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Consistent Dependency Networks
For several years, we used Bayesian networks to help individuals
visualize predictive relationships learned from data. When using this
representation in problem domains ranging from webtraffic analysis to
collaborative filtering, these individuals expressed a single, common
criticism. We developed dependency networks in response to this
criticism. In this section, we introduce a special case of the
dependencynetwork representation and show how it addresses this
complaint.
Consider Figure 1a, which contains a portion of a
Bayesiannetwork structure describing the demographic characteristics
of visitors to a web site. We have found that, when shown graphs like
this one and told they represent causal relationships, an untrained
person often gains an accurate impression of the relationships. In
many situations, however, a causal interpretation of the graph is
suspectfor example, when one uses a computationally efficient
learning procedure that excludes the possibility of hidden variables.
In these situations, the person only can be told that the
relationships are ``predictive'' or ``correlational.'' In these
cases, we have found that the Bayesian network becomes confusing. For
example, untrained individuals who look at Figure 1a will
correctly conclude that Age and Gender are predictive of Income, but
will wonder why there are no arcs from Income to Age and to
Genderafter all, Income is predictive of Age and Gender.
Furthermore, these individuals will typically be surprised to learn
that Age and Gender are dependent given Income.
Figure 1:
(a) A portion of a Bayesiannetwork structure describing
the demographic characteristics of users of a web site. (b) The
corresponding consistent dependencynetwork structure.

Of course, people can be trained to appreciate the (in)dependence
semantics of a Bayesian network, but often they lose interest in the
problem before gaining an adequate understanding; and, in almost all
cases, the mental activity of computing the dependencies interferes
with the process of gaining insights from the data.
To avoid this difficulty, we can replace the Bayesiannetwork
structure with one where the parents of each variable correspond to
its Markov blanketthat is, a structure where the parents of each
variable render that variable independent of all other variables. For
example, the Bayesiannetwork structure of Figure 1a
becomes that of Figure 1b. Equally important, we do not
change the feature of Bayesian networks wherein the conditional
probability of a variable given its parents is used to quantify the
dependencies. In our experience, individuals are quite comfortable
with this feature. Roughly speaking, the resulting model is a
dependency network.
Subsections
Next: Definition and Basic Properties
Up: Dependency Networks for Inference,
Previous: Introduction
Journal of Machine Learning Research,
20001019