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New research clarifies symmetrization of Bregman divergences on positive definite matrices

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This research paper explores the symmetrization of Bregman divergences within the cone of positive definite matrices. The authors demonstrate that computing canonical means for this symmetrization can be framed as a minimization problem. For forward symmetrization, the arithmetic mean on the primal space is identified as canonical, while for reverse symmetrization, the canonical mean is the arithmetic mean on the dual space, projected back to the primal space. The paper applies these findings to common mirror maps, identifying the arithmetic, log-Euclidean, and harmonic means as canonical for reverse symmetrization in specific cases, aiming to guide practitioners in selecting appropriate means. AI

IMPACT Provides theoretical insights into matrix operations relevant to machine learning algorithms.

RANK_REASON The cluster contains an academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New research clarifies symmetrization of Bregman divergences on positive definite matrices

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The cluster contains an academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Tushar Sial, Abhishek Halder ·

    Symmetrizing Bregman Divergence on the Cone of Positive Definite Matrices: Which Mean to Use and Why

    arXiv:2603.28917v3 Announce Type: replace-cross Abstract: This work uncovers variational principles behind symmetrizing the Bregman divergences induced by generic mirror maps over the cone of positive definite matrices. We show that computing the canonical means for this symmetri…

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