Solomonoff Induction: A Solution to the Problem of the Priors?
(2012) FTEM02 20122Theoretical 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 nonarbitrary 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:
http://lup.lub.lu.se/studentpapers/record/3577211
 author
 Vallinder, Aron ^{LU}
 supervisor

 Staffan Angere ^{LU}
 organization
 course
 FTEM02 20122
 year
 2012
 type
 H2  Master's Degree (Two Years)
 subject
 keywords
 Bayesianism, Problem of the Priors, Solomonoff Induction
 language
 English
 id
 3577211
 date added to LUP
 20130905 09:16:49
 date last changed
 20130905 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 nonarbitrary 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}, }