|Title:||The nonprobabilistic approach to learning the best prediction|
|Series:||Linköping Electronic Articles
in Computer and Information Science
|Issue:||Vol. 6 (2001), No. 016|
|Abstract:|| The problem of predicting a sequence
The new approach is to consider a set of all infinite sequences (over a given finite alphabet) and estimate the size of sets of predictable sequences with the help of the Hausdorff dimension. This approach enables us first, to show that there exist large sets of well predictable sequences which have zero measure for each stationary and ergodic measure. (In fact, it means that such sets are invisible in the framework of the ergodic and stationary source model and shows the necessity of the new approach.) Second, it is shown that there exist quite large sets of such sequences that can be predicted well by complex algorithms which use not only estimations of conditional probabilities.
| Original publication