M. Hansen and B. Yu. Model selection and minimum description length principle. J. Amer. Statist. Assoc., 96:746--774, 2001.  Home/Search   Document Not in Database   Summary   Related Articles   Check

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M. Hansen and B. Yu. Model selection and minimum description length principle. J. Amer. Statist. Assoc., 96:746--774, 2001.

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Hansen, M. and Yu, B. (2001). Model selection and minimum description length principle. J. Amer. Statist. Assoc. 96, 746-774.

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Hansen, M. and Yu, B. (1998). "Model selection and Minimum Description Length principle," J. Amer. Statist. Assoc, (submitted).

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M. Hansen and B. Yu. Model selection and minimum description length principle. JASA, 1998. submitted.

.... is the corresponding codelength of the (ideal) optimal code (ignoring the precision issue) Many favorable properties have been shown for MDL based statistical procedures in both parametric and nonparametric contexts (see the two recent reviews by Barron, Rissanen and Yu [1] and Hansen and Yu [13]) A crucial step in implementing a MDL procedure is to choose the form of the universal code. Three forms have been studied extensively: two stage, predictive and mixture, although new forms are appearing such as Normalized Maximum Likelihood (NML) Rissanen, 19] In order to compare these ....

M. Hansen and B. Yu. Model selection and minimum description length principle. JASA, 1998. submitted.

....a formal measure of information of the kind long sought for in statistical inference and modeling. This measure has led to the Minimum Description Length (MDL) principle for modeling in general and model selection in particular (see Rissanen 1978, Rissanen 1989, Barron, Rissanen and Yu 1998, Hansen and Yu 1998). A coding or compression algorithm is used when one surfs the web, listens to a CD, uses a cellular phone or works on a computer. In particular, when a music file is downloaded through Jorma Rissanen is Fellow, IBM Reserch at San Jose, CA. Email: RISSANEN ALMADEN.IBM.COM) y Bin Yu is Member ....

....the conventional BIC model selection criterion; MDL with a predictive gives the accumulated prediction error criterion; and MDL with a mixture code generalizes the Bayes factor to more than two classes. Thus, MDL provides a way to compare frequentist and Bayesian model selection criteria (see Hansen and Yu 1998). It remains open how MDL can be used to select among complex models such as Bayesian belief networks. Both information theory results (e.g. universal coding theorems) and statistical evaluation analyses are anticipated. 4 Rate distortion function and lossy compression Entropy gives the ....

Hansen, M. and Yu, B. (1998). "Model selection and Minimum Description Length principle," J. Amer. Statist. Assoc, (submitted).

....In Fig. 1 we plot the optimal threshold as a function of and compare it to BayesShrink and MapShrink. B Model Classes and Analytical Compression As a principle, MDL suggests that we select a model or model class that yields the shortest description of a dataset. Two recent review articles are [2, 17]: the first geared toward an audience versed in information theory and the second written for the statistics community. The MDL philosophy is descriptive in the sense that models are viewed as a means of expressing properties evident in data, 7 to paraphrase Rissanen (1989, p. 4) In our case, we ....

....MDL procedure, we must specify a description or code length corresponding to each approximating model. To provide a valid selection criterion (i.e. one that yields a consistent or prediction optimal procedure) we restrict our attention to optimal universal coding schemes based on model classes [27, 2, 17]. Distributional observations like the (approximate) Laplacian behavior of wavelet coefficients for natural signals can be easily incorporated into our MDL formulation. As in the previous section, let fi 1 ; fi n represent the noiseless wavelet coefficients for a given subband. The model ....

M. Hansen and B. Yu, "Model selection and Minimum Description Length principle," Journal of the American Statistical Association, submitted, 1998. (http://cm.bell-labs.com/who/cocteau/papers/)

.... is the corresponding codelength of the (ideal) optimal code (ignoring the precision issue) Many favorable properties have been shown for MDL based statistical procedures in both parametric and nonparametric contexts (see the two recent reviews by Barron, Rissanen and Yu [1] and Hansen and Yu [13]) A crucial step in implementing a MDL procedure is to choose the form of the universal code. Three forms have been studied extensively: two stage, predictive and mixture, although new forms are appearing such as Normalized Maximum Likelihood (NML) Rissanen, 19] In order to compare these ....

M. Hansen and B. Yu. Model selection and minimum description length principle. JASA, 1998. submitted.

....such a procedure, we must specify a description or code length corresponding to each candidate model. To provide a valid selection criterion (i.e. one that yields a consistent or prediction optimal procedure) we restrict our attention to optimal universal coding schemes based on model classes [24, 2, 16]. Distributional observations like the (approximate) Laplacian behavior of wavelet coefficients for natural signals can be easily incorporated into our MDL formulation. Given a binary index vector fl = fl 1 ; fl 2 ; fl n ) 2 f0; 1g n consider again the model M fl specified in (4) For ....

M. Hansen and B. Yu, "Model selection and Minimum Description Length principle," JASA, submitted, 1998. REFERENCES 31

....the ordinary sufficient statistics decomposition. Given several model classes the Minimum Description Length principle searches for the class where the stochastic complexity is smallest implying the most efficient removal of incompressible noise. For recent papers on such ideas we refer to [1] [2], 4] 5] ....

Hansen, M. and Yu, B. "Model selection and Minimum Description Length principle," JASA, submitted, 1998.

.... is the corresponding codelength of the (ideal) optimal code (ignoring the precision issue) Many favorable properties have been shown for MDL based statistical procedures in both parametric and nonparametric contexts (see the two recent reviews by Barron, Rissanen and Yu [1] and Hansen and Yu [13]) A crucial step in implementing a MDL procedure is to choose the form of the universal code. Three forms have been studied extensively: two stage, predictive and mixture, although new forms are appearing such as Normalized Maximum Likelihood (NML) Rissanen, 18] All these forms are equivalent ....

M. Hansen and B. Yu. Model selection and minimum description length principle. Journal of the American Statistical Association, 1998. submitted.

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Mark Hansen and Bin Yu. Model selection and minimum description length principle. J. Amer. Statist. Assoc., 96:746--774, 2001.

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Mark Hansen and Bin Yu. Model selection and minimum description length principle. In J. Amer. Statist. Assoc., volume 96, pages 746-- 774, 2001.

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