http://cs224w.stanford.edu We are more influenced by our friends - - PowerPoint PPT Presentation

CS224W: Machine Learning with Graphs Jure Leskovec, Stanford University

http://cs224w.stanford.edu

¡ We are more influenced by our friends

than strangers

2

¨ 68% of consumers consult

friends and family before purchasing home electronics

¨50% do research online

before purchasing electronics

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 3

Identify influential customers These customers endorse the product among their friends Convince them to adopt the product – Offer discount or free samples

The trend effect that Kate, Duchess of Cambridge has on

• thers, from cosmetic

surgery for brides, to sales of coral-colored jeans.”

“Kate Middleton effect

4 11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu

n According

to Newsweek, "The Kate Effect may be worth £1 billion to the UK fashion industry."

n Tony DiMasso, L. K.

Bennett’s US president, stated in 2012, "...when she does wear something, it always seems to go on a waiting list."

5 11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu

¡ Influential

persons often have many friends

¡ Kate is one of the

persons that have many friends in this social network

¡ For more Kates,

it’s not as easy as you might think!

6 11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu

¡ Given a directed

graph and k>0,

¡ Find k seeds (Kates)

to maximize the number of influenced people (possibly in many steps)

7 11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu

¡ Linear Threshold Model ¡ Independent Cascade Model

Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 8 11/7/19

, active neighbor of v w v w v

b q ³

å

¡ A node v has random threshold 𝜄" ~ U[0,1] ¡ A node v is influenced by each neighbor w

according to a weight 𝑐",% such that

¡ A node v becomes active when at least

(weighted) 𝜄" fraction of its neighbors are active

, neighbor of

1

v w w v

b £

å

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 9

Inactive Node Active Node Threshold Active neighbors

v w

0.5 0.3 0.2 0.5 0.1 0.4 0.3 0.2 0.6 0.2

Stop!

U X

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 10

¡ Independent Cascade Model

§ Directed finite 𝑯 = (𝑾, 𝑭) § Set 𝑻 starts out with new behavior

§ Say nodes with this behavior are “active”

§ Each edge (𝒘, 𝒙) has a probability 𝒒𝒘𝒙 § If node 𝒘 is active, it gets one chance to make 𝒙 active, with probability 𝒒𝒘𝒙

§ Each edge fires at most once

¡ Does scheduling matter? No

§ If 𝒗, 𝒘 are both active at the same time, it doesn’t matter which tries to activate 𝒙 first

§ But the time moves in discrete steps

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 11

¡ Initially some nodes S are active ¡ Each edge (𝒘, 𝒙) has probability (weight) 𝒒𝒘𝒙 ¡ When node v becomes active:

§ It activates each out-neighbor 𝒙 with prob. 𝒒𝒘𝒙

¡ Activations spread through the network

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 12

0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.2

e g f c b a d h i f g e

Problem: (k is a user-specified parameter)

¡ Most influential set of

size k: set S of k nodes producing largest expected cascade size f(S) if activated [Domingos-

Richardson ‘01]

¡ Optimization problem:

11/7/19 13 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu

) ( max

k size

• f

S

S f

0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.2 c b e a d g f h i Influence set Xd of d Influence set Xa of a

Why “expected cascade size”? Xa is a result of a random process. So in practice we would want to compute Xa for many random realizations and then maximize the “average” value f(S). For now let’s ignore this nuisance and simply assume that each node u influences a set of nodes Xu

Random realizations i

𝑔 𝑇 = 1 |𝐽| 6 𝑔

7(𝑇)

¡ S: is initial active set ¡ f(S): The expected size of final active set

§ f(S) is the size of the union of Xu: 𝒈(𝑻) = ∪𝒗∈𝑻 𝒀𝒗

¡ Set S is more influential if f(S) is larger

𝒈( 𝒃, 𝒄 ) < 𝒈({𝒃, 𝒅}) < 𝒈({𝒃, 𝒆})

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 14

graph G

c … influence set Xu of node u a b d

¡ Problem: Most influential set of k nodes:

set S on k nodes producing largest expected cascade size f(S) if activated

¡ The optimization problem: ¡ How hard is this problem?

§ NP-COMPLETE!

§ Show that finding most influential set is at least as hard as a set cover problem

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 16

) ( max

k size

• f

S

S f

¡ Extremely bad news:

§ Influence maximization is NP-complete

¡ Next, good news:

§ There exists an approximation algorithm!

§ For some inputs the algorithm won’t find globally

• ptimal solution/set OPT

§ But we will also prove that the algorithm will never do too badly either. More precisely, the algorithm will find a set S that where 𝒈 𝑻 ≥ 𝟏. 𝟕𝟒 ∗ 𝒈(𝑷𝑸𝑼), where OPT is the globally optimal set.

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 20

¡ Consider a Greedy Hill Climbing algorithm to

find S:

§ Input: Influence set 𝒀𝒗 of each node 𝒗: 𝒀𝒗 = {𝒘𝟐, 𝒘𝟑, … }

§ That is, if we activate 𝒗, nodes {𝒘𝟐, 𝒘𝟑, … } will eventually get active

§ Algorithm: At each iteration 𝒋 activate the node 𝒗 that gives largest marginal gain: 𝐧𝐛𝐲

𝒗

𝒈(𝑻𝒋T𝟐 ∪ {𝒗})

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 21

𝑇𝑗 … Initially active set 𝑔(𝑇7) … Size of the union of 𝑌W, 𝑣 ∈ 𝑇7

Algorithm:

¡ Start with 𝑻𝟏 = { } ¡ For 𝒋 = 𝟐 … 𝒍

§ Activate node 𝒗 that max 𝒈(𝑻𝒋T𝟐 ∪ {𝒗}) § Let 𝑻𝒋 = 𝑻𝒋T𝟐 ∪ {𝒗}

¡ Example:

§ Eval. 𝑔 𝑏 , … , 𝑔({𝑓}), pick argmax of them § Eval. 𝑔 𝒆, 𝑏 , … , 𝑔({𝒆, 𝑓}), pick argmax § Eval. 𝑔(𝒆, 𝒄, 𝑏}), … , 𝑔({𝒆, 𝒄, 𝑓}), pick argmax

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu

a b c a b c d d f(Si-1È{u}) e e

22

¡ Claim: Hill climbing produces a solution S

where: f(S) ³(1-1/e)*f(OPT) (f(S)>0.63*f(OPT))

[Nemhauser, Fisher, Wolsey ’78, Kempe, Kleinberg, Tardos ‘03]

¡ Claim holds for functions f(·) with 2 properties:

§ f is monotone: (activating more nodes doesn’t hurt) if S Í T then f(S) £ f(T) and f({})=0 § f is submodular: (activating each additional node helps less) adding an element to a set gives less improvement than adding it to one of its subsets: "S Í T

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 23

Gain of adding a node to a small set Gain of adding a node to a large set

f(S È {u}) – f(S) ≥ f(T È {u}) – f(T)

¡ Diminishing returns:

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 24

f(·) Set size |T|, |S|

Gain of adding a node to a small set Gain of adding a node to a large set

f(S È {u}) – f(S) ≥ f(T È {u}) – f(T)

f(S) f(S È{u}) f(T È{u})

"S Í T

f(T) Adding u to T helps less than adding it to S!

Also see the handout posted on the course website.

¡ We must show our f(·) is submodular: ¡ "S Í T ¡ Basic fact 1:

§ If 𝒈𝟐(𝒚), … , 𝒈𝒍(𝒚) are submodular, and 𝒅𝟐, … , 𝒅𝒍 ≥ 𝟏 then 𝑮 𝒚 = ∑𝒋 𝒅𝒋 b 𝒈𝒋 𝒚 is also submodular

(Non-negative combination of submodular functions is a submodular function)

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 26

Gain of adding a node to a small set Gain of adding a node to a large set

f(S È {u}) – f(S) ≥ f(T È {u}) – f(T)

¡ "S Í T: ¡ Basic fact 2: A simple submodular function

§ Sets 𝒀𝟐, … , 𝒀𝒏 § 𝒈 𝑻 = ⋃𝒍∈𝑻 𝒀𝒍

(size of the union of sets 𝒀𝒍, 𝒍 ∈ 𝑻)

§ Claim: 𝒈(𝑻) is submodular!

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 27

S T u

Gain of adding u to a small set Gain of adding u to a large set

f(S È {u}) – f(S) ≥ f(T È {u}) – f(T)

S Í T

The more sets you already have the less new area a given set u will cover

¡ Proof strategy:

§ We will argue that influence maximization is an instance of the Set cover problem:

§ Set cover problem: f(S) is the size of the union of nodes influenced by active set S

§ Note f(S) is “random” (a result of a random process) so we need to be a bit careful

§ Principle of deferred decision to the rescue!

¡ We will create many parallel possible worlds and then

average over them

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 28

c b e g f h i

a d

Random realizations i

𝑔 𝑇 = 1 |𝐽| 6 𝑔

7(𝑇)

¡ Principle of deferred decision:

§ Flip all the coins at the beginning and record which edges fire successfully § Now we have a deterministic graph! § Def: Edge is live if it fired successfully

§ That is, we remove edges that did not fire

¡ What is influence set 𝒀𝒗 of node 𝒗?

§ The set reachable by live-edge paths from 𝒗

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 29

c b e g f h i

a d

Influence sets for realization 𝒋: 𝑌e

7 = {a,f,c,g}

𝑌f

7 = {b,c},

𝑌g

7 = {c}

𝑌h

7 = {d,e,h}

…

Random realizations i

𝑔 𝑇 = 1 |𝐽| 6 𝑔

7(𝑇)

¡ What is an influence set 𝒀𝒗?

§ The set reachable by live-edge paths from 𝒗

¡ What is now f(S)?

§ fi(S) = size of the set reachable by live-edge paths from nodes in S

¡ For the i-th possible world

(realization of coin flips)

§ 𝑔𝑗(𝑇 = 𝑏, 𝑐 ) = 𝑏, 𝑔, 𝑑, 𝑕 ∪ 𝑐, 𝑑 = 5 § 𝑔𝑗 𝑇 = 𝑏, 𝑒 = 𝑏, 𝑔, 𝑑, 𝑕} ∪ {𝑒, 𝑓, ℎ = 7

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 30

c b e g f h i

a d

Influence sets for realization 𝒋: 𝑌e

7 = {a,f,c,g}

𝑌f

7 = {b,c},

𝑌g

7 = {c}

𝑌h

7 = {d,e,h}

Random realizations i

𝑔 𝑇 = 1 |𝐽| 6 𝑔

7(𝑇)

¡ Generate a possible world:

§ Fix outcome 𝑗 ∈ 𝐽 of coin flips

¡ 𝒀𝒘

𝒋 = set of nodes reachable from

𝒘 on live-edge paths

¡ 𝒈𝒋(𝑻) = size of cascades from 𝑻

given the coin flips 𝒋

¡ 𝒈𝒋 𝑻 = ⋃𝒘∈𝑻 𝒀𝒘

𝒋 Þ 𝒈𝒋(𝑻)

is submodular!

§ 𝒀𝒘

𝒋 are sets, 𝒈𝒋(𝑻) is the size of their union

¡ Expected influence set size:

𝒈 𝑻 =

𝟐 |𝑱| ∑𝒋∈𝑱 𝒈𝒋(𝑻) Þ 𝒈(𝑻) is submodular! § 𝒈(𝑻) is a linear combination of submodular functions

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 31

c a b d e f Possible worlds

Activate edges by coin flipping

c a b d e f c a b d e f c a b d e f 𝒀𝒃

𝟐

𝒀𝒃

𝟑

𝒀𝒃

𝟒

Random realizations i

𝑔 𝑇 = 1 |𝐽| 6 𝑔

7(𝑇)

¡ Find most influential set S of size k: largest

expected cascade size f(S) if set S is activated

¡ Want to solve:

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 32

c a b d e f

Network, each edge activates with prob. puv

Possible worlds

Activate edges by coin flipping

c a b d e f c a b d e f c a b d e f

Multiple realizations i. Each realization is a “possible world” … influence set of node a … influence set of node d

Consider S={a,d} then: f1(S)=5, f2(S)=4, f3(S)=3 and f(S) = 1/3*12=4

𝐛𝐬𝐡 𝐧𝐛𝐲

r st

𝒈 𝑻 = 𝟐 |𝑱| 6

𝒋∈𝑱

𝒈𝒋(𝑻)

Claim: When f(S) is monotone and submodular then Hill climbing produces active set S where: 𝒈 𝑻 ≥ 𝟐 −

𝟐 𝒇 ⋅ 𝒈(𝑷𝑸𝑼)

§ In other words: 𝑔 𝑇 ≥ 0.63 ⋅ 𝑔(𝑃𝑄𝑈)

¡ The setting:

§ Keep adding nodes that give the largest gain § Start with 𝑻𝟏 = {}, produce sets 𝑻𝟐, 𝑻𝟑, … , 𝑻𝒍 § Add elements one by one § Let 𝑷𝑸𝑼 = {𝒖𝟐 … 𝒖𝒍} be the optimal set (OPT) of size 𝒍

¡ We need to show: 𝒈 𝑻 ≥ (𝟐 −

𝟐 𝒇) 𝒈(𝑷𝑸𝑼)

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 34

(Do at home. See handout!)

We just proved: J

¡ Hill climbing finds solution S which

f(S) ³ (1-1/e)*f(OPT) i.e., f(S) ³ 0.63*f(OPT)

¡ This is a data independent bound

§ This is a worst case bound § No matter what is the input data, we know that the Hill-Climbing will never do worse than 0.63*f(OPT)

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 42

¡ How to evaluate influence maximization ƒ(S)?

§ Still an open question of how to compute it efficiently

¡ But: Very good estimates by simulation

§ Repeating the diffusion process often enough (polynomial in n; 1/ε) § Achieve (1± ε)-approximation to f(S) § Generalization of Nemhauser-Wolsey proof: Greedy algorithm is now a (1-1/e- ε)- approximation

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 43

¡ Find most influential set S of size k: largest

expected cascade size f(S) if set S is activated

¡ Want to solve:

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 44

c a b d e f

Network, each edge activates with prob. puv

Possible worlds

Activate edges by coin flipping

c a b d e f c a b d e f c a b d e f

Multiple realizations i. Each realization is a “parallel universe” … influence set of node a … influence set of node d

Consider S={a,d} then: f1(S)=5, f2(S)=4, f3(S)=3 and f(S) = 1/3*(5+4+3)=4

𝐛𝐬𝐡 𝐧𝐛𝐲

r st

𝒈 𝑻 = 𝟐 |𝑱| 6

𝒋∈𝑱

𝒈𝒋(𝑻)

¡ Notice: Greedy approach is slow!

§ For a given network G, repeat 10,000s of times:

§ Flip coin for each edge and determine influence sets under coin-flip realization i § Each node u is associated with 10,000s influence sets Xui

§ Greedy’s complexity is 𝑷(𝒍 ⋅ 𝒐 ⋅ 𝑺 ⋅ 𝒏)

§ 𝑜 … number of nodes in G § 𝑙 … number of nodes to be selected/influenced § 𝑆 … number of simulation rounds (number possible worlds) § 𝑛 … number of edges in G

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 45

¡ A collaboration network: co-authorships in

papers of the arXiv high-energy physics theory:

§ 10,748 nodes, 53,000 edges § Example cascade process: Spread of new scientific terminology/method or new research area

¡ Independent Cascade Model:

§ Each user’s threshold is uniform random on [0,1] § Case 1: Uniform probability p on each edge § Case 2: Edge from v to w has probability 1/deg(w) of activating w.

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 47

¡ Simulate the process 10,000 times for each

targeted set

§ Every time re-choosing edge outcomes randomly

¡ Compare with other 3 common heuristics

§ Degree centrality: Pick nodes with highest degree § Closeness centrality: Pick nodes in the “center” of the network § Random nodes: Pick a random set of nodes

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 48

puv = 0.01 puv = 0.10

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 49

Uniform edge firing probability puv

f(Sk) f(Sk) k k

puv=1/deg(v)

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 50

Non-uniform edge firing probability puv

k f(Sk)

Sketch-based Influence Maximization and Computation: Scaling up with Guarantees”, CIKM 2014

To perform influence maximization we need to…

¡ 1) Generate a number R of possible worlds ¡ 2) Identify 𝑙 nodes with the largest

influence in these possible worlds

¡ Problem:

§ For any given node set, evaluating its influence in a possible world takes 𝑃(𝑛) time (𝑛… number of edges)

¡ Solution: Use sketches to reduce estimation

time from 𝑃(𝑛) to 𝑃(1)

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 52

¡ Solution: Use sketches to reduce estimation

time from 𝑃(𝑛) to 𝑃(1) Idea:

¡ Compute small structure per node from which

to estimate its influence

¡ Then run influence maximization using these

estimates

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 53

Rough Idea:

¡ Take a possible world 𝐻(7) ¡ Give each node a uniform random

number from [0,1]

¡ Compute the rank of each node 𝑤,

which is the minimum number among the nodes that 𝑤 can reach

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 54

Intuition

¡ If 𝑤 can reach a large number of

nodes then its rank is likely to be small

¡ Hence, the rank of node 𝑤 can be

used to estimate the influence of node 𝑤 a graph in a possible word 𝐻(7)

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 55

Problem

¡ Influence estimation based on a

single rank/number can be inaccurate Solution

¡ Keep multiple ranks/numbers

§ E.g., keep the smallest 𝑑 values among the nodes that 𝑤 can reach

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 56

Problem

¡ Influence estimation based on

single rank/number can be inaccurate Solution

¡ Keep multiple ranks/numbers

§ E.g., keep the smallest 𝑑 values among the nodes that 𝑤 can reach

¡ Enables estimate on union of

these reachable sets

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 57

Problem

¡ Influence estimation based on

single rank/number can be inaccurate Solution

¡ Keep multiple ranks (say 𝑑 of them)

§ Keep the smallest 𝑑 values among the nodes that 𝑤 can reach in all possible worlds considered (but keep the

numbers fix across the worlds)

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 58

¡ Generate a number of

possible worlds

¡ Construct reachability

sketches for all node:

§ Result: each node has 𝑑 ranks

¡ Run Greedy for influence maximization

§ Whenever Greedy asks for the influence of a node set 𝑇, check ranks and add a 𝑣 node that has the smallest value (lexicographically)

§ After 𝑣 is chosen. Find its influence set of nodes 𝑔(𝑣), mark them as infected and remove their “numbers” from the sketches of other nodes

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 59

¡ Guarantees:

§ Expected running time is near-linear in the number of possible worlds § When 𝑑 is large, it provides (1 −

‡ ˆ − 𝜁) approx with respect to

the possible worlds considered

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 60

¡ Advantages:

§ Expected near-linear running time § Provides an approximation guarantee with respect to the possible worlds considered

¡ Disadvantage

§ Does not provide an approximation guarantee on the ”true” expected influence

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 61

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 62

GRE… greedy IRIE… state of the art heuristics DEG…degree based heuristics SK... Sketch-based

Sketch-based achieves the same performance as greedy in a fraction

• f the time!

¡ More realistic viral marketing:

§ Different marketing actions increase likelihood of initial activation, for several nodes at once

¡ Study more general influence models:

§ Find trade-offs between generality and feasibility

¡ Deal with negative influences:

§ Model competing ideas

¡ Obtain more data (better models) about how

activations occur in real social networks

11/7/19 Jure Leskovec, Stanford CS224W: Machine Learning with Graphs, http://cs224w.stanford.edu 63