منابع مشابه
On semimeasures predicting Martin-Löf random sequences
Solomonoff’s central result on induction is that the prediction of a universal semimeasureM converges rapidly and with probability 1 to the true sequence generating predictor μ, if the latter is computable. Hence, M is eligible as a universal sequence predictor in case of unknown μ. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Löf)...
متن کاملOn Semimeasures Predicting Martin-Loef Random Sequences
Solomonoff’s central result on induction is that the prediction of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating predictor μ, if the latter is computable. Hence, M is eligible as a universal sequence predictor in case of unknown μ. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Löf...
متن کاملUpper semicomputable sumtests for lower semicomputable semimeasures
A sumtest for a discrete semimeasure P is a function f mapping bitstrings to non-negative rational numbers such that ∑ P (x)f(x) ≤ 1 . Sumtests are the discrete analogue of Martin-Löf tests. The behavior of sumtests for computable P seems well understood, but for some applications lower semicomputable P seem more appropriate. In the case of tests for independence, it is natural to consider uppe...
متن کاملInfluence tests I: ideal composite hypothesis tests, and causal semimeasures
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete timeseries is defined using generalized structural equations. Several ideal tests are introduced, and it is argued that when Halting information is transmitted...
متن کاملUniversal Convergence of Semimeasures on Individual Random Sequences ∗ Marcus Hutter
Solomonoff’s central result on induction is that the posterior of a universal semimeasureM converges rapidly and with probability 1 to the true sequence generating posterior μ, if the latter is computable. Hence, M is eligible as a universal sequence predictor in case of unknown μ. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Löf) ...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2017
ISSN: 0029-4527
DOI: 10.1215/00294527-3839446