Research map / Optimization / Nonconvex and smooth optimization
On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Bures-Wasserstein instead of affine-invariant geometry | Riemannian trust region / steepest descent · weighted least squares (n=50, kappa 10 and 10^3) | convergence speed | Helped |
| use BW instead of AI geometry | Riemannian trust region · Lyapunov equations (Ex1/Ex2, full and low rank) | convergence speed | Helped |
| use BW instead of AI geometry | Riemannian trust region · trace regression (SynFull, SynLow) | convergence speed | Helped |
| use BW instead of AI geometry | Riemannian trust region · metric learning (glass, phoneme) | convergence speed | Helped |
| use BW instead of AI geometry | Riemannian trust region · log-det maximization | convergence speed | Hurt |
| use BW instead of AI geometry | RTR and RSGD · Gaussian mixture model | convergence speed | Hurt |
| use BW instead of AI geometry | Riemannian trust region · weighted least squares | runtime | Helped |
| use BW instead of AI geometry | condition number of Riemannian Hessian at optimum · linear, quadratic, polynomial costs | kappa: kappa_ai = O(kappa(X*)^alpha) vs kappa_bw = O(kappa(X*)^(alpha-1)) | Helped |
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