Maintaining State
All dialogue managers must maintain an internal state representing what has happened in the dialogue. In hand-crafted approaches the internal state is directly defined by the dialogue system designer. More recently, probabilistic approaches have been deve
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Maintaining State
All dialogue managers must maintain an internal state representing what has happened in the dialogue. In hand-crafted approaches the internal state is directly defined by the dialogue system designer. More recently, probabilistic approaches have been developed to better handle the uncertainty inherent in dialogue. As mentioned in the previous chapter, the probabilistic approach defines the internal state as a belief distribution over environment states. The important concepts used in this framework are: • • • • • •
s ∈ S—The environment state b ∈ B—The system’s belief state o ∈ O—The observation a ∈ A—The system’s action p(o|s, a)—The observation function p(s |s, a)—The transition function
Observations are assumed to depend conditionally on only the most recent environment state, while the environment states are assumed Markov (i.e. the current state depends conditionally on only the previous environment state and action). Under these assumptions the belief state is represented as a probability distribution and is updated via Bayes theorem as shown in Eq. 2.2. The resulting update is reproduced below: b(s) p(s |s, a) p(o |s ). (3.1) b (s ) ∝ s∈S
When the number of environment states grows, the belief state update becomes intractable. This chapter will discuss methods for computing the belief state efficiently.
B. Thomson, Statistical Methods for Spoken Dialogue Management, Springer Theses, DOI: 10.1007/978-1-4471-4923-1_3, © Springer-Verlag London 2013
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3 Maintaining State
3.1 Bayesian Networks Before going into the details of efficient algorithms for updating the belief state it is useful to introduce a graphical notation for representing the independence assumptions in a probabilistic model. The graphical model introduced here is known as a Bayesian Network. As will be shown in Sect. 3.5, Bayesian Networks do more than simply provide notation as there are several algorithms which operate directly on the graphical structure to efficiently update probability distributions. Detailed introductions on Bayesian Networks are given in Bishop (2006, Chap. 8) and Jensen (2001). A Bayesian network is defined as: • • • •
A directed acyclic graph where the nodes represent random variables, and the arrows joining the nodes represent conditional independence assumptions. The joint distribution of all variables in the graph factorises as the product of the conditional probability of each variable given its parents in the graph.
At first glance, this might seem a little complicated so it is worth considering an example. Let us take the case of a dialogue system which can offer the user information about restaurants and hotels in either the north or the south of the town. These possibilities are encoded in two random variables. One is the area, which will be labelled gar ea , and the other is the type of venue, gt ype . A third random variable in the system is what the user said, which will be labelled o. One possible Bayesian Network for this model would be the graph given in Fig. 3.
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