✦ LIBER ✦

Fractal dimension and logarithmic loss unpredictability

✍ Scribed by John M. Hitchcock

Book ID: 104325806
Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 217 KB
Volume: 304
Category: Article
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(03)00138-5

No coin nor oath required. For personal study only.

✦ Synopsis

We show that the Hausdor dimension equals the logarithmic loss unpredictability for any set of inÿnite sequences over a ÿnite alphabet. Using computable, feasible, and ÿnite-state predictors, this equivalence also holds for the computable, feasible, and ÿnite-state dimensions. Combining this with recent results of Fortnow and Lutz (Proc. 15th Ann. Conf. on Comput. Learning Theory (2002) 380), we have a tight relationship between prediction with respect to logarithmic loss and prediction with respect to absolute loss.

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