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- W1531193245 abstract "Solomonoff's optimal but noncomputable method for inductive inference assumes that observation sequences x are drawn from an recursive prior distribution µ(x). Instead of using the unknown µ(x) he predicts using the celebrated universal enumerable prior M(x) which for all x exceeds any recursive µ(x), save for a constant factor independent of x. The simplicity measure M(x) naturally implements Occam's razor and is closely related to the Kolmogorov complexity of x. However, M assigns high probability to certain data x that are extremely hard to compute. This does not match our intuitive notion of simplicity. Here we suggest a more plausible measure derived from the fastest way of computing data. In absence of contrarian evidence, we assume that the physical world is generated by a computational process, and that any possibly infinite sequence of observations is therefore computable in the limit (this assumption is more radical and stronger than Solomonoff's). Then we replace M by the novel Speed Prior S, under which the cumulative a priori probability of all data whose computation through an optimal algorithm requires more than O(n) resources is 1/n. We show that the Speed Prior allows for deriving a computable strategy for optimal prediction of future y, given past x. Then we consider the case that the data actually stem from a nonoptimal, unknown computational process, and use Hutter's recent results to derive excellent expected loss bounds for S-based inductive inference. We conclude with several nontraditional predictions concerning the future of our universe." @default.
- W1531193245 created "2016-06-24" @default.
- W1531193245 creator A5071172037 @default.
- W1531193245 date "2002-01-01" @default.
- W1531193245 modified "2023-09-27" @default.
- W1531193245 title "The Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions" @default.
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- W1531193245 doi "https://doi.org/10.1007/3-540-45435-7_15" @default.
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