Information Technology Reference
In-Depth Information
(3) If
s
u
,
i
=
1, then
i. Draw a topic from
u
's own topic distribution:
z
u
,
i
∼
Multi
(ʩ
u
)
;
w
(4) Draw a word
w
u
,
i
from the topic-word distribution:
w
u
,
i
∼
Multi
(ʦ
z
u
,
i
)
.
The generative process of visual descriptors is similar other than that the visual
descriptor
v
u
,
i
is sampled from topic-visual descriptor distribution
v
z
u
,
i
. Actually,
during the model learning process, we assume the prior distributions follow symmet-
ric Dirichlet, which are conjugate priors for multinomial (or Beta for Bernoulli). For
simplification, we do not draw the hyperparameters in the graphical model. Since
the tag and image are modeled simultaneously, we can infer the underlying influence
structure by considering multimodal information.
ʦ
4.3.3 Learning MmTIM by Gibbs Sampling
The mmTIM model includes three sets of latent variables, the binary switch labels
s
w
z
v
. We use Gibbs sam-
pling [
24
] for model learning: reverse the generation process, record the sampled
state variables, and compute the outputs. When using Gibbs sampling to train a gen-
erative model, a Markov chain is formed. The joint distribution is approximated by
drawing a sequence of samples and each latent variable is iteratively updated by
fixing other variables. The mechanism of the designed Gibbs sampler is illustrated
in Fig.
4.3
. The inputs first initialize the state variables. During the sampling process,
different counters are updated to record the state variable values, and construct the
conditional posterior probability according to the designed generation process. From
this probability, we can sample new state variables. The derivation of update rules for
new sampling is detailed in the appendix. We list the update rules for latent variables
concerning tag words as follows.
s
v
, the influencer
c
w
c
v
, and the topic assignments
z
w
,
,
,
N
U
,
S
(
u
i
,
N
U
,
Z
(
c
i
,
z
i
)
+
ʱ
ʻ
−
)
+
ʱ
ʩ
−
0
1
1
p
(
s
i
=
0
|
s
w
−
i
,
u
i
,
c
i
,
z
i
(4.1)
,
·
)
∝
·
N
U
(
u
i
)
+
2
ʱ
ʻ
−
1
N
U
(
c
i
)
+
T
ʱ
ʩ
−
1
Fig. 4.3
The mechanism of Gibbs sampling for mmTIM. Reference [
27
]
c
2013 Association for
Computing Machinery, Inc. Reprinted by permission
