
We outline a method for quantifying the error of a sequence prediction. With sequence predictions represented by semimeasures $ u(x)$ we define their error to be $-log_2 u(x)$. We note that enumerable semimeasures are those which model the sequence as the output of a computable system given unknown input. Using this we define the simulation complexity of a computable system $C$ relative to another $U$ giving an emph{exact} bound on their difference in error. This error in turn gives an exact upper bound on the number of predictions $ u$ gets incorrect.
Solomonoff induction, Sequence prediction, enumerable semimeasures, 004
Solomonoff induction, Sequence prediction, enumerable semimeasures, 004
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