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Patterns and Probabilities : = A Study in Algorithmic Randomness and Computable Learning.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Patterns and Probabilities :/
其他題名:	A Study in Algorithmic Randomness and Computable Learning.
作者:	Blando, Francesca Zaffora.
面頁冊數:	1 online resource (175 pages)
附註:	Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
Contained By:	Dissertations Abstracts International83-05B.
標題:	Probability. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28827888click for full text (PQDT)
ISBN:	9798494461186

Patterns and Probabilities : = A Study in Algorithmic Randomness and Computable Learning.
Blando, Francesca Zaffora.

Patterns and Probabilities :A Study in Algorithmic Randomness and Computable Learning. - 1 online resource (175 pages)

Source: Dissertations Abstracts International, Volume: 83-05, Section: B.

Thesis (Ph.D.)--Stanford University, 2020.

Includes bibliographical references

This dissertation bridges the theory of algorithmic randomness-a branch of computability theory-and the foundations of inductive learning. Algorithmic randomness provides a mathematical analysis of the notion of an individual object (such as a string of bytes representing a computer file or a sequence of experimental outcomes) displaying no effective patterns or regularities. Here, we investigate the role that algorithmic randomness plays in inductive learning when randomness is taken to be a property of sequences of observations, or data streams, and the learners are computationally limited. Our results constitute a first step towards a systematic classification and analysis of the learning scenarios where algorithmic randomness is beneficial for inductive learning, and the scenarios where it is instead detrimental for the learning process. We focus on three main themes. Firstly, we explore the connections between algorithmic randomness and Bayesian merging-of-opinions theorems. In particular, we show that algorithmic randomness leads to merging of opinions in the following sense. When two computable Bayesian agents perform the same experiment, agreeing on which data streams are algorithmically random suces to guarantee that they will eventually reach a consensus even if, at the beginning of the learning process, their beliefs are otherwise dissimilar. Secondly, we consider the role of algorithmic randomness in Bayesian convergence-to-the-truth results. More precisely, we show that there is a robust correspondence between algorithmic randomness and the collection of truth-conducive data streams. When a computable Bayesian agent is faced with an effective inductive problem, the algorithmically random data streams are in fact exactly the ones that ensure that their beliefs will asymptotically align with the truth. Lastly, we investigate a learning-theoretic approach-in the spirit of formal learning theory-for modelling algorithmic randomness itself. Building on the local irregularity and unruliness that is the hallmark of algorithmic randomness, we argue that the algorithmically random data streams can be systematically shown to be unlearnable: i.e., they coincide with the data streams from which no computable qualitative learning method can extrapolate any patterns.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798494461186Subjects--Topical Terms:

518898
Probability.
Index Terms--Genre/Form:

542853
Electronic books.

Patterns and Probabilities : = A Study in Algorithmic Randomness and Computable Learning.
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520 $a This dissertation bridges the theory of algorithmic randomness-a branch of computability theory-and the foundations of inductive learning. Algorithmic randomness provides a mathematical analysis of the notion of an individual object (such as a string of bytes representing a computer file or a sequence of experimental outcomes) displaying no effective patterns or regularities. Here, we investigate the role that algorithmic randomness plays in inductive learning when randomness is taken to be a property of sequences of observations, or data streams, and the learners are computationally limited. Our results constitute a first step towards a systematic classification and analysis of the learning scenarios where algorithmic randomness is beneficial for inductive learning, and the scenarios where it is instead detrimental for the learning process. We focus on three main themes. Firstly, we explore the connections between algorithmic randomness and Bayesian merging-of-opinions theorems. In particular, we show that algorithmic randomness leads to merging of opinions in the following sense. When two computable Bayesian agents perform the same experiment, agreeing on which data streams are algorithmically random suces to guarantee that they will eventually reach a consensus even if, at the beginning of the learning process, their beliefs are otherwise dissimilar. Secondly, we consider the role of algorithmic randomness in Bayesian convergence-to-the-truth results. More precisely, we show that there is a robust correspondence between algorithmic randomness and the collection of truth-conducive data streams. When a computable Bayesian agent is faced with an effective inductive problem, the algorithmically random data streams are in fact exactly the ones that ensure that their beliefs will asymptotically align with the truth. Lastly, we investigate a learning-theoretic approach-in the spirit of formal learning theory-for modelling algorithmic randomness itself. Building on the local irregularity and unruliness that is the hallmark of algorithmic randomness, we argue that the algorithmically random data streams can be systematically shown to be unlearnable: i.e., they coincide with the data streams from which no computable qualitative learning method can extrapolate any patterns.
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