Fast and Accurate Estimation of MDL - Induced SNR Penalty in SDM Link with Non-Uniform Noise Loading
Tonghui JiQi WuZhaopeng XuHonglin JiYang YuLulu LiuShangcheng WangZhongliang SunJunpeng LiangLinsheng FanJianwei TangJinlong WeiJuhao LiWeisheng Hu
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Minimum description length
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The minimum description length (MDL) principle states that one should prefer the model that yields the shortest description of the data when the complexity of the model itself is also accounted for. MDL provides a versatile approach to statistical modeling. It is applicable to model selection and regularization. Modern versions of MDL lead to robust methods that are well suited for choosing an appropriate model complexity based on the data, thus extracting the maximum amount of information from the data without over-fitting. The modern versions of MDL go well beyond the familiar $$\frac{k} {2} \log n$$ formula.
Minimum description length
Regularization
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The concept of overfitting in model selection is explained and demonstrated with an example. After providing some background information on information theory and Kolmogorov complexity, we provide a short explanation of Minimum Description Length and error minimization. We conclude with a discussion of the typical features of overfitting in model selection.
Minimum description length
Overfitting
Minification
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The minimum description length (MDL) principle states that one should prefer the model that yields the shortest description of the data when the complexity of the model itself is also accounted for. MDL provides a versatile approach to statistical modeling. It is applicable to model selection and regularization. Modern versions of MDL lead to robust methods that are well suited for choosing an appropriate model complexity based on the data, thus extracting the maximum amount of information from the data without over-fitting. The modern versions of MDL go well beyond the familiar $$\frac{k} {2} \log n$$ formula.
Minimum description length
Regularization
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The minimun description length (MDL) is a powerful criterion for model selection that is gaining increasing interest from both theorists and practicioners. It allows for automatic selection of the best model for representing data without having a priori information about them. It simply uses both data and model complexity, selecting the model that provides the least coding length among a predefined set of models. In this paper, we briefly review the basic ideas underlying the MDL criterion and its applications in different fields, with particular reference to the dimension reduction problem. As an example, the role of MDL in the selection of the best principal components in the well known PCA is investigated.
Minimum description length
Data Reduction
Information Theory
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Minimum description length
Occam's razor
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Code (set theory)
Selection principle
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The concept of overfitting in model selection is explained and demonstrated with an example. After providing some background information on information theory and Kolmogorov complexity, we provide a short explanation of Minimum Description Length and error minimization. We conclude with a discussion of the typical features of overfitting in model selection.
Minimum description length
Overfitting
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The minimum description length(MDL) method is one of the pioneer methods of parametric order estimation with a wide range of applications. We investigate the definition of two-stage MDL for parametric linear model sets and exhibit some drawbacks of the theory behind the existing MDL. We introduce a new description length which is inspired by the Kolmogorov complexity principle.
Minimum description length
Parametric model
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Abstract The minimum description length (MDL) principle articulated in the last decade by Rissanen and his co-workers yields new criteria for statistical model selection. MDL criteria permit data-based choices from among alternative statistical descriptions of data without necessarily assuming that the data were sampled randomly. This article explains the MDL principle informally, indicates the criteria it yields in the common cases of multinomial distributions and Gaussian regression, and illustrates MDL's use with numerical examples. We hope thereby to stimulate experimentation and debate about the pedagogical and practical implications of the MDL approach.
Minimum description length
Multinomial distribution
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Minimum description length
Inductive Reasoning
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