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Information Consistency of Nonparametric Gaussian Process Methods




Abstract—Bayesian nonparametric models are widely and successfully used for statistical prediction. While posterior consistency properties are well studied in quite general settings, results have been proved using abstract concepts such as metric entropy, and they come with subtle conditions which are hard to validate and not intuitive when applied to concrete models. Furthermore, convergence rates are difficult to obtain. By focussing on the concept of information consistency for Bayesian Gaussian process (GP)models, consistency results and convergence rates are obtained via a regret bound on cumulative log loss. These results depend strongly on the covariance function of the prior process, thereby giving a novel interpretation to penalization with reproducing kernel Hilbert space norms and to commonly used covariance function classes and their parameters. The proof of the main result employs elementary convexity arguments only. A theorem of Widom is used in order to obtain precise convergence rates for several covariance functions widely used in practice.

Author(s): Seeger, MW. and Kakade, SM. and Foster, DP.
Journal: IEEE Transactions on Information Theory
Volume: 54
Number (issue): 5
Pages: 2376-2382
Year: 2008
Month: May
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1109/TIT.2007.915707
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web


  title = {Information Consistency of Nonparametric Gaussian Process Methods},
  author = {Seeger, MW. and Kakade, SM. and Foster, DP.},
  journal = {IEEE Transactions on Information Theory},
  volume = {54},
  number = {5},
  pages = {2376-2382},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = may,
  year = {2008},
  month_numeric = {5}