Bayes not Bust! Why Simplicity is no Problem for Bayesians

Dowe, David L.; Gardner, Steven Lawrence; Oppy, Graham

doi:10.1093/bjps/axm033

Cited by 54 publications

(49 citation statements)

References 33 publications

(26 reference statements)

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“…We can think informally of the w i s at a time as a row of life-game-like cells that wraps into a circle, each of which either possesses the fundamental property (represented as ' ' on the cell, and encoded as '1'), or does not possess that property (represented as ' ' on the cell, and encoded as '0'). 4 We can think of W at the next time step as another circle of such cells just below. This W is, I hope, a very simple case for the kind of important features we seem to need to construct a metaphysics in our world: some unproblematically fundamental objects, one maximally simple fundamental property, and a succession of times.…”

Section: The Toy World Wmentioning

confidence: 99%

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Toward an Algorithmic Metaphysics

Petersen

2013

Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence

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Abstract. There are writers in both metaphysics and algorithmic information theory (AIT) who seem to think that the latter could provide a formal theory of the former. This paper is intended as a step in that direction. It demonstrates how AIT might be used to define basic metaphysical notions such as object and property for a simple, idealized world. The extent to which these definitions capture intuitions about the metaphysics of the simple world, times the extent to which we think the simple world is analogous to our own, will determine a lower bound for basing a metaphysics for our world on AIT.Keywords: metaphysics, formal metaphysics, computational metaphysics, algorithmic metaphysics, algorithmic information theory, real patterns.Both philosophers and mathematicians have flirted with the idea that algorithmic information theory (AIT) could provide some foundation for basic notions in metaphysics. The main inspiration for this paper is one such hint from the philosophy side: in Daniel Dennett's sketch of a metaphysics based on "real patterns", he explicitly appeals to incompressibility, and offhandedly mentions the work of AIT theorist Gregory Chaitin in this connection.1 Meanwhile AIT theorists since Andrey Kolmogorov frequently speak about, for example, the "information content" of objects generally, rather than of binary strings in particular. (Of course, "the original incentive to develop a theory of algorithmic information content of individual objects was Ray Solomonoff 's invention of a universal a priori probability . . . "2 ) This paper aims to help bridge this gap between metaphysics and AIT. As befits a philosophy paper, it contains little in the way of technical results, but some ruminations aiming to pave the way for technical results to come. And as is typical of work bridging discipline X to discipline Y , X theorists are likely to complain that the treatment of X is far too simplistic and sloppy, and that the treatment of Y engages trivial details-while Y theorists complain conversely.

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Section: The Toy World Wmentioning

confidence: 99%

“…Work such as [8] and [7] extend Solomonoff's original insights for formalizing inductive reasoning. The Bayesian approach of [16] is closely related (as argued in [17]), and has demonstrated potential to characterize approximate truth [4] and perhaps more elusive philosophical fruit [3].…”

mentioning

confidence: 99%

Toward an Algorithmic Metaphysics

Petersen

2013

Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence

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“…According to the MML criterion, we choose the model class/order and the parameter estimate that correspond to the shortest two-part message. MML is closely related to the Kolmogorov complexity [19,17], is invariant under 1-to-1 parameter transformations [20,17], and has general statistical consistency properties [6,5].…”

Section: Parameter Estimationmentioning

confidence: 99%

Learning a Generative Model for Structural Representations

Torsello

Dowe

2008

AI 2008: Advances in Artificial Intelligence

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Abstract. Graph-based representations have been used with considerable success in computer vision in the abstraction and recognition of object shape and scene structure. Despite this, the methodology available for learning structural representations from sets of training examples is relatively limited. This paper addresses the problem of learning archetypal structural models from examples. To this end we define a generative model for graphs where the distribution of observed nodes and edges is governed by a set of independent Bernoulli trials with parameters to be estimated from data in a situation where the correspondences between the nodes in the data graphs and the nodes in the model are not known ab initio and must be estimated from local structure. This results in an EM-like approach where we alternate the estimation of the node correspondences with the estimation of the model parameters. The former estimation is cast as an instance of graph matching, while the latter estimation, together with model order selection, is addressed within a Minimum Message Length (MML) framework. Experiments on a shape recognition task show the effectiveness of the proposed learning approach.

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“…The first encodes the model class/order and the parameters, while the second assumes a Shannon-optimal encoding of the data given the model. MML is closely related to the Kolmogorov complexity, is invariant under 1-to-1 parameter transformations [7], and has general statistical consistency properties [1].…”

Section: Parameter Estimationmentioning

confidence: 99%

Supervised Learning of a Generative Model for Edge-Weighted Graphs

Torsello¹,

Dowe²

2008

2008 19th International Conference on Pattern Recognition

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This paper addresses the problem of learning archetypal structural models from examples. To this end we define a generative model for graphs where the distribution of observed nodes and edges is governed by a set of independent Bernoulli trials with parameters to be estimated from data in a situation where the correspondences between the nodes in the data graphs and the nodes in the model are not not known ab initio and must be estimated from local structure. This results in an EM-like approach where we alternate the estimation of the node correspondences with the estimation of the model parameters. Parameter estimation and model order selection is addressed within a Minimum Message Length (MML) framework.

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Bayes not Bust! Why Simplicity is no Problem for Bayesians

Cited by 54 publications

References 33 publications

Toward an Algorithmic Metaphysics

Toward an Algorithmic Metaphysics

Learning a Generative Model for Structural Representations

Supervised Learning of a Generative Model for Edge-Weighted Graphs

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