Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
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Cambridge University Press, Cambridge, UK (2023)
16 Pith papers cite this work, alongside 421 external citations. Polarity classification is still indexing.
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UNVERDICTED 16representative citing papers
The Riemannian Multiobjective Proximal Gradient Method (RMPGM) directly optimizes vector-valued composite objectives on Riemannian manifolds and converges globally to Pareto stationary points with an O(1/k) rate.
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
A Riemannian L-BFGS method with adapted Cauchy-point bound handling outperforms classical interior-point and L-BFGS-B solvers on mixed manifold-plus-bounds problems by orders of magnitude.
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
Negative curvature makes barrier parameters for geodesic balls and triangles in hyperbolic space grow polynomially with diameter, blocking efficient interior-point methods for exponentially large domains in scaling problems.
A Grassmannian-metric-ball model of data uncertainty yields a closed-form robust least-squares solver that strengthens robustness and scaling in finite-horizon data-driven predictive control.
A new adaptive two-metric projection method for ℓ1 minimization with global convergence, finite-time manifold identification, and superlinear local rate under an error bound condition.
A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
Extends a prior Riemannian optimizer framework to compute the nearest matrix with repeated eigenvalues by jointly tracking left and right eigenvectors on the manifold.
Riemannian conditional gradient methods are introduced for composite optimization on manifolds, achieving O(1/k) convergence for adaptive and diminishing steps and O(1/ε²) iteration complexity for Armijo steps.
Monotonic Basin Hopping outperforms MultiStart for locating lower-energy ground states in the random field XY model after reformulating the Hamiltonian on spheres for Riemannian optimization.
A hybrid tensor network framework interpolates between classical and quantum models via controllable post-selection, with a trainable hyperparameter that complements bond dimension to enhance quantum machine learning.
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Nearest matrix with multiple eigenvalues by Riemannian optimization
Extends a prior Riemannian optimizer framework to compute the nearest matrix with repeated eigenvalues by jointly tracking left and right eigenvectors on the manifold.