYkPBh7vzTAzL0ylMOi6387K6tr6xmZhq7i9s7u3Xzo4bJgk04z7LJGJboXUcCkU91Gg5K1UcxqHkjfD4d3Ubz5xbUSiHnGU8iCmfSUiwShaye+c3nZFt1R2K+4MZJl4OSlDjnq39NXpJSyLuUImqTFtz00xGFONgkk+KXYyw1PKhrTP25YqGnMTjGfHTsiZVXokSrQthWSm/p4Y09iYURzazpjiwCx6U/E/r51hdB2MhUoz5IrNF0WZJJiQ6eekJzRnKEeWUKaFvZWwAdWUoc2naEPwFl9eJo1qxbuoVB8uy7WbPI4CHMMJnIMHV1CDe6iDDwwEPMMrvDnKeXHenY9564qTzxzBHzifPxuJjjQ=</latexit>
[C. Aslay, W. Lu, F. Bonchi, A. Goyal, and L. Viral marketing meets social advertising: Ad allocation with minimum
regret”, PVLDB 2015]

Challenges
•  Allocate promoted posts subject to user
attention constraints, balancing ad-user
match (click-through probabilities) against
user influence, and network effect against
advertiser budget.
•  max possible revenue =
•  service rendered could be more or less à
regret.
•  new objective: minimize regret!
X
i
Bi
<latexit sha1_base64="iI8SFuRy08Z3TR/Z/LbaPT3ACio=">AAAB8XicbVA9SwNBEJ2LXzF+RS1tFoNgFe5iQAuLoI1lBPOByXHsbfaSJbt7x+6eEI78CxsLRWz9N3b+GzfJFZr4YODx3gwz88KEM21c99sprK1vbG4Vt0s7u3v7B+XDo7aOU0Voi8Q8Vt0Qa8qZpC3DDKfdRFEsQk474fh25neeqNIslg9mklBf4KFkESPYWOmxr1MRMHQTsKBccavuHGiVeDmpQI5mUP7qD2KSCioN4Vjrnucmxs+wMoxwOi31U00TTMZ4SHuWSiyo9rP5xVN0ZpUBimJlSxo0V39PZFhoPRGh7RTYjPSyNxP/83qpia78jMkkNVSSxaIo5cjEaPY+GjBFieETSzBRzN6KyAgrTIwNqWRD8JZfXiXtWtW7qNbu65XGdR5HEU7gFM7Bg0towB00oQUEJDzDK7w52nlx3p2PRWvByWeO4Q+czx8Q8ZB/</latexit>

Budget and Regret
•  Host:
•  Owns directed social graph G = (V,E) and Topic-specific CTP model
instance
•  Sets user attention bound κu for each user u ∊ V
•  Advertiser i:
•  agrees to pay CPE(i) for each click up to his budget Bi
• total monetary value of the clicks πi(Si) = σi(Si) × cpe(i)
•  Exp. revenue of the host from assigning seed set Si to ad i: min(πi(Si), Bi)
Host’s regret
•  πi(Si) < Bi : Lost revenue opportunity
•  πi(Si) > Bi : Free service to the advertiser

Regret Minimization
•  Theorem: Regret minimization is NP-hard and NP-hard to
approximate.
•  Regret function is neither submodular nor monotone.
• Mon. decreasing and submodular for πi(Si) < Bi and
πi(Si U {u}) < Bi
• Mon. increasing and submodular for πi(Si) > Bi and
πi(Si U {u}) > Bi
• Neither monotone nor submodular for πi(Si) < Bi and
πi(Si U {u}) > Bi
Bi
πi(Si) πi(Si U {u})

Regret Minimization
•  Simple Greedy Algorithm
•  Select the (ad i, user u) pair that gives the max. reduction in
regret at each step, while respecting the attention constraints
•  Stop the allocation to i when Ri(Si) starts to increase

Regret Minimization
•  Theorem: Suppose the attention bound of
every user is the #advertisers. Then Greedy
achieves a regret where
•  is typically very small in practice.
•  TIRM scalable Greedy algorithm using rr-sets.
h,<latexit sha1_base64="GAXHjoxyGoNAFNeVidiT4vuFKRI=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tFoNgIeEuClpYBGwsI5gPSI6wt5lLluztHbt7QjjyI2wsFLH199j5b9wkV2jig4HHezPMzAsSwbVx3W+nsLa+sblV3C7t7O7tH5QPj1o6ThXDJotFrDoB1Si4xKbhRmAnUUijQGA7GN/N/PYTKs1j+WgmCfoRHUoeckaNldq9IZLRBemXK27VnYOsEi8nFcjR6Je/eoOYpRFKwwTVuuu5ifEzqgxnAqelXqoxoWxMh9i1VNIItZ/Nz52SM6sMSBgrW9KQufp7IqOR1pMosJ0RNSO97M3E/7xuasIbP+MySQ1KtlgUpoKYmMx+JwOukBkxsYQyxe2thI2ooszYhEo2BG/55VXSqlW9y2rt4apSv83jKMIJnMI5eHANdbiHBjSBwRie4RXenMR5cd6dj0VrwclnjuEPnM8fFpaOug==</latexit>

hX
i=1
piBi
2
,
<latexit sha1_base64="oGG1Ri5coL7cp1BD+facRJy4vwM=">AAACDXicbVDLSsNAFJ3UV62vqEs3g1VwISWpgi4Uim5cVrAPaGKYTCft0JlJmJkIJeQH3Pgrblwo4ta9O//G6WOhrQcuHM65l3vvCRNGlXacb6uwsLi0vFJcLa2tb2xu2ds7TRWnEpMGjlks2yFShFFBGppqRtqJJIiHjLTCwfXIbz0QqWgs7vQwIT5HPUEjipE2UmAfeIxAT6U8yOilm9/3oRdJhLMkoPAqoHlWzY9hYJedijMGnCfulJTBFPXA/vK6MU45ERozpFTHdRLtZ0hqihnJS16qSILwAPVIx1CBOFF+Nv4mh4dG6cIolqaEhmP190SGuFJDHppOjnRfzXoj8T+vk+ro3M+oSFJNBJ4silIGdQxH0cAulQRrNjQEYUnNrRD3kUlDmwBLJgR39uV50qxW3JNK9fa0XLuYxlEEe2AfHAEXnIEauAF10AAYPIJn8ArerCfrxXq3PiatBWs6swv+wPr8ARzpmus=</latexit>
pi = maxx2V ⇧i({x})/Bi.<latexit sha1_base64="6YRSpU5bSNVKFJy+q8lja2PN/1Y=">AAACDnicbVC7TsMwFHV4lvIKMLJYVJXKEpKCBANIFSyMRaIPqYkix3Vbq44T2Q5qFeULWPgVFgYQYmVm429w2wzQcqQrHZ9zr3zvCWJGpbLtb2NpeWV1bb2wUdzc2t7ZNff2mzJKBCYNHLFItAMkCaOcNBRVjLRjQVAYMNIKhjcTv/VAhKQRv1fjmHgh6nPaoxgpLflmOfYpvIIhGvnpyKUcNjPo1qlPK65+Z8cn1z61oG+WbMueAi4SJyclkKPum19uN8JJSLjCDEnZcexYeSkSimJGsqKbSBIjPER90tGUo5BIL52ek8GyVrqwFwldXMGp+nsiRaGU4zDQnSFSAznvTcT/vE6iehdeSnmcKMLx7KNewqCK4CQb2KWCYMXGmiAsqN4V4gESCCudYFGH4MyfvEiaVcs5tap3Z6XaZR5HARyCI1ABDjgHNXAL6qABMHgEz+AVvBlPxovxbnzMWpeMfOYA/IHx+QOiL5qL</latexit>
pi<latexit sha1_base64="enio4NQE/hjSyMPuiWw4zoSYBNE=">AAAB63icbVBNSwMxEJ34WetX1aOXYBE8ld0q6MFDwYvHCvYD2qVk02wbmmSXJCuUpX/BiwdFvPqHvPlvzLZ70NYHA4/3ZpiZFyaCG+t532htfWNza7u0U97d2z84rBwdt02caspaNBax7obEMMEVa1luBesmmhEZCtYJJ3e533li2vBYPdppwgJJRopHnBKbS8mA40Gl6tW8OfAq8QtShQLNQeWrP4xpKpmyVBBjer6X2CAj2nIq2KzcTw1LCJ2QEes5qohkJsjmt87wuVOGOIq1K2XxXP09kRFpzFSGrlMSOzbLXi7+5/VSG90EGVdJapmii0VRKrCNcf44HnLNqBVTRwjV3N2K6ZhoQq2Lp+xC8JdfXiXtes2/rNUfrqqN2yKOEpzCGVyAD9fQgHtoQgsojOEZXuENSfSC3tHHonUNFTMn8Afo8weqgI34</latexit>

Incentivized Social Advertising

CPE Model with Seed User Incentives
•  Host
•  Sells ad-engagements to advertisers
•  Inserts promoted posts to feed of users in exchange for monetary
incentives
•  Seed users take a cut on the social advertising revenue
•  Advertiser
•  Pays a fixed CPE to host for each
engagement
•  Pays monetary incentive to each seed
user engaging with her ad
•  Total payment subject to her budget
[C. Aslay, F. Bonchi, L., and W. Lu. Revenue Maximization in Incentivized Social Advertising”, PVLDB 2017]

•  Given
•  a social graph G = (V,E)
•  TIC propagation model
•  h advertisers with budget Bi and CPE(i) for each ad i
•  seed user incentives ci(u) for each user u∈V and for each ad i
•  Find an allocation S = (S1, …, Sh) maximizing the overall revenue of the host:

•  Revenue-Maximization problem is NP-hard
•  Restricted special case with h = 1:
•  NP-Hard Submodular-Cost Submodular-Knapsack (SCSK) problem
Partition matroid
Submodular knapsack constraints
•  Family 𝘊 of feasible solutions form an Independence System
•  Two greedy approximation algorithms w.r.t. sensitivity to seed user
costs during the node selection
[R.K. Iyer and J. Bilmes. Submodular optimization with submodular cover and submodular knapsack constraints.  
NIPS 2013]

•  Cost-agnostic greedy algorithm
•  Selects (node,ad) pair giving the max. marginal gain in revenue
•  Approximation guarantee follows from 𝘊 forming an independence
system
where
•  R and r are, respectively, upper and lower rank of 𝘊
•  κπ is the curvature of total revenue function π(.)

•  Cost-sensitive greedy algorithm
•  Selects the (node,ad) pair giving the max. rate of marginal gain in
revenue per marginal gain in payment
•  Approximation guarantee obtained
where
•  ρmax and ρmin are, respectively, max. and min. singleton payments
•  κρi is the curvature of ad i’s payment function ρi(.)
SDM, May 2019, Calgary,  
Canada.

Social Welfare

Utility vs Adoption

Welfare maximization
●  Welfare := Sum of utilities
○  Utility := value – price + noise.
●  Find a seedset for each item that maximizes
the overall (expected) social welfare
[P. Banerjee, W. Chen, and L. Maximizing Welfare in Social Networks under A Utility Driven Inﬂuence  
Diffusion model. SIGMOD 2019].

Welfare maximization: In other
contexts
○  Under network externalities
■  Does not consider the recursive propagation in a
network
■  Primary objective – maximize social welfare; no
budget constraints
[N. Economides. Network externalities, complementarities, and invitations to enter. Euro. Jl. Political  
Economy. Vol. 12 (1996)].  
[S. Bhattacharya, W. Dvorak, M. Henzinger, and M. Starnberger. Welfare maximization with friends-of-friends
network externalities. Theory of Comp. Sys. 2017].
○  Combinatorial Auctions
■  Allocate items to agents to maximize SW
■  No recursive propagation
e.g., [M. Kapralov, I. Post, and J. Vondrak. Online submodular welfare maximization: Greedy is  
optimal. SODA 2013].

Another Example
1
1
-1
2
2
3
6
Itemset Utility

Welfare vs Adoption
#Adoptions = 4
Welfare = 4
Allocations maximizing #adoptions need not maximize social welfare.
budget
1
1
2

Welfare vs Adoption
#Adoptions = 3
Welfare = 6
Allocations maximizing #adoptions need not maximize social welfare.

Propagation Example
v1<latexit sha1_base64="/0lg2bRe/hVcUgqYFvado2ixONc=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeCF48V7Qe0oWy2m3bpZhN2J4US+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW//4PCofHzSMnGqGW+yWMa6E1DDpVC8iQIl7ySa0yiQvB2M7+Z+e8K1EbF6wmnC/YgOlQgFo2ilx0nf65crbtVdgKwTLycVyNHol796g5ilEVfIJDWm67kJ+hnVKJjks1IvNTyhbEyHvGupohE3frY4dUYurDIgYaxtKSQL9fdERiNjplFgOyOKI7PqzcX/vG6K4a2fCZWkyBVbLgpTSTAm87/JQGjOUE4toUwLeythI6opQ5tOyYbgrb68Tlq1qndVrT1cV+r1PI4inME5XIIHN1CHe2hAExgM4Rle4c2Rzovz7nwsWwtOPnMKf+B8/gAJWI2g</latexit>
v2<latexit sha1_base64="0BJM1pmLuFkBdRn/CAp9h4NzT4k=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeCF48V7Qe0oWy2m3bpZhN2J4US+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW//4PCofHzSMnGqGW+yWMa6E1DDpVC8iQIl7ySa0yiQvB2M7+Z+e8K1EbF6wmnC/YgOlQgFo2ilx0m/1i9X3Kq7AFknXk4qkKPRL3/1BjFLI66QSWpM13MT9DOqUTDJZ6VeanhC2ZgOeddSRSNu/Gxx6oxcWGVAwljbUkgW6u+JjEbGTKPAdkYUR2bVm4v/ed0Uw1s/EypJkSu2XBSmkmBM5n+TgdCcoZxaQpkW9lbCRlRThjadkg3BW315nbRqVe+qWnu4rtTreRxFOINzuAQPbqAO99CAJjAYwjO8wpsjnRfn3flYthacfOYU/sD5/AEK3I2h</latexit>
v3<latexit sha1_base64="Fl36rZAFZI1qZ3etVqL6zaI1Xi8=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0laQY8FLx4r2lpoQ9lsJ+3SzSbsbgol9Cd48aCIV3+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RQ2Nre2d4q7pb39g8Oj8vFJW8epYthisYhVJ6AaBZfYMtwI7CQKaRQIfArGt3P/aYJK81g+mmmCfkSHkoecUWOlh0m/3i9X3Kq7AFknXk4qkKPZL3/1BjFLI5SGCap113MT42dUGc4Ezkq9VGNC2ZgOsWuppBFqP1ucOiMXVhmQMFa2pCEL9fdERiOtp1FgOyNqRnrVm4v/ed3UhDd+xmWSGpRsuShMBTExmf9NBlwhM2JqCWWK21sJG1FFmbHplGwI3urL66Rdq3r1au3+qtJo5HEU4QzO4RI8uIYG3EETWsBgCM/wCm+OcF6cd+dj2Vpw8plT+APn8wcMYI2i</latexit>
a b
t = 1. item(set) utility
a 1
b - 1
a, b 3

Propagation Example
a b
t = 2.
a
item(set) utility
a 1
b - 1
a, b 3

Propagation Example
a b
t = 3.
a
a
item(set) utility
a 1
b - 1
a, b 3

Utility Based IC Model
•  UIC model supports any value and price
functions.
•  utility = value – price + noise.
•  capture uncertainty in our knowledge of value
via noise à global or local.
•  Complementary focus: supermodular value,
additive (or submodular) price, global noise.

Properties of social welfare
●  monotone in sets of (seed, item) pairs?
○  Wrinkle: adding a high priced item can
decrease utility.
○  Reachability property to the rescue!

●  monotone in sets of (seed, item) pairs
○  Wrinkle: adding a high priced item can
decrease utility.
○  Reachability property to the rescue!

●  neither submodular, nor supermodular
○  Not submodular because utility is
supermodular

Why welfare is not submodular?
●  Utility is supermodular
Not adopted

Why welfare is not submodular?
●  Utility is supermodular
Adopted

●  neither submodular, nor supermodular
○  Not supermodular because reachability
is submodular

Why welfare is not supermodular
Marginal gain = 2

Why welfare is not supermodular
Marginal gain = 0

Algorithmic Options?

A simple greedy still does the job!
bundleGRD()
provides (1- 1/e - )
approximation
Does not require
knowledge of value/
price functions as
input!
~b = (b1, ..., bm)<latexit sha1_base64="8HR2BmsGBTUvoFHH7uD+mLttJ9g=">AAACAnicbVDLSgMxFM3UV62vUVfiJlgKFcowUwXdCAU3LivYB7TDkEnTNjTJDEmmUIbixl9x40IRt36FO//GtJ2Fth64cDjnXu69J4wZVdp1v63c2vrG5lZ+u7Czu7d/YB8eNVWUSEwaOGKRbIdIEUYFaWiqGWnHkiAeMtIKR7czvzUmUtFIPOhJTHyOBoL2KUbaSIF90h0TnIZTeAPLYeBVoOM4FRgG/Dywi67jzgFXiZeRIshQD+yvbi/CCSdCY4aU6nhurP0USU0xI9NCN1EkRniEBqRjqECcKD+dvzCFJaP0YD+SpoSGc/X3RIq4UhNuDi1xpIdq2ZuJ/3mdRPev/ZSKONFE4MWifsKgjuAsD9ijkmDNJoYgLKm5FeIhkghrk1rBhOAtv7xKmlXHu3Cq95fFWi2LIw9OwRkoAw9cgRq4A3XQABg8gmfwCt6sJ+vFerc+Fq05K5s5Bn9gff4AIfiUqw==</latexit>
✏<latexit
sha1_base64="FFpV7GpkkkeRpfN/x3Cvl4MBQjo=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0o6DHgxWME84BkCbOT3mTI7Mw6MyuEkJ/w4kERr/6ON//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03jco0wwZTQul2RA0KLrFhuRXYTjXSJBLYika3M7/1hNpwJR/sOMUwoQPJY86odVK7i6nhQsleqexX/DnIKglyUoYc9V7pq9tXLEtQWiaoMZ3AT204odpyJnBa7GYGU8pGdIAdRyVN0IST+b1Tcu6UPomVdiUtmau/JyY0MWacRK4zoXZolr2Z+J/XyWx8E064TDOLki0WxZkgVpHZ86TPNTIrxo5Qprm7lbAh1ZRZF1HRhRAsv7xKmtVKcFmp3l+Va7U8jgKcwhlcQADXUIM7qEMDGAh4hld48x69F+/d+1i0rnn5zAn8gff5A02FkCI=</latexit>

Prefix-preserving seed selection
b1<latexit sha1_base64="ztLqcu68PYWTcRrTaW/Cj8ctAKc=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lqQY8FLx4r2g9oQ9lsJ+3SzSbsboQS+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ7dzvPKHSPJaPZpqgH9GR5CFn1FjpIRh4g3LFrboLkHXi5aQCOZqD8ld/GLM0QmmYoFr3PDcxfkaV4UzgrNRPNSaUTegIe5ZKGqH2s8WpM3JhlSEJY2VLGrJQf09kNNJ6GgW2M6JmrFe9ufif10tNeONnXCapQcmWi8JUEBOT+d9kyBUyI6aWUKa4vZWwMVWUGZtOyYbgrb68Ttq1qndVrd3XK41GHkcRzuAcLsGDa2jAHTShBQxG8Ayv8OYI58V5dz6WrQUnnzmFP3A+fwDq0Y2M</latexit>
b2<latexit sha1_base64="V5AJK9qEdnJUfdPG6kJm1wyLVAE=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lqQY8FLx4r2g9oQ9lsN+3SzSbsToQS+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW//4PCofHzSNnGqGW+xWMa6G1DDpVC8hQIl7yaa0yiQvBNMbud+54lrI2L1iNOE+xEdKREKRtFKD8GgNihX3Kq7AFknXk4qkKM5KH/1hzFLI66QSWpMz3MT9DOqUTDJZ6V+anhC2YSOeM9SRSNu/Gxx6oxcWGVIwljbUkgW6u+JjEbGTKPAdkYUx2bVm4v/eb0Uwxs/EypJkSu2XBSmkmBM5n+TodCcoZxaQpkW9lbCxlRThjadkg3BW315nbRrVe+qWruvVxqNPI4inME5XIIH19CAO2hCCxiM4Ble4c2Rzovz7nwsWwtOPnMKf+B8/gDsVY2N</latexit>
(1 1/e)OPTb2<latexit sha1_base64="KlMnJ2y9Tndnf9YkK9wq/qu0C0s=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBahHqxJFfRY8OLNCv2CNoTNdtIu3WzC7qZQQv+JFw+KePWfePPfuG1z0OqDgcd7M8zMCxLOlHacL6uwtr6xuVXcLu3s7u0f2IdHbRWnkkKLxjyW3YAo4ExASzPNoZtIIFHAoROM7+Z+ZwJSsVg09TQBLyJDwUJGiTaSb9sV98K9hPOHRtPPAr828+2yU3UWwH+Jm5MyytHw7c/+IKZpBEJTTpTquU6ivYxIzSiHWamfKkgIHZMh9AwVJALlZYvLZ/jMKAMcxtKU0Hih/pzISKTUNApMZ0T0SK16c/E/r5fq8NbLmEhSDYIuF4UpxzrG8xjwgEmgmk8NIVQycyumIyIJ1SaskgnBXX35L2nXqu5VtfZ4Xa7X8ziK6ASdogpy0Q2qo3vUQC1E0QQ9oRf0amXWs/VmvS9bC1Y+c4x+wfr4Bg1pkf4=</latexit>
(1 1/e)OPTb1<latexit sha1_base64="Xl+ZzCDGwozG4JG4O664dHCnX04=">AAAB+XicbVDLSgNBEJyNrxhfqx69DAYhHow7UdBjwIs3I+QFybLMTnqTIbMPZmYDYcmfePGgiFf/xJt/4yTZg0YLGoqqbrq7/ERwpR3nyyqsrW9sbhW3Szu7e/sH9uFRW8WpZNBisYhl16cKBI+gpbkW0E0k0NAX0PHHd3O/MwGpeBw19TQBN6TDiAecUW0kz7Yr5IJcwvlDo+llvkdmnl12qs4C+C8hOSmjHA3P/uwPYpaGEGkmqFI94iTazajUnAmYlfqpgoSyMR1Cz9CIhqDcbHH5DJ8ZZYCDWJqKNF6oPycyGio1DX3TGVI9UqveXPzP66U6uHUzHiWphogtFwWpwDrG8xjwgEtgWkwNoUxycytmIyop0yaskgmBrL78l7RrVXJVrT1el+v1PI4iOkGnqIIIukF1dI8aqIUYmqAn9IJercx6tt6s92VrwcpnjtEvWB/fC+SR/Q==</latexit>
(1 1/e)OPTbmax<latexit sha1_base64="P5Sj78nE5km5NYsQ3FzEdzoTc9k=">AAAB/XicbVDLSgMxFM3UV62v8bFzEyxCXVhnqqDLght3VugL2mHIpGkbmmSGJCPWYfBX3LhQxK3/4c6/MW1noa0HLhzOuZd77wkiRpV2nG8rt7S8srqWXy9sbG5t79i7e00VxhKTBg5ZKNsBUoRRQRqaakbakSSIB4y0gtH1xG/dE6loKOp6HBGPo4GgfYqRNpJvH5TcU/eMnNzW6n4S+AlHD2nq20Wn7EwBF4mbkSLIUPPtr24vxDEnQmOGlOq4TqS9BElNMSNpoRsrEiE8QgPSMVQgTpSXTK9P4bFRerAfSlNCw6n6eyJBXKkxD0wnR3qo5r2J+J/XiXX/ykuoiGJNBJ4t6scM6hBOooA9KgnWbGwIwpKaWyEeIomwNoEVTAju/MuLpFkpu+flyt1FsVrN4siDQ3AESsAFl6AKbkANNAAGj+AZvII368l6sd6tj1lrzspm9sEfWJ8/0teUMg==</latexit>
bmax := maxi bi.<latexit sha1_base64="/E96VXH+oDWhe1Un+mswtzoDmkk=">AAACAHicbVDLSgMxFM3UV62vURcu3ASL4GqYqYKiCAU3LivYB7TDkEkzbWiSGZKMWIbZ+CtuXCji1s9w59+YtrPQ1gOXezjnXpJ7woRRpV332yotLa+srpXXKxubW9s79u5eS8WpxKSJYxbLTogUYVSQpqaakU4iCeIhI+1wdDPx2w9EKhqLez1OiM/RQNCIYqSNFNgHYZBx9JjDy2toekB7V2FAHRjYVddxp4CLxCtIFRRoBPZXrx/jlBOhMUNKdT030X6GpKaYkbzSSxVJEB6hAekaKhAnys+mB+Tw2Ch9GMXSlNBwqv7eyBBXasxDM8mRHqp5byL+53VTHV34GRVJqonAs4eilEEdw0kasE8lwZqNDUFYUvNXiIdIIqxNZhUTgjd/8iJp1Rzv1KndnVXr9SKOMjgER+AEeOAc1MEtaIAmwCAHz+AVvFlP1ov1bn3MRktWsbMP/sD6/AEPgZVm</latexit>
choose seeds greedily and in a prefix-preserving
way.
bmax<latexit sha1_base64="oePrIZLfxdjdQmCNEWJUiufwv48=">AAAB7nicbVDLSgNBEOz1GeMr6tHLYBA8hd0o6DHgxWME84BkCbOTTjJkZnaZmRXDko/w4kERr36PN//GSbIHTSxoKKq66e6KEsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZxqhg0Wi1i3I2pQcIUNy63AdqKRykhgKxrfzvzWI2rDY/VgJwmGkg4VH3BGrZNaUS+T9GnaK5X9ij8HWSVBTsqQo94rfXX7MUslKssENaYT+IkNM6otZwKnxW5qMKFsTIfYcVRRiSbM5udOyblT+mQQa1fKkrn6eyKj0piJjFynpHZklr2Z+J/XSe3gJsy4SlKLii0WDVJBbExmv5M+18ismDhCmebuVsJGVFNmXUJFF0Kw/PIqaVYrwWWlen9VrtXyOApwCmdwAQFcQw3uoA4NYDCGZ3iFNy/xXrx372PRuublMyfwB97nD6Hej8E=</latexit>

Prefix-preserving seed selection
•  Key : generate enough rr-sets to let us
handle every budget in the budget vector.
•  Challenge: #rr-sets needed (sample
complexity) is not monotone in the budget!
[P. Banerjee, W. Chen, and L. Maximizing Welfare in Social Networks under A Utility Driven Inﬂuence  
Diffusion model. SIGMOD 2019].
Algorithm PRIMA.

Why does greedy work?
●  Items I à sequence of “atomic” blocks.
●  marginalGain(block | previous blocks) >= 0.
●  Nodes reachable from an adopting node adopt the block.
●  Prefix-preserving greedy allocation ensures full blocks’ seeds
are approximately optimal
●  For arbitrary allocations,
utility(partial block) utility(corresponding full block)
(by supermodularity).
<latexit sha1_base64="4/s3xIM2h235MIQTNROwgf7Gps0=">AAAB63icbVBNS8NAEJ34WetX1aOXxSJ4KkkV9Fjw4rGC/YA2lM120i7dbOLuRiihf8GLB0W8+oe8+W/ctDlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dZwqhi0Wi1h1A6pRcIktw43AbqKQRoHATjC5zf3OEyrNY/lgpgn6ER1JHnJGTS71BT4OKlW35s5BVolXkCoUaA4qX/1hzNIIpWGCat3z3MT4GVWGM4Gzcj/VmFA2oSPsWSpphNrP5rfOyLlVhiSMlS1pyFz9PZHRSOtpFNjOiJqxXvZy8T+vl5rwxs+4TFKDki0WhakgJib542TIFTIjppZQpri9lbAxVZQZG0/ZhuAtv7xK2vWad1mr319VG40ijhKcwhlcgAfX0IA7aEILGIzhGV7hzYmcF+fd+Vi0rjnFzAn8gfP5AxW1jkI=</latexit>

Comparison against the
baselines: two items

Comparison against the
baselines: multiple items

Network externalities vs
propagation

Summary
•  Networks are essential for campaigns but
they merely provide the plumbing.
•  Interesting campaigns emerge from
distinguishing between influence and
adoption, multi-item interactions (competition,
complementarity), economic models of
“consumption”.
•  Asking questions about alternative
objectives.

Open Questions
•  Dealing with problems studied over
– adaptive setting
– evolving networks
– continuous time
•  do “economic” notions have a useful role to
play in problems related to infection
propagation/containment, misinformation
mitigation, biology, social good, … ?
•  Newer applications? SDM, May 2019, Calgary, Canada.

Thanks!
Amit Goyal Smriti Bhagat Cigdem Aslay Glenn Bevilacqua
Suresh V. Wei Chen Francesco Bonchi Wei Lu Sharan Vaswani
Xiaokui Xiao Prithu Banerjee . . .

SDM 2019 Keynote

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