Tangent-linearized Gaussian inference on manifolds has explicit non-asymptotic W2 stability bounds that predict a calibration transition near sqrt of the operator norm of covariance over reach approximately equal to 1/6.
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Distributional Stability of Tangent-Linearized Gaussian Inference on Smooth Manifolds
Tangent-linearized Gaussian inference on manifolds has explicit non-asymptotic W2 stability bounds that predict a calibration transition near sqrt of the operator norm of covariance over reach approximately equal to 1/6.