Conditional independence and
natural conditional functions. International Journal of Approximate
Reasoning 12 (1995), n. 1, pp. 43-68.
- The concept of conditional independence within the
framework of Spohn's theory of natural conditional functions is studied.
Basic properties of conditional independence within this framework
are recalled and further results analogical to the results concerning
stochastic conditional independence are proved. First, the intersection
of two conditional independence models is shown to be a conditional
independence model. Using this result it is proved that the conditional
independence models for natural conditional functions have no finite
complete axiomatic characterization (by means of a simple deductive
system describing relationships among conditional independence statements).
The last part is devoted to the marginal problem for natural conditional
functions: it is shown that the (pairwise) consonancy is equivalent to the
consistency iff the running intersection property holds.
- AMS classification 68T30
- natural conditional function
- conditional independence
- axiomatic characterization
- marginal problem
- running intersection property
postscript version (361 kB) is available.
The paper builds on the following works:
- P.P. Shenoy: Conditional independence in valuation-based
systems. International Journal of Approximate Reasoning
10 (1994), n. 3, pp. 203-234.
- W. Spohn:
Ordinal conditional functions: a dynamic theory of epistemic
states. In Causation in Decision, Belief Change, and Statistics
volume II. (W.L. Harper, B. Skyrms eds.), Kluwer, Dordrecht
1988, pp. 105-134.
- D. Hunter: Graphoids and natural conditional functions.
International Journal of Approximate Reasoning
5 (1991), pp. 485-504.
- M. Studeny:
Conditional independence relations have no finite complete
characterization. In Information Theory, Statistical Decision Functions
and Random Processes. Transactions of the 11th Prague Conference vol. B
(S. Kubik, J.A. Visek eds.), Kluwer, Dordrecht - Boston - London
(also Academia, Prague) 1992, pp. 377-396.