Marco presented us with examples of ordinary or "natural" reasoning which are not accounted for in most theories of inference, causality, or rationality. Consider the following cases: Martha's lawn is wet. There are two possible causes for this: her sprinkler-system might have been on or it might have rained. While we don't know what was actually the case, the fact of her lawn being wet makes both of these possible causes appear more likely. In other words, as Marco pointed out, our inferences can move in opposite directions: the causal direction (if we know that it rained, we can explain and predict that the lawn is wet) and the evidentiary direction (if we know that the lawn is wet, we reason toward likely causes). Many theories of causal inference cannot handle this bi-directionality. While it is easy to reason from known causes to their effects, it is harder to model our reasoning from known effects to likely causes (on some accounts, this latter form of reasoning is fallacious). Let's continue our story by noting that the lawn of Martha's neighbor George is also wet. Assuming that they have separate sprinkler systems, we can now make the following inference: the fact that George's lawn is also wet makes it more likely that rain caused Martha's lawn to be wet and less likely that Martha's sprinkler system caused the wetness of her lawn. This inference comes quite naturally but is fairly complicated: Knowledge about George's lawn affects our assessment of the likelihood that Martha's sprinkler was on, i.e., the likelihood of an event that is rather distant in our network of beliefs about causal relations. Again, such distant effects in a network of beliefs are difficult to model by many extant theories.
Marco suggests that "Bayesian Belief Networks" provide such modeling, and in his work at USC's Artificial Intelligence Laboratory he implements Bayesian Networks in expert systems. The potential benefits of this are readily apparent: Looking at disease, for example, a symptom increases the likelihood of a precipitating event and of a diagnosis; a precipitating event increases the likelihood of symptoms and diagnosis; a diagnosis increases the likelihood of symptoms and precipitating events. For the purpose of explanation and prediction, it doesn't really matter where and with what information one enters the network of belief. If we can calculate the total probability for the entire network, we can see very quickly how information about some node in the network becomes distributed to revised probability-assessments at all other nodes throughout the network. This can tell us, for example, what (additional) evidence I might need to decide between various diagnoses which are all compatible with the presenting symptoms.
Unfortunately, there was not enough time to discuss Marco's further-reaching philosophical claim that Bayesian Networks (and its associated independence-based semantics) solve long-standing philosophical issues concerning causal inference. As with all Bayesian theories of inference, one would need to discuss in particular whether these networks presuppose an ideal situation where the causal relations in the entire network are already known. Until we continue this conversation, we must content ourselves with references to two 1995-articles: (with Young-Gyun Kim) "On the Detection of Conflicts in Diagnostic Bayesian Networks Using Abstraction" (in Besnard and Hanks, eds., Uncertainty in Artificial Intelligence, San Francisco: Morgan-Kaufmann, pp. 362-367); (with Moninder Singh) "Construction of Bayesian Belief Networks from Data: A Brief Survey and an Efficient Algorithm" (International Journal of Approximate Reasoning, 12:2, pp. 111-131). For abstracts and further information about USC's Bayesian Networks Group see its homepage at:
www.cs.sc.edu/RES_ACT/Bayes_Folder/Bayes.html.
Alfred Nordmann
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