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In-Depth Information
x
j
is represented by a feature vector
x
(
x
j
) in
R
d
, for example, the
head velocities at each frame. For each sequence, a vector of “sub-
structure” variables
h
=
{
h
1
, h
2
, ..., h
m
} is assumed. These variables are
not observed in the training examples and will therefore form a set
of hidden variables in the model.
Given the above definitions, the latent conditional model is defined
as:
h
∑
P
(
y
x,
θ
)
=
P
(
y
h,
x,
θ
)
P
(
h
x,
θ
)
1
where
θ
are the parameters of the Latent-Dynamic CRF model. These
are learned automatically during training using a gradient ascent
approach to search for the optimal parameter values. More details can
be found in Morency et al. (2007).
The Latent-Dynamic CRF model was applied to the problem of
learning individual dynamics of backchannel feedback. Figure 7 shows
y
y
y
y
y
h
1
h
2
h
3
h
4
h
n
x
1
x
2
x
3
x
4
x
n
Figure 6.
Graphical representation of the LDCRF model.
x
j
represents the
j
th
observation
(corresponding to the
j
th
observation of the sequence),
h
j
is a hidden state assigned to
x
j
,
and
y
j
the class label of
x
j
(i.e., positive or negative). Gray circles are observed variables.
Figure 7.
Recognition of backchannel feedback based on individual dynamics only.
Comparison of the Latent-Dynamic CRF model with previous approaches for probabilistic
sequential modeling.
(Color image of this fi gure appears in the color plate section at the end of the topic.)
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