Two Kinds of Probabilistic Induction

Problems in probabilistic induction are of two general kinds. In the first, we have a linearly ordered sequence of symbols that must be extrapolated. In the second we want to extrapolate an unordered set of finite strings. A very general formal solution to the first kind of problem is well known and much work has been done in obtaining good approximations to it [LI 93, Ris 78, Ris 89, Sol 64a, Sol 64b, Sol 78, Wal 68]. Though the second kind of problem is of much practical importance, no general solution has been published. We present two general solutions for unordered data. We also show how machines can be constructed to summarize sequential and unordered data in optimum ways.

• Type: Journal
• Year: 1999
• Where: CJ
• Authors: Ray J. Solomonoff
• Keywords: CJ 1999, General, General Formal Solution, Unordered Set