So if d (x,x 0)< √ 2, dg(x,x 0)2 ≤ F (d (x,x 0)) with F :y ∈ R+ ↦→ 1 2 arcosh   1 2 ( ey2 + √ e2y2 − 1 + 1 ) 1 − 1√ 2y   2

As 1 − 1√ 2re ≤ 1, √ e2r2e − 1 ≥ er2 e − 1, the bound found for the ﬁrst case (see ( 60)) is larger than the one found for the second case (see ( 61))

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Gaussian Mixture Model with unknown diagonal covariances via continuous sparse regularization

math.ST · 2025-09-16 · unverdicted · novelty 6.0

Extends BLASSO to multivariate GMMs with component-specific unknown diagonal covariances and derives non-asymptotic recovery guarantees under an explicit separation condition using Fisher-Rao geometry.

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Gaussian Mixture Model with unknown diagonal covariances via continuous sparse regularization math.ST · 2025-09-16 · unverdicted · none · ref 12
Extends BLASSO to multivariate GMMs with component-specific unknown diagonal covariances and derives non-asymptotic recovery guarantees under an explicit separation condition using Fisher-Rao geometry.

So if d (x,x 0)< √ 2, dg(x,x 0)2 ≤ F (d (x,x 0)) with F :y ∈ R+ ↦→ 1 2 arcosh   1 2 ( ey2 + √ e2y2 − 1 + 1 ) 1 − 1√ 2y   2

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