The minimum description length principle in coding and modeling
Barron, A.; Rissanen, J.; Bin Yu
Information Theory, IEEE Transactions on
Volume 44, Issue 6, Oct 1998 Page(s):2743 - 2760
Digital Object Identifier   10.1109/18.720554
Summary:We review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling. Stochastic complexity is formulated as the solution to optimum universal coding problems extending Shannon's basic source coding theorem. The normalized maximized likelihood, mixture, and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms. We assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference. Context tree modeling, density estimation, and model selection in Gaussian linear regression serve as examples

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