Information geometry of U-Boost and Bregman divergence

Noboru Murata*, Takashi Takenouchi, Takafumi Kanamori, Shinto Eguchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

130 Citations (Scopus)


We aim at an extension of AdaBoost to U-Boost, in the paradigm to build a stronger classification machine from a set of weak learning machines. A geometric understanding of the Bregman divergence defined by a generic convex function U leads to the U-Boost method in the framework of information geometry extended to the space of the finite measures over a label set. We propose two versions of U-Boost learning algorithms by taking account of whether the domain is restricted to the space of probability functions. In the sequential step, we observe that the two adjacent and the initial classifiers are associated with a right triangle in the scale via the Bregman divergence, called the Pythagorean relation. This leads to a mild convergence property of the U-Boost algorithm as seen in the expectation-maximization algorithm. Statistical discussions for consistency and robustness elucidate the properties of the U-Boost methods based on a stochastic assumption for training data.

Original languageEnglish
Pages (from-to)1437-1481
Number of pages45
JournalNeural Computation
Issue number7
Publication statusPublished - 2004 Jul 1

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience


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