4 ms·

Perhaps the most general model is that of algorithmic probability (the probability of a string being output when inputting random strings into a Universal Turin

Perhaps the most general model is that of algorithmic probability (the probability of a string being output when inputting random strings into a Universal Turing Machine): https://en.wikipedia.org/wiki/Algorithmic_probability https://en.wikipedia.org/wiki/Algorithmic_probability. See also Solomonoff induction and the universal semimeasure.

nonbel 8y ago
Sorry, but I really have no patience for these purely "philosophical" discussions of probability. I don't see a single equation on that page but I can assure you that to compute a probability you are assuming some form of the likelihood, ie the way you calculate P(D|H), applies to your problem.
- antidesitter 8y ago
  Sorry, but I really have no patience for these purely "philosophical" discussions of probability. I’m not sure what you mean by this. Can you elaborate? I don't see a single equation on that page If equations are what you’re looking for, here are a few good starting points: https://link.springer.com/chapter/10.1007/978-0-387-84816-7_1 https://link.springer.com/chapter/10.1007/978-0-387-84816-7_... (Ray Solomonoff, founder of algorithmic information theory) https://www.springer.com/gp/book/9783540221395 https://www.springer.com/gp/book/9783540221395 (Marcus Hutter) https://link.springer.com/book/10.1007/978-3-642-44958-1 https://link.springer.com/book/10.1007/978-3-642-44958-1 but I can assure you that to compute a probability you are assuming some form of the likelihood, ie the way you calculate P(D|H), applies to your problem. You should really take the time to read the Scholarpedia article (or above sources) on algorithmic probability and Solomonoff induction. It’s one of the most beautiful and elegant examples of mathematically formalizing perennial philosophical intuitions. The reason I brought up algorithmic probability is because there is a precise mathematical sense in which it is “optimal”. Again, I encourage you to read about universal semimeasures.
  - nonbel 8y ago
    >">Sorry, but I really have no patience for these purely "philosophical" discussions of probability. I’m not sure what you mean by this. Can you elaborate?" There is nothing in that link that I can apply to a problem. It is all too general and abstract. What I wanted to see is any example of algorithmic probability being applied to a real world problem. I am certain that to calculate the probability they need to define/derive a model of the phenomenon being modeled to use as the likelihood. Also, I don't have easy access to those books, nor do I want to get them and flip through looking for what you are talking about, but if I did I am sure I would find that the probability calculation requires a model.
    - antidesitter 8y ago
      Solomonoff's article is available here: http://www.raysolomonoff.com/publications/alp-theory-and-applications.pdf http://www.raysolomonoff.com/publications/alp-theory-and-app.... This is also a good guide: https://arxiv.org/pdf/cs/0703024.pdf https://arxiv.org/pdf/cs/0703024.pdf. There is nothing in that link that I can apply to a problem. It is all too general and abstract. Algorithmic probability is a framework for general prediction, so it has applications in reinforcement learning (see AIXI), grammar discovery in linguistics, text compression, continuation of integer sequences, etc. See http://www.scholarpedia.org/article/Applications_of_algorithmic_information_theory http://www.scholarpedia.org/article/Applications_of_algorith.... I am certain that to calculate the probability they need to define/derive a model of the phenomenon being modeled to use as the likelihood... I am sure I would find that the probability calculation requires a model Yes, and that model is a universal computer, as stated in the articles I linked to.
      - nonbel 8y ago
        >"Yes, and that model is a universal computer, as stated in the articles I linked to." This basically says "the model is anything at all". From the first example in the first link, I see the probability in that case is conditional on the binomial model correctly describing the phenomenon (equation 8). This is what I expected is going on.

nonbel 8y ago

Sorry, but I really have no patience for these purely "philosophical" discussions of probability. I don't see a single equation on that page but I can assure you that to compute a probability you are assuming some form of the likelihood, ie the way you calculate P(D|H), applies to your problem.

antidesitter 8y ago
Sorry, but I really have no patience for these purely "philosophical" discussions of probability. I’m not sure what you mean by this. Can you elaborate? I don't see a single equation on that page If equations are what you’re looking for, here are a few good starting points: https://link.springer.com/chapter/10.1007/978-0-387-84816-7_1 https://link.springer.com/chapter/10.1007/978-0-387-84816-7_... (Ray Solomonoff, founder of algorithmic information theory) https://www.springer.com/gp/book/9783540221395 https://www.springer.com/gp/book/9783540221395 (Marcus Hutter) https://link.springer.com/book/10.1007/978-3-642-44958-1 https://link.springer.com/book/10.1007/978-3-642-44958-1 but I can assure you that to compute a probability you are assuming some form of the likelihood, ie the way you calculate P(D|H), applies to your problem. You should really take the time to read the Scholarpedia article (or above sources) on algorithmic probability and Solomonoff induction. It’s one of the most beautiful and elegant examples of mathematically formalizing perennial philosophical intuitions. The reason I brought up algorithmic probability is because there is a precise mathematical sense in which it is “optimal”. Again, I encourage you to read about universal semimeasures.
- nonbel 8y ago
  >">Sorry, but I really have no patience for these purely "philosophical" discussions of probability. I’m not sure what you mean by this. Can you elaborate?" There is nothing in that link that I can apply to a problem. It is all too general and abstract. What I wanted to see is any example of algorithmic probability being applied to a real world problem. I am certain that to calculate the probability they need to define/derive a model of the phenomenon being modeled to use as the likelihood. Also, I don't have easy access to those books, nor do I want to get them and flip through looking for what you are talking about, but if I did I am sure I would find that the probability calculation requires a model.
  - antidesitter 8y ago
    Solomonoff's article is available here: http://www.raysolomonoff.com/publications/alp-theory-and-applications.pdf http://www.raysolomonoff.com/publications/alp-theory-and-app.... This is also a good guide: https://arxiv.org/pdf/cs/0703024.pdf https://arxiv.org/pdf/cs/0703024.pdf. There is nothing in that link that I can apply to a problem. It is all too general and abstract. Algorithmic probability is a framework for general prediction, so it has applications in reinforcement learning (see AIXI), grammar discovery in linguistics, text compression, continuation of integer sequences, etc. See http://www.scholarpedia.org/article/Applications_of_algorithmic_information_theory http://www.scholarpedia.org/article/Applications_of_algorith.... I am certain that to calculate the probability they need to define/derive a model of the phenomenon being modeled to use as the likelihood... I am sure I would find that the probability calculation requires a model Yes, and that model is a universal computer, as stated in the articles I linked to.
    - nonbel 8y ago
      >"Yes, and that model is a universal computer, as stated in the articles I linked to." This basically says "the model is anything at all". From the first example in the first link, I see the probability in that case is conditional on the binomial model correctly describing the phenomenon (equation 8). This is what I expected is going on.