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Schwarz, Wallace, and Rissanen: Intertwining Themes in Theories of Model Selection
, 2000
"... Investigators interested in model order estimation have tended to divide themselves into widely separated camps; this survey of the contributions of Schwarz, Wallace, Rissanen, and their coworkers attempts to build bridges between the various viewpoints, illuminating connections which may have pr ..."
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Investigators interested in model order estimation have tended to divide themselves into widely separated camps; this survey of the contributions of Schwarz, Wallace, Rissanen, and their coworkers attempts to build bridges between the various viewpoints, illuminating connections which may have previously gone unnoticed and clarifying misconceptions which seem to have propagated in the applied literature. Our tour begins with Schwarz's approximation of Bayesian integrals via Laplace's method. We then introduce the concepts underlying Rissanen 's minimum description length principle via a Bayesian scenario with a known prior; this provides the groundwork for understanding his more complex nonBayesian MDL which employs a "universal" encoding of the integers. Rissanen's method of parameter truncation is contrasted with that employed in various versions of Wallace's minimum message length criteria.
Master Thesis
, 91
"... this paper. 129 in encoding y using q(y) is \Gamma ln q(y) + ln p l (yjx(y)) = ln ..."
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this paper. 129 in encoding y using q(y) is \Gamma ln q(y) + ln p l (yjx(y)) = ln
What Is Better: GMM of Two . . .
, 2002
"... In this report, we provide a theoretical discussion on temporal data cluster analysis: does the data come from one source or two sources; is it better to cluster the data into two clusters or leave it as one cluster. Here we analyse only the simplest case: when the data comes from two symmetric Gaus ..."
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In this report, we provide a theoretical discussion on temporal data cluster analysis: does the data come from one source or two sources; is it better to cluster the data into two clusters or leave it as one cluster. Here we analyse only the simplest case: when the data comes from two symmetric Gaussian probabilitydensityfunctions (pdfs), i.e., with same variance and same absolute value of the mean, with the same prior probability per Gaussian. The data consists of segments with an apriori known segment length. It will be shown that if the data belongs to two different Gaussian models, the likelihood of two clusters is always higher or equal than the one of a GMM with two Gaussians for any mean, variance, and segment length. If the data belongs to the GMM, the likelihood of two clusters might be either higher or less than the GMM one.
WHAT IS BETTER: GMM OF TWO GAUSSIANS OR TWO CLUSTERS WITH ONE GAUSSIAN?
, 2002
"... Abstract. In this report, we provide a theoretical discussion on temporal data cluster analysis: does the data come from one source or two sources; is it better to cluster the data into two clusters or leave it as one cluster. Here we analyse only the simplest case: when the data comes from two symm ..."
Abstract
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Abstract. In this report, we provide a theoretical discussion on temporal data cluster analysis: does the data come from one source or two sources; is it better to cluster the data into two clusters or leave it as one cluster. Here we analyse only the simplest case: when the data comes from two symmetric Gaussian probabilitydensityfunctions (pdfs), i.e., with same variance and same absolute value of the mean, with the same prior probability per Gaussian. The data consists of segments with an apriori known segment length. It will be shown that if the data belongs to two different Gaussian models, the likelihood of two clusters is always higher or equal than the one of a GMM with two Gaussians for any mean, variance, and segment length. If the data belongs to the GMM, the likelihood of two clusters might be either higher or less than the GMM one.