Remember that SI works by accounting for all the infinite multitude of hypothesis that can generate the given string. Given an algorithmically random TB of data, SI will take into consideration surely a TB hypothesis with high probability but also all the bigger hypothesis with exponentially lower probabilities.
OK, so it will predict one of multiple different ~ 1 terabyte programs as having different likelihoods. I’d still rather it predict random{0,1} for less than 10 bytes, as the most probable. Inability to recognize noise as noise seems like a fundamental problem.
There is an SI that works over programs (which I was referring to originally), and there is an SI that works over computable distributions (that will produce random{0,1} with high probability).
No, it will always make a prediction according to the the infinitely many programs which are consistent with the observed string. In the observed string is 1 terabyte of uniform random noise, the shortest of these programs will be most likely ~ 1 terabyte long, but Solomonoff induction also considers the longer ones.
Remember that SI works by accounting for all the infinite multitude of hypothesis that can generate the given string. Given an algorithmically random TB of data, SI will take into consideration surely a TB hypothesis with high probability but also all the bigger hypothesis with exponentially lower probabilities.
OK, so it will predict one of multiple different ~ 1 terabyte programs as having different likelihoods. I’d still rather it predict random{0,1} for less than 10 bytes, as the most probable. Inability to recognize noise as noise seems like a fundamental problem.
random{0,1} is not an algorithm, so...
Explained here.
There is an SI that works over programs (which I was referring to originally), and there is an SI that works over computable distributions (that will produce random{0,1} with high probability).
No, it will always make a prediction according to the the infinitely many programs which are consistent with the observed string. In the observed string is 1 terabyte of uniform random noise, the shortest of these programs will be most likely ~ 1 terabyte long, but Solomonoff induction also considers the longer ones.