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Asymptotic Log-loss of Prequential Maximum Likelihood Codes | | Peter Grunwald
; Steven de Rooij
; | | Date: |
1 Feb 2005 | | Subject: | Learning; Information Theory ACM-class: E.4 | cs.LG cs.IT | | Abstract: | We analyze the Dawid-Rissanen prequential maximum likelihood codes relative to one-parameter exponential family models M. If data are i.i.d. according to an (essentially) arbitrary P, then the redundancy grows at rate c/2 ln n. We show that c=v1/v2, where v1 is the variance of P, and v2 is the variance of the distribution m* in M that is closest to P in KL divergence. This shows that prequential codes behave quite differently from other important universal codes such as the 2-part MDL, Shtarkov and Bayes codes, for which c=1. This behavior is undesirable in an MDL model selection setting. | | Source: | arXiv, cs.LG/0502004 | | Services: | Forum | Review | PDF | Favorites | |
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