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Why It Matters
The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices.
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Discovered via ArXiv and published by ArXiv.
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Original description
The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices. Euclidean, Bures-Wasserstein and affine-invariant metrics are common choices, but their relative effectiveness depends on the objective. We introduce a two-parameter family defined by $X^{p}LX^{q}+X^{q}LX^{p}=U$, solved for $L$ at each tangent vector $U$, that contains all three as exact members, at $(0,0)$, $(1,0)$ and $(1,1)$, and extends past them. We treat the choice of member as a particular way of preconditioning for a given problem. To this end, we analyze the...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.17089v1 · Indexed about 1 hour ago