28 - Bayesian Networks

Summary

Representing Probabilities in Networks

Much human reasoning is about propositions and quantities that are uncertain. Our beliefs about many things are provisional (that is, subject to change) and qualified (that is, having various levels of confidence). AI systems, too, need to be able to deal with uncertain information. An AI agent's facts, statements, and rules should most appropriately be thought of as provisional and qualified. After all, some of its information is provided by humans and some originates from sensors with limited precision and reliability. Yet, much of the early work in AI ignored the uncertain nature of knowledge. In fact, Marvin Minsky observed that his edited volume of early AI papers contained “no explicit use of probabilistic notions.”

Most AI researchers nowadays, however, acknowledge that much of the knowledge needed by machines needs to be qualified by probability values and that reasoning with this knowledge can therefore most appropriately be done with the tools of probability theory. But just as is the case with logical reasoning, probabilistic reasoning is subject to AI's old nemesis, the combinatorial explosion. Suppose, for example, that an agent's knowledge consists of a set of propositions. Because of possible interdependencies among the propositions, accurate probabilistic reasoning depends on knowing more than just the probability of each of those propositions individually. Instead, probability values for various combinations of the propositions taken together, called “joint probabilities,” are usually required; this leads, in the general case, to impractically large representations and intractable computations.

Earlier AI systems that could deal with uncertainty, such as MYCIN and PROSPECTOR, made simplifying assumptions to ease these representational and computational difficulties.