Database Reference
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variable
z
n−
1
through a conditional distribution
p
(
z
n
|
z
n−
1
). The following
characterize a HMM:
•
N
— the number of states in the model. The individual states are denoted
as
Z
=
{
z
1
,z
2
...z
N
}
and the state at time t as
q
t
.
•
M
— the number of distinct observation symbols per state. The
observation symbols correspond to the physical output of the system
being modeled. The symbols are represented as
X
=
{x
1
,x
2
...x
M
}
.
•
The state transition probability distribution
A
=
{a
i,j
}
where
a
i,j
=
P
[
q
t
+1
=
z
j
|
q
t
=
z
i
] 1
≤
i, j
≤
N
.
•
The observation symbol probability distribution in state
j
,
B
=
{
b
i
(
k
)
}
1
≤
j
≤
N
where
b
i
(
k
)=
P
[
x
k
at t
|
q
t
=
z
j
]
,
.
1
≤
k
≤
M
•
The initial state distribution
π
=
{
π
i
}
where
π
=
P
[
q
1
=
z
i
]
,
1
≤
i
≤
N
.
Antwarg
et al
. (2012) present the notion of HMM tree. Each node in
the tree is a HMM which uses the same states from the higher level or
only some of them but with different transition probabilities. Because the
number of available training instances drops as we move down the tree, the
number of hidden states should generally drop accordingly. In particular, if
the number of observations is very large, then we can choose a large number
of hidden states to capture more features. The hierarchical structure that
forms a tree is used to differentiate between cases and better estimate HMM
parameters.
Consider the task of intention prediction which aims to predict what the
user wants to accomplish when performing a certain sequence of activities.
Predicting user intentions when using a system can improve the services
provided to users by adjusting the system services to their needs. This goal
is achieved by training a specific learning algorithm in order to generate
models that will maximize the accuracy of the prediction. The challenge
in predicting the intention of the user given a sequence of interactions
can be categorized as a problem with a sequential problem space which
is commonly solved using sequence learning algorithms.
Using intention prediction methods will enable a company to improve
the services provided to users by adjusting the system services to their
needs (e.g. the interface). Predicting user intentions can be also used for
assisting users to perform or complete tasks, to alert them regarding the
availability of features, and to increase their general knowledge. Effective
assistance will allow users to acquire the new skills and knowledge they
need to easily operate an unfamiliar device or function.
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