Fetching the paper…
Reading the bibliography…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation.
On the point for which the sum of the distances to n n given points is minimum
E. Weiszfeld · 1937
Earlier work this paper cites.
Lés élements aléatoires de nature quelconque dans un espace distancié
Maurice Fréchet · 1948
Earlier work this paper cites.
Statistics of directional data
K. V. Mardia · 1972
Earlier work this paper cites.
Riemannian center of mass and mollifier smoothing
H. Karcher · 1977
Earlier work this paper cites.
Problem complexity and method efficiency in optimization, 1983
A. Nemirovski and D. Yudin · 1983
Earlier work this paper cites.
Shape manifolds, Procrustean metrics, and complex projective spaces
D. G. Kendall · 1984
Earlier work this paper cites.
Active shape models-their training and application
T.F. Cootes, C.J. Taylor, D.H. Cooper, and J. Graham · 1995
Earlier work this paper cites.
Derivatives of the matrix exponential and their computation
Igor Najfeld and Timothy F Havel · 1995
Earlier work this paper cites.
On the exponential metric increasing property
Rajendra Bhatia · 2003
Earlier work this paper cites.
Clustering on the unit hypersphere using von mises-fisher distributions
Arindam Banerjee, Inderjit S Dhillon, Joydeep Ghosh, and Suvrit Sra · 2005
Earlier work this paper cites.
Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces
Stephan Huckemann and Herbert Ziezold · 2006
Earlier work this paper cites.
Modern Geometric Structures and Fields. Transl. from the Russian by D. Chibisov
S. P. Novikov and I. A. Taimanov · 2006
Cited alongside, same era.
Diffusion tensor imaging of the brain
Andrew L Alexander, Jee Eun Lee, Mariana Lazar, and Aaron S. Field · 2007
Cited alongside, same era.
Riemannian geometry for the statistical analysis of diffusion tensor data
P. Thomas Fletcher and Sarang Joshi · 2007
Cited alongside, same era.
Robust statistics on riemannian manifolds via the geometric median
P. Thomas Fletcher, Suresh Venkatasubramanian, and Sarang C. Joshi · 2008
Cited alongside, same era.
Random number generatrion form von mises-fisher distribution
S. Jung · 2010
Cited alongside, same era.
The differential of the exponential map, jacobi fields and exact principal geodesic analysis
Low-rank matrix completion via preconditioned optimization on the grassmann manifold
Nicolas Boumal and P.-A. Absil · 2015
Later among the works it cites.
Geometric median and robust estimation in banach spaces
Stanislav Minsker · 2015
Later among the works it cites.
Scale and curvature effects in principal geodesic analysis
Drew Lazar and Lizhen Lin · 2017
Later among the works it cites.
Bayesian nonparametric inference on the Stiefel manifold
Lizhen Lin, Vinayak Rao, and David B. Dunson · 2017
Later among the works it cites.
Extrinsic local regression on manifold-valued data
Lizhen Lin, Brian St. Thomas, Hongtu Zhu, and David B. Dunson · 2017
Later among the works it cites.
Learning invariant riemannian geometric representations using deep nets
Suhas Lohit and Pavan K. Turaga · 2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Stefan Sommer, François Lauze, and Mads Nielsen · 2010
Cited alongside, same era.
Regression on manifolds: estimation of the exterior derivative
Anil Aswani, Peter Bickel, Claire Tomlin, et al · 2011
Cited alongside, same era.
Robust empirical mean Estimators
M. Lerasle and R. I. Oliveira · 2011
Cited alongside, same era.
Nonparametric Inference on Manifolds: With Applications to Shape Spaces
A. Bhattacharya and R. Bhattacharya · 2012
Cited alongside, same era.
A geometric approach to low-rank matrix completion
W. Dai, E. Kerman, and O. Milenkovic · 2012
Cited alongside, same era.
An omnibus CLT for Fréchet means and nonparametric inference on non-Euclidean spaces
R. Bhattacharya and L. Lin · 2013
Cited alongside, same era.
Robust and scalable Bayes via a median of subset posterior measures
Stanislav Minsker, Sanvesh Srivastava, Lizhen Lin, and David B. Dunson · 2017
Later among the works it cites.
Communication efficient parallel algorithms for optimization on manifolds
Bayan Saparbayeva, Michael Minyi Zhang, and Lizhen Lin · 2018
Later among the works it cites.
Regularization, sparse recovery, and median-of-means tournaments
Gábor Lugosi and Shahar Mendelson · 2019
Later among the works it cites.
Averages of unlabeled networks: Geometric characterization and asymptotic behavior
Eric D. Kolaczyk, Lizhen Lin, Steven Rosenberg, Jackson Walters, and Jie Xu · 2020
Closest in time.
Robust machine learning by median-of-means: Theory and practice
Guillaume Lecué and Matthieu Lerasle · 2020
Closest in time.