SI doesn’t put all its mass on the single machine that predicts the universe, it allocates mass to all machines that have not yet erred in proportion to their simplicity,
If your SI can’t make predictions ITFP, that’s rather beside the point. “Not erring” only has a straightforward implementation if you are expecting the predictions to be deterministic. How could an SI compare a deterministic theory to a probablistic one?
How could an SI compare a deterministic theory to a probablistic one?
The deterministic theory gets probability proportional to 2^-length + (0 if it was correct so far else -infty), the probabilistic theory gets probability proportional to 2^-length + log(probability it assigned to the observations so far).
That said, I was not suggesting a solomonoff inductor in which some machines were outputting bits and others were outputting probabilities.
I suspect that there’s a miscommunication somewhere up the line, and my not-terribly-charitable-guess is that it stems from you misunderstanding the formalism of Solomonoff induction and/or the point I was making about it. I do not expect to clarify further, alas. I’d welcome someone else hopping in if they think they see the point I was making & can transmit it.
If your SI can’t make predictions ITFP, that’s rather beside the point. “Not erring” only has a straightforward implementation if you are expecting the predictions to be deterministic. How could an SI compare a deterministic theory to a probablistic one?
The deterministic theory gets probability proportional to 2^-length + (0 if it was correct so far else -infty), the probabilistic theory gets probability proportional to 2^-length + log(probability it assigned to the observations so far).
That said, I was not suggesting a solomonoff inductor in which some machines were outputting bits and others were outputting probabilities.
I suspect that there’s a miscommunication somewhere up the line, and my not-terribly-charitable-guess is that it stems from you misunderstanding the formalism of Solomonoff induction and/or the point I was making about it. I do not expect to clarify further, alas. I’d welcome someone else hopping in if they think they see the point I was making & can transmit it.