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.
Solomonoff induction on a random string
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.