a 3-dimensio nal space is explored rather than a 2-dimensional space. Note that no
path connects to nodes on other planes. Thus, the inference of triangular-chain CRFs
straightforwardly uses jZj-way parallel inferences for linear-chain CRFs. There fore,
for a value of z = k, we perform the inference on the k space and repeat this proce-
dure for all values of z using a modified Viterbi decoding algorithm to find the best
path in the parallel search spaces.
To decrease the time com plexity, the pruning method is employed to reduce the
space of Z by removing planes with p
l
(z|x) < e [15]. We easily calculate p
l
(z|x).
Because Z(z, x) should be calculated before pruning is performed, a recursions are
finished fir st. Thus, we apply the pr uning method only during training. If we wish to
predict the best labels without marginal probabilities in predicting a new instance,
we can omit calculation of Z(x); hence we cannot prune less confident planes. How-
ever, we can take advantage of the pruning method in some applications that require
marginal probabilities (e.g., active learning). The pruning technique reduces training
time, allowing triangul ar-chain CRFs to be scaled for large-scale problems.
8.6 JOINT PREDICTION OF DIALOGUE ACTS AND NAMED ENTITIES
Current state-of-the-art SLU systems use cascade or pipeline schemes [10], which are
often derived by training the NE model; the schemes then use the model’s predic-
tion as a feature for the DA classifier. The NE plays an important role in identifying
the DA; it can thus also improve the performance of the DA classifier in cascading
scheme. However, the cascade approach has a significant drawback: The NE recog-
nition module cannot take advantage of information from the DA identification mod-
ule. Our assumption here is that the problems of modeling DA and modeling NE are
significantly correlated; that is, DA information influences the NE recognition task
and vice versa. Thus, we need to concurrently optimize the DA and NE models. This
problem can be solved using a complex model to reflect inter-dependency between
the two. The triangular-chain CRFs are thus applied to the joint SLU task.
This section evaluates triangular-chain CRFs in a real-world dialogue application
for ambient intelligence: an automated call center. Our method is found to perform
better for SLU tasks since it effectively captures the dependencies between NEs and
DAs. Empirical results show an improvement in both DA classification and NE
recognition.
8.6.1 Data Sets and Experiment Setup
We evaluated our method on two goal-or iented dialogue data Sets: Air-Travel
(English; travel agency service—DARPA-Communicator) and Telebank (Korean;
automated response system for a banking service). All data Sets were collected
and anno tated to develop spoken dialogue systems that consist of annotated DAs
and NEs. In practice, a realistic dialogue system for human–computer interfaces
functions best if the dialogue is short and restrictive. In these data Sets, the average
206 CHAPTER 8 Machine Learning Approaches

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