Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 the case of unknown μ. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Lof) random sequences remained open. Such a convergence result would be particularly interesting and natural, since randomness can be defined in terms of M itself.  show that there are universal semimeasures M which do not converge to μ on all μ-random sequences, i.e.  give a partial negative ansr to the open problem.  also provide a positive ansr for some non-universal semimeasures.  define the incomputable measure D as a mixture over all computable measures and the enumerable semimeasure W as a mixture over all enumerable nearly measures.  show that W converges to D and D to μ on all random sequences. The Hellinger distance measuring closeness of two distributions plays a central role.
['Marcus Hutter', 'Andrej Muchnik']
I am writing a research paper on a idea On semimeasures predicting Martin-Löf random sequences
[{"from": "human", "value": "I am writing a research paper on a idea On semimeasures predicting Martin-L\u00f6f random sequences"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 \u03bc, if the latter is computable. Hence, M is eligible as a universal sequence predictor in the case of unknown \u03bc. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Lof) random sequences remained open. Such a convergence result would be particularly interesting and natural, since randomness can be defined in terms of M itself.  show that there are universal semimeasures M which do not converge to \u03bc on all \u03bc-random sequences, i.e.  give a partial negative ansr to the open problem.  also provide a positive ansr for some non-universal semimeasures.  define the incomputable measure D as a mixture over all computable measures and the enumerable semimeasure W as a mixture over all enumerable nearly measures.  show that W converges to D and D to \u03bc on all random sequences. The Hellinger distance measuring closeness of two distributions plays a central role."}]