19. In an hour from now…
I actually kind of liked it.
Bla bla …
sentiment …
bla bla bla …
networks …
Dude, that was even
more boring than his
gray shirt, eh?!
Yeah right. Great
talk… He didn’t even
talk about deep
learning.
20. Modeling person-to-person opinions:
The NLP approach
Bla bla …
sentiment …
bla bla bla …
networks …
Dude, that was even
more boring than his
gray shirt, eh?!
I actually kind of liked it.
Yeah right. Great
talk… He didn’t even
talk about deep
learning.
21. Modeling person-to-person opinions:
The social-network–analysis approach
Social balance theory
“The enemy
of my enemy
is my friend”
“The enemy
of my friend
is my enemy”
“The friend
of my friend
is my friend”
22. Modeling person-to-person opinions:
A unified view
–
++
–
“The friend
of my enemy
is my enemy”
–
Yeah right.
Great talk… He
didn’t even talk
about deep
learning.
Social balance theory
23. Modeling person-to-person opinions:
A unified view
+
“The friend
of my friend
is my friend”
+
+
The talk was amazing!
I couldn’t attend
— I was stuck on
the Autobahn.
Social balance theory
24. Model
Represent social network as a signed graph:
G = (V, E, p, x)
}
fully
observed
partially
observed
x 2 {0, 1}|E|
p 2 [0, 1]|E|
text-based
sentiment
predictions
edge signs
0 = –
1 = +
Task: Infer unobserved portion of x
“Boring!”
v 2 V
e1 2 E
x1 = 0
p1 = 0.04
x4 = ?
p4 = 0.55
“Okay.”
25. We want to infer unobserved portion of such that we
1. agree with text-based sentiment predictions, i.e.,
2. get triangles in line with social theories
Trade-off:
Objective function
x
x ⇡ p
T
}
}
Cost for deviating
from text-based
sent. prediction
Cost of triangle type
xt 2 {0, 1}3
EDGE COST
TRIANGLE
COST
x⇤
= arg minx2{0,1}|E|
X
e2E
|xe pe| +
X
t2T
d(xt)
26. HL-MRF (Broecheler et al., 2010)
• Markov random field (MRF) with continuous variables
• Potentials are sums of hinge-loss terms of linear
functions of variables.
• Relaxed objective function equal to original
formulation when is binary, i.e., ,
• but interpolates over continuous domain .
• Objective function convex.
• Efficiently solvable.
Relaxation as hinge-loss Markov
random field (HL-MRF)
x 2 {0, 1}|E|
[0, 1]|E|
x
. .
x