Probabilistic Dialogue Modelling
Oliver Lemon
CSLI
Stanford University
lemon@csli.stanford.edu,
Prashant Parikh
IRCS
University of Pennsylvania
pjparikh@aol.com
Stanley Peters
CSLI
Stanford University
peters@csli.stanford.edu
Abstract
We show how Bayesian networks and re-
lated probabilistic methods provide an ef-
ficient way of capturing the complex bal-
ancing of different factors that determine
interpretation and generation in dialogue.
As a case study, we show how a prob-
abilistic approach can be used to model
anaphora resolution in dialogue1.
1 Introduction
The use of probabilistic and decision-theoretic in-
ference in dialogue modelling and management has
been explored in preliminary fashion by (Pulman,
1996) and (Keizer, 2001). Probabilistic meth-
ods look promising when modelling systems where
there is uncertainty, and simple true/false judge-
ments obscure some of the subtleties of represen-
tation and processing that are required of an accu-
rate model. Dialogue systems are of this nature be-
cause uncertainty is present due to speech recogni-
tion noise, speech-act uncertainty, and so on. Epis-
temic uncertainty is rife in dialogue, and probability
distributions provide a natural model of the ambigu-
ities that thus arise. For these reasons it is natural to
explore probabilistic representations and algorithms
in dialogue management, rather than purely deter-
ministic models. We have experience building deter-
ministic dialogue managers (see e.g. (Lemon et al.,
1This research was (partially) funded under the Wallenberg
laboratory for research on Information Technology and Au-
tonomous Systems (WITAS) Project, Link¨oping University, by
the Wallenberg Foundation, Sweden.
2001; Lemon et al., 2002)) which use deterministic
context update rules.
This paper briefly describes our construction of a
Bayes Net modelling dialogue context. We will con-
sider a series of examples of increasing complexity
involving anaphoric resolution in Section 3.1. We
will point out how they are to be resolved intuitively,
and then discuss how our Bayesian net fares. We
will see that many of the best insights of determin-
istic approaches (e.g. in the axiomatic BDI tradition
and in the planning literature) can be preserved, of-
ten in less brittle forms, in a probabilistic setting.
1.1 Probabilistic modelling ideas
Our approach to resolving anaphora (and dialogue
moves) was to generate a probability distribution of
the random variable of interest (e.g. salience of ref-
erent) and then choose the value of the variable cor-
responding to the highest probability as the interpre-
tation (e.g. the referent). This decision has a theo-
retical justification that can be found in a theorem in
(Parikh, 1990) in the context of his game-theoretic
model of language use. The theorem states that un-
der certain conditions (which hold in our context)
the correct interpretation of an utterance is the most
likely one.
2 Interpretation and Generation
The two major aspects of dialogue management are
the interpretation of incoming (user) utterances, and
the timely and appropriate generation of utterances
by the dialogue system. To cover these aspects we
have constructed a Bayes Net as shown in Figure 1.
     Philadelphia, July 2002, pp. 125-128.  Association for Computational Linguistics.
                  Proceedings of the Third SIGdial Workshop on Discourse and Dialogue,
In the implementation of this network we used
CIspace’s Java-based Bayes Net toolkit.2
The conditional probability table for the nodes
representing the dialogue move at time a0 and
salience list at time a0 are obviously the core of
the network. These tables are too large to present
in this paper. We constructed them by hand, us-
ing heuristics gained from experience in program-
ming rule-based dialogue systems. In future, the ta-
bles could be learned from data, or could instantiate
continuous-valued functions of rule-based systems.
Salience
List
t−1
System
Utterancet
User 
DialogueMove
t
User
Dialogue
Movet−1
Dialogue
Move
System
t−1
List
Salience
t
t
Activity
Input 
User 
Logical 
Form t
Figure 1: A Prototype Bayes Net for dialogue man-
agement
3 Anaphora resolution
Several different factors enter into the resolution of
anaphora in a dialogue. How recently a potential
referent was referred to is one important factor, an-
other is the embedding activity within which the
anaphoric reference was made (e.g. the type of verb
phrase in which the referent appears), a third is the
intra-sentential location of the relevant noun phrases
in the preceding dialogue, a fourth is the relative
prominence of a potential referent in the dialogue
situation, and so on. The basic idea is that condi-
2www.cs.ubc.ca/labs/lci/CIspace/
tional probability distributions are generated dynam-
ically in the Bayesian network. When we look at a
distribution corresponding to a node we are inter-
ested in, then the most salient object in the context
will be the one whose value has the highest proba-
bility.
We point out that an obvious deterministic way
to rank different combinations of factors (in an
optimality-theoretic way, for example), and choose
the most salient object based on this ranking, does
not seem to work – because any potential ranking
of principles (e.g. “Recency overrides subject place-
ment”) would have to be context-dependent, and this
defeats the idea of a ranking. See the examples in
Figures 5 and 6.
3.1 Examples
Here we work with two basic activities of the
WITAS robot helicopter (see (Lemon et al., 2002))
which our dialogue system interfaces to – moving
and searching. The helicopter can move to vari-
ous landmarks (e.g. the tower, the church) and way-
points, and can see various objects (e.g. landmarks,
vehicles). Our results use the network in Figure 1. In
reading the tables (the figures appear after the refer-
ences), use the following key:
U=user, S=system, r=red car, g=green car,
w=waypoint, s= search, m=move. All examples
start with an even distribution of 0.2 for all variables
(all objects are equally salient) at the start of each
dialogue.
3.1.1 Activity and recency
We will start with what may be the simplest type
of example of anaphoric reference, in Figure 2. Here
it is intuitively clear that “it” is intended to pick out
the green car. The contribution of “see it” is mod-
elled as an observed even distribution over all possi-
ble referents which can be seen (i.e. a1a3a2 and a4a5a2 each
get a 0.5 weight). The conditional probability table
for Salience List at time a0 is then used to compute the
new probability distribution over the object-activity
pairs (a1a7a6a9a8a10a4a11a6a9a8a13a12a14a6a9a8a13a1a3a2a11a8a10a4a5a2 ). Here we see that the
green car is the most salient after the user’s second
utterance (a4a11a6 ), and that this salience increases after
the utterance “it”, because a4 was both the most re-
cent NP, and is also a possible object in the context
of the “seeing” activity.
In the example in Figure 3, the anaphoric pronoun
“it” should pick out the red car and not the waypoint,
even though the waypoint was referred to more re-
cently. Intuitively, this is because the embedding ac-
tivity of looking for the red car is tied to the pro-
noun, and this fact overrides the most recent refer-
ent. Here, the waypoint is not a possible object in
the “seeing” activity, whereas the red car has been
introduced as part of that activity. Thus the pronoun
“it” in the user’s final utterance has the effect of rais-
ing the probabilities of all the objects which can be
seen, and this in fact overrides the recency effect of
the utterance of “waypoint”.
An extended example (not shown) shows how ac-
tivity information can outweigh recency in an inter-
leaved fashion and then that a newly introduced ref-
erent can become the most salient. Having consid-
ered the ways in which activity and recency interact
in determining salience for anaphoric resolution, we
then investigated adding another determining factor
in the model – the syntactic placement of the refer-
ring expression.
3.1.2 Placement, activity, and recency
Figure 4 shows how subject placement influences
availability for anaphoric reference. Here, the sub-
ject (“red car”) of the user’s second utterance is in-
tuitively the one picked out by the later anaphoric
expression, and not the green car, even though “the
green car” is the most recent NP. See Figure 4 for our
results, using an extension of the network in Figure
1, where the “Activity a0 ” node was enriched to in-
clude syntactic information about the input – specif-
ically, what referring expressions appear in subject
and object places. Note here that the red car be-
comes the most salient object after the user’s sec-
ond utterance. We model the referential import of
this sentence as an input triple “a1a1a0 a4 ”to the Activ-
ity a0 node – denoting: red car (subject), no activity,
green car (object). The updated table for this node
ensures that objects in subject place are given more
weight than those in object place.
In Figure 5, the subject (“red car”) of the user’s
second utterance is intuitively the one picked out by
the later anaphoric expression, and not the green car,
even though “the green car” is involved in the “see-
ing” activity.
In Figure 6 the red car is most salient after the
second utterance, but the waypoint becomes more
salient, even though the red car was in subject po-
sition, because the waypoint is involved in the ac-
tivity of moving, as is the pronoun “it”, and so is
a better candidate for anaphoric resolution. Com-
bined with Figure 5 this shows that no static ranking
of anaphoric binding principles will cover all situ-
ations, and that a probabilistic approach is useful –
even as a theoretical model.
Obviously this model could be made more com-
plex with representations for direct and indirect ob-
jects, and so forth, but we leave this for future work.
4 Conclusion
We presented a Bayes Net which we have imple-
mented to deal with dialogue move interpretation
and reference resolution, and gave examples of its
use for weighing a variety of factors (recency, activ-
ity, placement) in anaphoric resolution in particular.
We saw that many of the insights of deterministic ap-
proaches (e.g. the WITAS Project, see (Lemon et al.,
2002)) can be preserved, often in less brittle forms,
in a probabilistic setting. We also have unpublished
results for dialogue move classification.

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