Modeling Topic-Partitioned Assortatitivy and Disassortativity in Dyadic Event DataAaron ScheinUMass Amherst

Mingyuan ZhouUniv. of Texas Austin

David M. BleiColumbia Univ.

Hanna WallachMicrosoft Research

Example results on 1995-2000 data:

1

2

3

4

5

1 : � Topic matrix

2 :

X⇤

(t)k kth core tensor slice, summed over time

3 : ⇥

�X

t

⇤

(t)k

�Topic-partitioned sender matrix

4 : ⇥

�X

t

⇤

(t)k

�TTopic-partitioned receiver matrix

5 :

�X

t

Y(t)��T

k Data, summed over time, thinned by topic k

y(t)i

a�!j⇠ Pois

CX

c1=1

✓ic1

CX

c2=1

✓jc2

KX

k=1

�(t)

c1k�!c2

�ak

!

'Y(t)

⇥

⇥T ⇤(t)�

N

N

A

N

C

C

C

K

K

A

Poisson Tucker decomposition:A Tucker decomposition…

…with a Poisson assumption.

Observed multiplex network

Inferred latent compression

Topic-partitioned network structure

Dyadic event data

number of times actor i took action a towards actor j during time t

y(t)i

a�!j:

who did what to whom, when

Picture © Kalev Leetaru, available on the GDELT blog

Shrinkage priors:

rc ⇠ Gamma

✓�0C,1

�

◆

wk ⇠ Gamma

✓⇢0K

,1

�

◆

Gamma CP decomposition:A CP decomposition…

…with a Gamma assumption.

⇤(t) r

rT

w

'C

C

K

C

C

K

�(t)

c1k�!c2

⇠(Gamma (⇠rc1wk, 1/dt) c1 = c2Gamma (rc1rc2wk, 1/dt) c1 6= c2

Other priors:

✓ic ⇠ Gamma

✓ai,

1

bi

◆

�k ⇠ Dir (⌫1 . . . ⌫A)

ai, bi ⇠ Gamma

✓a0,

1

b0

◆

dt ⇠ Gamma

✓e0,

1

f0

◆

⇠ ⇠ Gamma

✓g0,

1

h0

◆

(Dis-, Non-)Assortativitivity

• 249 country actors• 20 high level action types• 1995-2012 daily events

ICEWS dataset: