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The sensitivity of belief networks to imprecise probabilities: an experimental investigation
Artificial Intelligence, 85 (1-2): 363 - 397 (1996)
DOI: DOI: 10.1016/0004-3702(96)00002-1
Аннотация
Bayesian belief networks are being increasingly used as a knowledge
representation for reasoning under uncertainty. Some researchers
have questioned the practicality of obtaining the numerical probabilities
with sufficient precision to create belief networks for large-scale
applications. In this work, we investigate how precise the probabilities
need to be by measuring how imprecision in the probabilities affects
diagnostic performance. We conducted a series of experiments on a
set of real-world belief networks for medical diagnosis in liver
and bile disease. We examined the effects on diagnostic performance
of (1) varying the mappings from qualitative frequency weights into
numerical probabilities, (2) adding random noise to the numerical
probabilities, (3) simplifying from quaternary domains for diseases
and findings--absent, mild, moderate, and severe--to binary domains--absent
and present, and (4) using test cases that contain diseases outside
the network. We found that even extreme differences in the probability
mappings and large amounts of noise lead to only modest reductions
in diagnostic performance. We found no significant effect of the
simplification from quaternary to binary representation. We also
found that outside diseases degraded performance modestly. Overall,
these findings indicate that even highly imprecise input probabilities
may not impair diagnostic performance significantly, and that simple
binary representations may often be adequate. These findings of robustness
suggest that belief networks are a practical representation without
requiring undue precision.
