Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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Cambridge University Press, Cambridge, UK (2023)
21 Pith papers cite this work, alongside 421 external citations. Polarity classification is still indexing.
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UNVERDICTED 21representative citing papers
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
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.
LoRA-Muon applies Muon's spectral steepest descent to low-rank factors with split weight decay, acting as a transferable proxy for full-rank Muon and Shampoo optimizers.
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
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 review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
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.
citing papers explorer
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Fast Computation of Free-Support Wasserstein Medians
Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
-
Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
-
A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds
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.
-
Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy
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 landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
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.
-
Profile Likelihood Inference for Anisotropic Hyperbolic Wrapped Normal Models on Hyperbolic Space
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.
-
Diffusion Processes on Implicit Manifolds
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.
-
LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold
LoRA-Muon applies Muon's spectral steepest descent to low-rank factors with split weight decay, acting as a transferable proxy for full-rank Muon and Shampoo optimizers.
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Operator-norm bounds and a quadratic lower-growth example for the special Euclidean algebra se(3)
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
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Wasserstein Least Squares: A Canonical Regression Method for Probability Distributions
Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
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A Riemannian quasi-Newton algorithm for optimization with Euclidean bounds
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.
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Scale selection for geometric medians on product manifolds
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 obstructs the existence of good barriers for interior-point methods
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.
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Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach
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.
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On the resolution of $\ell_1$-norm minimization via a two-metric adaptive projection method
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.
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Density Evolution: A Multiscale View of Density Estimation
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
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Generalization of Zeroth-Order Method for Quotients of Quadratic Functions
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.
-
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.
-
Riemannian conditional gradient methods for composite optimization problems
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.
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Nonconvex optimization methods for ground states in disordered continuous-spin models
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.
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Entanglement is Half the Story: Post-Selection vs. Partial Traces
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.