Fast Proxy Centers for the Jeffreys Centroid
Author Information
Author(s): Frank Nielsen
Primary Institution: Sony Computer Science Laboratories, Tokyo, Japan
Hypothesis
The study proposes new proxy centers for the Jeffreys centroid that can be computed more efficiently.
Conclusion
The Jeffreys–Fisher–Rao center and the Gauss–Bregman center provide effective approximations to the Jeffreys centroid for various statistical distributions.
Supporting Evidence
- The Jeffreys–Fisher–Rao center matches the Jeffreys centroid for same-mean normal distributions.
- The Gauss–Bregman center approximates the Jeffreys centroid well when truncated to a few iterations.
- Both new centers are suggested as replacements for the numerical Jeffreys centroid in practical applications.
Takeaway
This study introduces two new ways to find the center of a group of probability distributions quickly, which helps in analyzing data more efficiently.
Methodology
The study defines and experimentally evaluates two new centers based on the Fisher–Rao geometry and Gauss-type double sequences.
Limitations
The study does not provide closed-form solutions for all types of distributions and focuses primarily on categorical and multivariate normal distributions.
Digital Object Identifier (DOI)
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