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Graph-based composite local Bregman divergences on discrete sample spaces.

Takafumi Kanamori1, Takashi Takenouchi2

  • 1Nagoya University, RIKEN Center for Advanced Intelligence Project, Furocho, Chikusaku, Nagoya 464-8603, Japan.

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|September 9, 2017
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Summary
This summary is machine-generated.

This study introduces a new statistical inference framework using local scoring rules on discrete sample spaces. The method offers a robust and efficient estimator, showing improved accuracy based on neighborhood system structure.

Keywords:
Bregman divergenceCoincidence axiomLocalityRobustnessScoring rule

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Area of Science:

  • Statistical inference
  • Graph theory
  • Machine learning

Background:

  • Traditional statistical inference methods often struggle with discrete sample spaces and require normalization constants.
  • Scoring rules are essential for evaluating model fit but can be computationally intensive.
  • Understanding the relationship between sample space structure and estimation accuracy is crucial.

Purpose of the Study:

  • To develop a general framework for statistical inference on discrete sample spaces using graph-defined neighborhood systems.
  • To introduce and analyze localized scoring rules that bypass the need for normalization constants.
  • To propose a robust and computationally efficient estimator based on the developed framework.

Main Methods:

  • Utilizing undirected graphs to define neighborhood systems on discrete sample spaces.
  • Employing localized scoring rules and establishing their connection to composite local Bregman divergence.
  • Investigating the statistical consistency of local scoring rules based on graphical structures.
  • Developing a novel robust and efficient estimator.

Main Results:

  • Demonstrated a close relationship between local scoring rules and composite local Bregman divergence.
  • Established the statistical consistency of local scoring rules concerning the sample space's graphical structure.
  • Proposed a robust and computationally efficient estimator.
  • Numerical experiments revealed a correlation between neighborhood system characteristics and estimation accuracy.

Conclusions:

  • The developed framework provides a powerful tool for statistical inference on discrete sample spaces.
  • Localized scoring rules offer a computationally advantageous alternative to traditional scoring rules.
  • The proposed estimator demonstrates robustness and efficiency, with performance influenced by the neighborhood system's structure.