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Minimum Message Length and Kolmogorov Complexity
 Computer Journal
, 1999
"... this paper is to describe some of the relationships among the different streams and to try to clarify some of the important differences in their assumptions and development. Other studies mentioning the relationships appear in [1, Section IV, pp. 10381039], [2, sections 5.2, 5.5] and [3, p. 465] ..."
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Cited by 107 (26 self)
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this paper is to describe some of the relationships among the different streams and to try to clarify some of the important differences in their assumptions and development. Other studies mentioning the relationships appear in [1, Section IV, pp. 10381039], [2, sections 5.2, 5.5] and [3, p. 465]
MML clustering of multistate, Poisson, von Mises circular and Gaussian distributions
 Statistics Computing
, 2000
"... Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also statistically consistent and efficient. We provide a brief overview of MML inductive inference ..."
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Cited by 34 (10 self)
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Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also statistically consistent and efficient. We provide a brief overview of MML inductive inference
Graphical Models for Discovering Knowledge
, 1995
"... There are many different ways of representing knowledge, and for each of these ways there are many different discovery algorithms. How can we compare different representations? How can we mix, match and merge representations and algorithms on new problems with their own unique requirements? This cha ..."
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Cited by 29 (2 self)
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There are many different ways of representing knowledge, and for each of these ways there are many different discovery algorithms. How can we compare different representations? How can we mix, match and merge representations and algorithms on new problems with their own unique requirements? This chapter introduces probabilistic modeling as a philosophy for addressing these questions and presents graphical models for representing probabilistic models. Probabilistic graphical models are a unified qualitative and quantitative framework for representing and reasoning with probabilities and independencies. 4.1 Introduction Perhaps one common element of the discovery systems described in this and previous books on knowledge discovery is that they are all different. Since the class of discovery problems is a challenging one, we cannot write a single program to address all of knowledge discovery. The KEFIR discovery system applied to health care by Matheus, PiatetskyShapiro, and McNeill (199...
Introduction to Minimum Encoding Inference
 DEPT. OF STATISTICS, OPEN UNIVERSITY, WALTON HALL, MILTON
, 1994
"... This paper examines the minimumencoding approaches to inference, Minimum Message Length (MML) and Minimum Description Length (MDL). This paper was written with the objective of providing an introduction to this area for statisticians. We describe coding techniques for data, and examine how these tec ..."
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Cited by 23 (4 self)
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This paper examines the minimumencoding approaches to inference, Minimum Message Length (MML) and Minimum Description Length (MDL). This paper was written with the objective of providing an introduction to this area for statisticians. We describe coding techniques for data, and examine how these techniques can be applied to perform inference and model selection.
Circular Clustering Of Protein Dihedral Angles By Minimum Message Length
 In Proceedings of the 1st Pacific Symposium on Biocomputing (PSB1
, 1996
"... this paper is given in [DADH95] and is available from ftp://www.cs.monash.edu.au/www/publications/1995/TR237.ps.Z.) Section 2introduces the MML principle and how it can be used for this circular clustering problem. The remaining sections give the results of the secondary structure groups [KaSa83] th ..."
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Cited by 15 (11 self)
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this paper is given in [DADH95] and is available from ftp://www.cs.monash.edu.au/www/publications/1995/TR237.ps.Z.) Section 2introduces the MML principle and how it can be used for this circular clustering problem. The remaining sections give the results of the secondary structure groups [KaSa83] that resulted from applying Snob to cluster our dihedral angle data.
Bayes not Bust! Why Simplicity is no Problem for Bayesians
, 2007
"... The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike’s Information Criterion (AIC), a nonBayesian formalisation of the notion of simplicity. ..."
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Cited by 14 (10 self)
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The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike’s Information Criterion (AIC), a nonBayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallace’s Minimum Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1to1 reparametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster’s objections to Bayesianism. Hence an important part of the attack on
MML mixture modelling of multistate, Poisson, von Mises circular and Gaussian distributions
 In Proc. 6th Int. Workshop on Artif. Intelligence and Statistics
, 1997
"... Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also consistent and efficient. We provide a brief overview of MML inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)), and how it has both an informationtheoretic and a Bayesian interp ..."
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Cited by 11 (5 self)
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Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also consistent and efficient. We provide a brief overview of MML inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)), and how it has both an informationtheoretic and a Bayesian interpretation. We then outline how MML is used for statistical parameter estimation, and how the MML mixture modelling program, Snob (Wallace and Boulton (1968), Wallace (1986), Wallace and Dowe(1994)) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with selection of the number of components. The message length is (to within a constant) the logarithm of the posterior probability of the theory. So, the MML theory can also be regarded as the theory with the highest posterior probability. Snob currently assumes that variables are uncorrelated, and permits multivariate data from Gaussian, discrete multistate, Poisson and von Mises circular dist...
Intrinsic Classification by MML—the Snob Program
 Proc. Seventh Australian Joint Conf. Artificial Intelligence
, 1994
"... Abstract: We provide a brief overview ofMinimum Message Length (MML) inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)). We then outline how MML is used for statistical parameter estimation, and how the MML intrinsic classification program, Snob (Wallace and Boulton (1968), ..."
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Cited by 6 (0 self)
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Abstract: We provide a brief overview ofMinimum Message Length (MML) inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)). We then outline how MML is used for statistical parameter estimation, and how the MML intrinsic classification program, Snob (Wallace and Boulton (1968), Wallace (1986), Wallace (1990)) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with model selection in intrinsic classification. We mention here the most recent extensions to Snob, permitting Poisson and von Mises circular distributions. We also survey some applications of Snob (albeit briefly), and further provide some documentation on how the user can guide Snob’s search through various models of the given data to try to obtain that model whose message length is a minimum.
MML, HYBRID BAYESIAN NETWORK GRAPHICAL MODELS, STATISTICAL CONSISTENCY, INVARIANCE AND UNIQUENESS
"... The problem of statistical — or inductive — inference pervades a large number of human activities and a large number of (human and nonhuman) actions requiring ‘intelligence’. Human and other ‘intelligent ’ activity often entails making inductive inferences, remembering and recording observations fr ..."
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Cited by 4 (4 self)
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The problem of statistical — or inductive — inference pervades a large number of human activities and a large number of (human and nonhuman) actions requiring ‘intelligence’. Human and other ‘intelligent ’ activity often entails making inductive inferences, remembering and recording observations from which one can make
CIRCULAR CLUSTERING BY MINIMUM MESSAGE LENGTH OF PROTEIN DIHEDRAL ANGLES
, 1995
"... Early work on proteins identified the existence of helices and extended sheets in protein secondary structures, a highlevel classification which remains popular today. Using the Snob program for informationtheoretic Minimum Message Length (MML) intrinsic classification, we are able to take the pro ..."
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Cited by 4 (4 self)
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Early work on proteins identified the existence of helices and extended sheets in protein secondary structures, a highlevel classification which remains popular today. Using the Snob program for informationtheoretic Minimum Message Length (MML) intrinsic classification, we are able to take the protein dihedral angles as determined by Xray crystallography, and cluster sets of dihedral angles into groups. Previous work by Hunter and States had applied a similar Bayesian classification method, AutoClass, to protein data with site position represented by 3 Cartesian coordinates for each of the αCarbon, βCarbon and Nitrogen, totalling 9 coordinates. By using the von Mises circular distribution in the Snob program rather than the Normal distribution in the Hunter and States model, we are instead able to represent local site properties by the two dihedral angles, φ and ψ. Since each site can be modelled as having 2 degrees of freedom, this orientationinvariant dihedral angle representation of the data is more compact than that of nine highlycorrelated Cartesian coordinates. Using the informationtheoretic message length concepts discussed in the paper, such a more concise model is more likely to represent the underlying generating process from which the data comes. We report on the results of our classification, plotting the classes in (φ,ψ)space and introducing a symmetric informationtheoretic distance measure to build a minimum spanning tree between the classes. We also give a transition matrix between the classes and note the existence of three classes in the region φ ≈−1. 09 rad and ψ ≈−0. 75 rad which are close on the spanning tree and have high intertransition probabilities. These properties give rise to a tight, abundant, selfperpetuating, αhelical structure.