🚀 go-pugleaf

           Department of Computer Science, University of Toronto
              (GB = Galbraith Building, 35 St. George Street)

       -------------------------------------------------------------

                                    AI
              GB221, at 11:00 a.m., Thursday 14 January 1993

                               Adam J. Grove
                          NEC Research Institute

                       " From Statistics to Beliefs"

  An intelligent agent must make decisions even if it lacks complete
knowledge about the world. One general approach to this problem is to use
the facts that are known, and assign degrees of belief to other assertions
whose truth is uncertain.

  I will talk about three techniques for assigning degrees of belief.  All
three can be viewed as applications of (subjective) probability theory,
where the probability distribution is determined by the principle of
indifference. That is, they assign equal degree of belief to all basic
``situations'' consistent with the knowledge base. The methods differ
because there are competing intuitions about what the basic situations are.

  Various natural patterns of reasoning, such as the preference for the
most specific statistical data available, turn out to follow from some or
all of the techniques. This is an improvement over earlier theories, such
as work on direct inference and reference classes, which arbitrarily
postulate these patterns with no deeper explanation nor a guarantee of
consistency.

  The three methods we investigate have surprising characterizations: there
are connections to the principle of maximum entropy, a principle of maximal
independence, and a `center of mass' principle. These connections hold only
if the language uses unary predicates exclusively. This is particularly
interesting in first case, because although our methods makes sense for
more general languages, there seems to be no parallel extension to the
widely-used maximum entropy principle.

  Finally, I will briefly discuss some connections between the three
methods.  These connections give insight into how and why the specific
language chosen (for the knowledge base) is much more critical in inductive
reasoning than it is for traditional deductive logic.

(This is joint work with Fahiem Bacchus (University of Waterloo), Joseph Y.
Halpern (IBM Almaden Research Center), and Daphne Koller (Stanford
University).)