The proposed approach as Fr´echet manifold learning with multidimensional scaling for samples of metric space valued data is illustrated with distributional data for baby names, bike rentals and age pyramids and it is demonstrated how it can be applied for a novel distributional regression method that features one-dimensional distributions as predictors.
It is shown that inner products in the random feature space approximate well-defined rotation-invariant Grassmannian kernels that depend only on the principal angles between subspaces, which accurately preserve Grassmannian geometry while reducing computation, memory, and storage.
Rémi Delogne, L. Jacques· Trans. Mach. Learn. Res.· 0 citations
This work develops a bootstrap algorithm on Riemannian manifolds that is both computationally efficient and accurate for hypothesis testing and confidence region construction, and establishes high-order asymptotics under an appropriate coordinate representation induced by a second-order retraction.
Cheng-Zhu Huang, An-Ru R. Zhang· Annals of Statistics· 0 citations
This approach reframes structural constraints as geometric priors and suggests a route for incorporating biological, spectral, or hardware-derived distributional information into both learning systems, viz., classical and quantum learning.
Numerical experiments show that GW quantization opens up many modeling possibilities beyond normal clustering methods and that the introduced algorithm leads to useful numerical solutions with approximation quality often in line with theoretically optimal rates.
Hyperspheres are emphasized throughout as a particular manifold of interest, motivated by applications over preshape spaces for statistical shape analysis and the resulting intrinsic formulation is contrasted with the extrinsic, embedding-based gradient average of manifold learning.
We develop notions of covariance and principal component analysis (PCA) for probability measures on Riemannian manifolds of bounded geometry and a discrete counterpart for distributions on the vertex sets of weighted simple graphs. Rather than anchoring variation at the Fr\'{e}chet mean, whose uniqueness and usefulness...
L. Hartmann, Wen-Wen Li, W. Mio· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
