Model Complexity in Statistical Manifolds: The Role of Curvature

Bruno Mera, Paulo Mateus, Alexandra M. Carvalho

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Model complexity plays an essential role in its selection, namely, by choosing a model that fits the data and is also succinct. Two-part codes and the minimum description length have been successful in delivering procedures to single out the best models, avoiding overfitting. In this work, we pursue this approach and complement it by performing further assumptions in the parameter space. Concretely, we assume that the parameter space is a smooth manifold, and by using tools of Riemannian geometry, we derive a sharper expression than the standard one given by the stochastic complexity, where the scalar curvature of the Fisher information metric plays a dominant role. Furthermore, we compute a sharper approximation to the capacity for exponential families and apply our results to derive optimal dimensional reduction in the context of principal component analysis.

Original languageEnglish
Pages (from-to)5619-5636
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number9
Publication statusPublished - 2022 Sept 1


  • Maximum likelihood decoding
  • information geometry
  • principal component analysis (PCA)

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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