Advanced

Solomonoff Induction: A Solution to the Problem of the Priors?

Vallinder, Aron LU (2012) FTEM02 20122
Theoretical Philosophy
Abstract (Swedish)
In this essay, I investigate whether Solomonoff’s prior can be used to solve the problem of the priors for Bayesianism. In outline, the idea is to give higher prior probability to hypotheses that are "simpler", where simplicity is given a precise formal definition. I begin with a review of Bayesianism, including a survey of past proposed solutions of the problem of the priors. I then introduce the formal framework of Solomonoff induction, and go through some of its properties, before finally turning to some applications. After this, I discuss several potential problems for the framework. Among these are the fact that Solomonoff’s prior is incomputable, that the prior is highly dependent on the choice of a universal Turing machine to use in... (More)
In this essay, I investigate whether Solomonoff’s prior can be used to solve the problem of the priors for Bayesianism. In outline, the idea is to give higher prior probability to hypotheses that are "simpler", where simplicity is given a precise formal definition. I begin with a review of Bayesianism, including a survey of past proposed solutions of the problem of the priors. I then introduce the formal framework of Solomonoff induction, and go through some of its properties, before finally turning to some applications. After this, I discuss several potential problems for the framework. Among these are the fact that Solomonoff’s prior is incomputable, that the prior is highly dependent on the choice of a universal Turing machine to use in the definition, and the fact that it assumes that the hypotheses under consideration are computable. I also discuss whether a bias toward simplicity can be justified. I argue that there are two main considerations favoring Solomonoff’s prior: (i) it allows us to assign strictly positive probability to every hypothesis in a countably infinite set in a non-arbitrary way, and (ii) it minimizes the number of "retractions" and "errors" in the worst case. (Less)
Please use this url to cite or link to this publication:
author
Vallinder, Aron LU
supervisor
organization
course
FTEM02 20122
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Bayesianism, Problem of the Priors, Solomonoff Induction
language
English
id
3577211
date added to LUP
2013-09-05 09:16:49
date last changed
2013-09-05 09:16:49
@misc{3577211,
  abstract     = {In this essay, I investigate whether Solomonoff’s prior can be used to solve the problem of the priors for Bayesianism. In outline, the idea is to give higher prior probability to hypotheses that are "simpler", where simplicity is given a precise formal definition. I begin with a review of Bayesianism, including a survey of past proposed solutions of the problem of the priors. I then introduce the formal framework of Solomonoff induction, and go through some of its properties, before finally turning to some applications. After this, I discuss several potential problems for the framework. Among these are the fact that Solomonoff’s prior is incomputable, that the prior is highly dependent on the choice of a universal Turing machine to use in the definition, and the fact that it assumes that the hypotheses under consideration are computable. I also discuss whether a bias toward simplicity can be justified. I argue that there are two main considerations favoring Solomonoff’s prior: (i) it allows us to assign strictly positive probability to every hypothesis in a countably infinite set in a non-arbitrary way, and (ii) it minimizes the number of "retractions" and "errors" in the worst case.},
  author       = {Vallinder, Aron},
  keyword      = {Bayesianism,Problem of the Priors,Solomonoff Induction},
  language     = {eng},
  note         = {Student Paper},
  title        = {Solomonoff Induction: A Solution to the Problem of the Priors?},
  year         = {2012},
}