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.
So, I've been hearing a lot about the awesomeness of Solomonoff induction, at least as a theoretical framework. However, my admittedly limited understanding of Solomonoff induction suggests that it would form an epicly bad hypothesis if given a random string. So my question is, if I misunderstood, how does it deal with randomness? And if I understood correctly, isn't this a rather large gap?
Edit: Thanks for all the comments! My new understanding is that Solomonoff induction is able to understand that it is dealing with a random string (because it finds itself giving equal weight to programs that output a 1 or a 0 for the next bit), but despite that is designed to keep looking for a pattern forever. While this is a horrible use of resources, the SI is a theoretical framework that has infinite resources, so that's a meaningless criticism. Overall this seems acceptable, though if you want to actually implement a SI you'll need to instruct it on giving up. Furthermore, the SI will not include randomness as a distinct function in its hypothesis, which could lead to improper weighting of priors, but will still have good predictive power -- and considering that Solomonoff induction was only meant for computable functions, this is a pretty good result.