Near Optimal Sample Complexity For Matrix And Tensor Normal Models Via Geodesic Convexity
summary
Proves that maximum-likelihood estimation for matrix/tensor-normal factors attains the same sample scaling as the vector Gaussian case up to a small extra condition: N times the ambient dimension D must exceed (∑_a d_a^2)/ε^2 and ε must be sufficiently small to guarantee per-factor ε error. Analysis uses geodesic strong convexity (Pizier lower bound on the Hessian), Gaussian concentration to show a small geodesic gradient, and tensor-scaling control so the flip-flop achieves exponential convergence to the MLE.
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