Fetching the paper…
Reading the bibliography…
For sets $\mathcal Q$ and $\mathcal Y$, the generalized Fr\'echet mean $m \in \mathcal Q$ of a random variable $Y$, which has values in $\mathcal Y$, is any minimizer of $q\mapsto \mathbb E[\mathfrak c(q,Y)]$, where $\mathfrak c \colon \mathcal Q \times \mathcal Y \to \mathbb R$ is a cost function.
“Les éléments aléatoires de nature quelconque dans un espace distancié”
Maurice Fréchet · 1948
Earlier work this paper cites.
“Curvature measures”
Herbert Federer · 1959
Earlier work this paper cites.
“On expected figures and a strong law of large numbers for random elements in quasi-metric spaces”
Herbert Ziezold · 1977
Earlier work this paper cites.
“Empirical processes: theory and applications” 2
David Pollard · 1990
Earlier work this paper cites.
“Weak convergence and empirical processes” With applications to statistics, Springer Series in Statistics
Aad. van Vaart and Jon. Wellner · 1996
Earlier work this paper cites.
“Mathematical theory of medial axis transform”
Hyeong Choi, Sung Choi and Hwan Moon · 1997
Earlier work this paper cites.
“Applications of empirical process theory” 6
Sara. van Geer · 2000
Earlier work this paper cites.
“Geometry of the space of phylogenetic trees”
Louis. Billera, Susan. Holmes and Karen Vogtmann · 2001
Earlier work this paper cites.
“A Bennett concentration inequality and its application to suprema of empirical processes”
Olivier Bousquet · 2002
Earlier work this paper cites.
“Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature”
Karl-Theodor Sturm · 2002
Earlier work this paper cites.
“Large sample theory of intrinsic and extrinsic sample means on manifolds. I”
Rabi Bhattacharya and Vic Patrangenaru · 2003
Cited alongside, same era.
“Probability measures on metric spaces of nonpositive curvature”
Karl-Theodor Sturm · 2003
Cited alongside, same era.
“On the optimality of conditional expectation as a Bregman predictor”
Arindam Banerjee, Xin Guo and Hui Wang · 2005
Cited alongside, same era.
“A Riemannian Framework for Tensor Computing” doi: 10.1007/s11263-005-3222-z
Xavier Pennec, Pierre Fillard and Nicholas Ayache · 2006
Cited alongside, same era.
“Lectures on empirical processes” Theory and statistical applications, With a preface by Juan A. Cuesta Albertos and Carlos Matrán, EMS Series of Lectures in Mathematics
Eustasio del Barrio, Paul Deheuvels and Sara van Geer · 2007
Cited alongside, same era.
“On the boundedness of Bernoulli processes”
Witold Bednorz and Rafał Latała · 2014
Later among the works it cites.
“Upper and lower bounds for stochastic processes” Modern methods and classical problems 60
Michel Talagrand · 2014
Later among the works it cites.
“Encyclopedia of distances”
Michel Deza and Elena Deza · 2016
Later among the works it cites.
“On almost sure rates of convergence for sample average approximations” http://www.optimization-online.org/DB_HTML/2017/01/5834.html , 2017
Dirk Banholzer, Jörg Fliege and Ralf Werner · 2017
Later among the works it cites.
“Old and new challenges in Hadamard spaces”, 2018
Miroslav Bacak · 2018
Closest in time.
“Limiting behaviour of Fréchet means in the space of phylogenetic trees”
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
I.. Berg and I.. Nikolaev · 2008
Cited alongside, same era.
“Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth”
Stephan. Huckemann · 2011
Cited alongside, same era.
“Principal components analysis in the space of phylogenetic trees”
Tom.. Nye · 2011
Cited alongside, same era.
“Computing medians and means in Hadamard spaces”
Miroslav Bačák · 2014
Cited alongside, same era.
“Convex analysis and optimization in Hadamard spaces” 22
Miroslav Bačák · 2014
Cited alongside, same era.
D. Barden, H. Le and M. Owen · 2018
Closest in time.
“Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics”
A. Ahidar-Coutrix, T. Gouic and Q. Paris · 2019
Closest in time.
“Fréchet analysis of variance for random objects”
Paromita Dubey and Hans-Georg Müller · 2019
Closest in time.
“A smeary central limit theorem for manifolds with application to high-dimensional spheres”
Benjamin Eltzner and Stephan. Huckemann · 2019
Closest in time.
“Fréchet regression for random objects with Euclidean predictors”
Alexander Petersen and Hans-Georg Müller · 2019
Closest in time.