Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
Principal geodesic analysis for the study of nonlinear statistics of shape,
5 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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UNVERDICTED 5representative citing papers
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.
Introduces Wasserstein Tangential PCA (WT-PCA) as a variational dynamical approach to log-PCA on the Wasserstein space and derives its empirical statistical convergence rate in 2-Wasserstein distance.
Introduces Riemannian Nyström approximation via subspace projections and Haar-Grassmann sketching for tangent operators, plus a randomized Newton method, tested on SPD and Grassmann 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.
citing papers explorer
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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.
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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.
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Another Look at Log-PCA for Probability Measures: A Dynamical Formulation and Statistical Convergence
Introduces Wasserstein Tangential PCA (WT-PCA) as a variational dynamical approach to log-PCA on the Wasserstein space and derives its empirical statistical convergence rate in 2-Wasserstein distance.
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Nystr\"om Approximation on Manifolds
Introduces Riemannian Nyström approximation via subspace projections and Haar-Grassmann sketching for tangent operators, plus a randomized Newton method, tested on SPD and Grassmann manifolds.
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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.