Fractal dimension and logarithmic loss unpredictability
نویسنده
چکیده
We show that the Hausdorff dimension equals the logarithmic loss unpredictability for any set of infinite sequences over a finite alphabet. Using computable, feasible, and finite-state predictors, this equivalence also holds for the computable, feasible, and finite-state dimensions. Combining this with recent results of Fortnow and Lutz (2002), we have a tight relationship between prediction with respect to logarithmic loss and prediction with respect to absolute loss.
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ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 1-3 شماره
صفحات -
تاریخ انتشار 2003