Isn’t there a very wide middle ground between (1) assigning 100% of your mental probability to a single model, like a normal curve and (2) assigning your mental probability proportionately across every conceivable model ala Solomonoff?
I mean the whole approach here sounds more philosophical than practical. If you have any kind of constraint on your computing power, and you are trying to identify a model that most fully and simply explains a set of observed data, then it seems like the obvious way to use your computing power is to put about a quarter of your computing cycles on testing your preferred model, another quarter on testing mild variations on that model, another quarter on all different common distribution curves out of the back of your freshman statistics textbook, and the final quarter on brute-force fitting the data as best you can given that your priors about what kind of model to use for this data seem to be inaccurate.
I can’t imagine any human being who is smart enough to run a statistical modeling exercise yet foolish enough to cycle between two peaks forever without ever questioning the assumption of a single peak, nor any human being foolish enough to test every imaginable hypothesis, even including hypotheses that are infinitely more complicated than the data they seek to explain. Why would we program computers (or design algorithms) to be stupider than we are? If you actually want to solve a problem, you try to get the computer to at least model your best cognitive features, if not improve on them. Am I missing something here?
Isn’t there a very wide middle ground between (1) assigning 100% of your mental probability to a single model, like a normal curve and (2) assigning your mental probability proportionately across every conceivable model ala Solomonoff?
Yes, the question is what that middle ground looks like—how you actually come up with new models. Gelman and Shalizi say it’s a non-Bayesian process depending on human judgement. The behaviour that you rightly say is absurd, of the Bayesian Flying Dutchman, is indeed Shalizi’s reductio ad absurdum of universal Bayesianism. I’m not sure what gwern has just been arguing, but it looks like doing whatever gets results through the week while going to the church of Solomonoff on Sundays.
An algorithmic method of finding new hypotheses that works better than people is equivalent to AGI, so this is not an issue I expect to see solved any time soon.
An algorithmic method of finding new hypotheses that works better than people is equivalent to AGI, so this is not an issue I expect to see solved any time soon.
Eh. What seems AGI-ish to me is making models interact fruitfully across domains; algorithmic models to find new hypotheses for a particular set of data are not that tough and already exist (and are ‘better than people’ in the sense that they require far less computational effort and are far more precise at distinguishing between models).
The hypothesis-discovery methods are universal; you just need to feed them data. My view is that the hard part is picking what data to feed them, and what to do with the models they discover.
Edit: I should specify, the models discovered grow in complexity based on the data provided, and so it’s very difficult to go meta (i.e. run hypothesis discovery on the hypotheses you’ve discovered), because the amount of data you need grows very rapidly.
I don’t think any robot scientists would be eligible for Nobel prizes; Nobel’s will specifies persons. We’ve had robot scientists for almost a decade now, but they tend to excel in routine and easily automatized areas. I don’t think they will make Nobel-level contributions anytime soon, and by the time they do, the intelligence explosion will be underway.
Isn’t there a very wide middle ground between (1) assigning 100% of your mental probability to a single model, like a normal curve and (2) assigning your mental probability proportionately across every conceivable model ala Solomonoff?
I mean the whole approach here sounds more philosophical than practical. If you have any kind of constraint on your computing power, and you are trying to identify a model that most fully and simply explains a set of observed data, then it seems like the obvious way to use your computing power is to put about a quarter of your computing cycles on testing your preferred model, another quarter on testing mild variations on that model, another quarter on all different common distribution curves out of the back of your freshman statistics textbook, and the final quarter on brute-force fitting the data as best you can given that your priors about what kind of model to use for this data seem to be inaccurate.
I can’t imagine any human being who is smart enough to run a statistical modeling exercise yet foolish enough to cycle between two peaks forever without ever questioning the assumption of a single peak, nor any human being foolish enough to test every imaginable hypothesis, even including hypotheses that are infinitely more complicated than the data they seek to explain. Why would we program computers (or design algorithms) to be stupider than we are? If you actually want to solve a problem, you try to get the computer to at least model your best cognitive features, if not improve on them. Am I missing something here?
Yes, the question is what that middle ground looks like—how you actually come up with new models. Gelman and Shalizi say it’s a non-Bayesian process depending on human judgement. The behaviour that you rightly say is absurd, of the Bayesian Flying Dutchman, is indeed Shalizi’s reductio ad absurdum of universal Bayesianism. I’m not sure what gwern has just been arguing, but it looks like doing whatever gets results through the week while going to the church of Solomonoff on Sundays.
An algorithmic method of finding new hypotheses that works better than people is equivalent to AGI, so this is not an issue I expect to see solved any time soon.
Eh. What seems AGI-ish to me is making models interact fruitfully across domains; algorithmic models to find new hypotheses for a particular set of data are not that tough and already exist (and are ‘better than people’ in the sense that they require far less computational effort and are far more precise at distinguishing between models).
Yes, I had in mind a universal algorithmic method, rather than a niche application.
The hypothesis-discovery methods are universal; you just need to feed them data. My view is that the hard part is picking what data to feed them, and what to do with the models they discover.
Edit: I should specify, the models discovered grow in complexity based on the data provided, and so it’s very difficult to go meta (i.e. run hypothesis discovery on the hypotheses you’ve discovered), because the amount of data you need grows very rapidly.
Hmmm. Are we going to see a Nobel awarded to an AI any time soon?
I don’t think any robot scientists would be eligible for Nobel prizes; Nobel’s will specifies persons. We’ve had robot scientists for almost a decade now, but they tend to excel in routine and easily automatized areas. I don’t think they will make Nobel-level contributions anytime soon, and by the time they do, the intelligence explosion will be underway.