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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DMW relaxes and lower-bounds GW by transporting distributions of sampled distance matrices, with finite-sample bounds depending on intrinsic dimension and sliced/multi-scale variants for computation.
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.
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.
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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.
A spectral generalized covariance measure enables conditional independence testing on non-Euclidean data with uniform bootstrap validity and power guarantees under doubly robust conditions.
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.
Provides integral representation of nonnegative functionals on Archimedean cones without semiring or quadratic module assumptions and solves moment problems on compacts of characters.
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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Distance-Matrix Wasserstein Statistics for Scalable Gromov--Wasserstein Learning
DMW relaxes and lower-bounds GW by transporting distributions of sampled distance matrices, with finite-sample bounds depending on intrinsic dimension and sliced/multi-scale variants for computation.
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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.
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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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Weyl asymptotic formulas in the nilpotent Lie group setting
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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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.
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Testing Conditional Independence via the Spectral Generalized Covariance Measure: Beyond Euclidean Data
A spectral generalized covariance measure enables conditional independence testing on non-Euclidean data with uniform bootstrap validity and power guarantees under doubly robust conditions.
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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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Moment problems on compacts of characters of an unital commutative algebra
Provides integral representation of nonnegative functionals on Archimedean cones without semiring or quadratic module assumptions and solves moment problems on compacts of characters.