The theory of Bayesian networks is very promising as a means of reasoning under uncertainty. However it is not easy to determine an appropriate network. Two standard ways of fixing an AI model are knowledge elicitation from an expert and machine learning from data. While an expert can usually provide a graph representing the known causal relations within her field, she can have problems providing the probabilities which must accompany it. On the other hand it is relatively simple for a machine to determine probabilities from a database yet it can be hard to find an appropriate graph to make up the Bayesian network. Thus an expert is often asked for a causal graph while a machine determines the associated probabilities.
Unfortunately even this compromise can prove inadequate on its own, since
Bayesian network theory imposes a strong independence assumption on the network
which may not in fact hold. Consequently we propose a two-stage methodology for
Bayesian networks:
-1 Qualitative elicitation. The expert provides a causal
graph.
-2 Restructuring and quantitative augmentation. The causal graph is
transformed into a graph for which the independence assumption holds relative to
probabilities found by machine.
We thus face three key questions:
- Which philosophical interpretations of
causality and probability will provide foundations for Bayesian networks? In
particular we are interested in the extent to which these notions are subjective
or objective.
- How do we decide whether the independence assumption is
satisfied? The main alternatives appear to be direct statistical testing versus
assessing the reliability of the derived Bayesian network in practice.
- How
can one best transform the causal network into a Bayesian network that satisfies
independence? We need to assess various strategies here including deleting and
inserting nodes, adding arrows, and subjective re-appraisal.
For more on the two-stage methodology see:
pai_jw_00_f: Jon Williamson: "Foundations for Bayesian networks", to appear in David Corfield & Jon Williamson(eds.): `Philosophical aspects of Bayesianism', Postscript, Zipped postscript.
For more on the qualitative / quantitative aspect visit http://q-squared.doc.ic.ac.uk/