Frequency Prediction of Functions

Prediction of functions is one of processes considered in inductive inference. There is a ”black box” with a given total function f in it. The result of the inductive inference machine F (< f(0), f(1), · · · , f(n) > ) is expected to be f(n + 1). Deterministic and probabilistic prediction of functions has been widely studied. Frequency computation is a mechanism used to combine features of deterministic and probabilistic algorithms. Frequency computation has been used for several types of inductive inference, especially, for learning via queries. We study frequency prediction of functions and show that that there exists an interesting hierarchy of predictable classes of functions.