3. Our
focus
–
Classifica5on
confidence
Example
input
graph
Our
intui5on
-‐
A
is
most
probably
conserva5ve
-‐
B
may
be
conserva5ve
person
è It’s
good
to
have
confidence
for
our
predic5on
e.g.,
A
is
conserva5ve
with
confidence
score
0.9
B
is
conserva5ve
with
confidence
score
0.55
4. Contribu5ons
• Novel
Algorithm
– Simple,
fast,
and
incorporates
confidence
• Theore5cal
Analysis
– Convergence
guarantee
&
speed
– Equivalence
to
LP
and
Bayesian
inference
• Empirical
Analysis
– Higher
accuracy
than
compe5tors
– Three
different
real
network
datasets
7. Our
Idea
B
A
Smoothness
assump5on
+
confidence
IF
a
node
has
a
lot
of
red/blue
neighbors
THEN
we
can
confidently
say
that
it
is
red/blue
Confident
Not
confident
More
evidence,
more
confidence
à
Bayesian
inference
8. Cases
to
consider
• Case1:
without
unlabeled
neighbors
– Easy
but
unrealis5c
• Case2:
with
unlabeled
neighbors
– We
want
to
handle
this
case
?
?
?
9. Case1:
No
unlabeled
neighbors
?
Prior
knowledge
evidence
+
Result
Detail
DCM
(Dirichlet
compound
mul5nomial)
leads
to
simple
result:
∝
fik:
probability
that
i
has
label
k
nik:
number
of
i’s
neighbors
with
label
k
αk：
prior
10. Case2:
With
unlabeled
neighbors
A
B
Classifica>on
result
for
A
affects
B
Classifica>on
result
for
B
affects
A
In
this
case
we
need
to
solve
the
recursive
equa5on:
Aij:
entry
of
adjacency
matrix
Detail
11. Yes,
we
can
solve
it
(Please
see
the
paper
for
detail)
• Simple:
We
just
need
to
do
matrix
inversion
• Fast:
power
itera5on
for
sparse
matrix
inversion
is
fast
(PUU
is
sparse)
• Confidence:
this
equa5on
is
from
Bayesian
inference
13. Convergence
guarantee
&
speed
Theorem
1:
The
itera5ve
algorithm
of
SocNL
always
converges
on
arbitrary
graphs
if
use
non-‐zero
prior
values
Theorem
2:
SocNL
converges
faster
if
use
larger
prior
values
Theorem
3:
Time
complexity
of
each
itera5on
of
SocNL
is
O(
K(N+M)
)
14. Equivalence
Theorem
4:
SocNL
is
equivalent
to
normal
LP
if
uses
prior
values
=
0
Theorem
5:
SocNL
is
equivalent
to
Bayesian
inference
over
DCM
if
ignores
unlabeled
nodes
*
DCM:
Dirichlet
compound
mul5nomial
