Fetching the paper…
Reading the bibliography…
We illustrate the potential applications in machine learning of the Christoffel function, or more precisely, its empirical counterpart associated with a counting measure uniformly supported on a finite set of points.
Bergman kernels for weighted polynomials and weighted equilibrium measures of ℂ n \mathbb{C}^{n}
R. J. Berman (2009) · 1946
Earlier work this paper cites.
A remark on Stirling’s formula
H. Robbins (1955) · 1955
Earlier work this paper cites.
Remarks on Some Nonparametric Estimates of a Density Function
M. Rosenblatt (1956) · 1956
Earlier work this paper cites.
On Estimation of a Probability Density Function and Mode
E. Parzen (1962) · 1962
Earlier work this paper cites.
Über die konvexe Hülle von n zufällig gewählten Punkten
A. Rényi and R. Sulanke (1963) · 1963
Earlier work this paper cites.
Sur un problème d’estimation géométrique
J. Geffroy (1964) · 1964
Earlier work this paper cites.
Real Analysis and Probability
R. B. Ash (1972) · 1972
Earlier work this paper cites.
Orthogonal polynomials
G. Szegö (1974) · 1974
Earlier work this paper cites.
Estimation du Support et du Contour du Support d’une Loi de Probabilité
J. Chevalier (1976) · 1976
Earlier work this paper cites.
Detection of abnormal behavior via nonparametric estimation of the support
L. Devroye and G.L. Wise (1980) · 1980
Earlier work this paper cites.
Bernstein’s Inequality in L p L^{p} for 0 < p < 1 0<p<1 and ( C , 1 ) (C,1) Bounds for Orthogonal Polynomials
A. Máté and P. Nevai (1980) · 1980
Earlier work this paper cites.
Géza Freud, orthogonal polynomials and Christoffel functions. A case study
P. Nevai P (1986) · 1986
Earlier work this paper cites.
Szegö’s extremum problem on the unit circle
A. Máté and P. Nevai and V. Totik (1991) · 1991
Earlier work this paper cites.
Asymptotics for the Christoffel function for Jacobi like weights on a ball in ℝ m \mathbb{R}^{m}
L. Bos (1994) · 1994
Earlier work this paper cites.
Estimation of non-sharp support boundaries
W. Hardle, B.U.Park and A.B.Tsybakov (1995) · 1995
Earlier work this paper cites.
Asymptotical minimax recovery of sets with smooth boundaries
E. Mammen and A.B.Tsybakov (1995) · 1995
Earlier work this paper cites.
Measuring mass concentrations and estimating density contour clusters, an excess mass approach
W. Polonik (1995) · 1995
Cited alongside, same era.
Christoffel functions and Fourier series for multivariate orthogonal polynomials
Y. Xu (1995) · 1995
Cited alongside, same era.
Asymptotics for orthogonal polynomials and Christoffel functions on a ball
Y. Xu (1996) · 1996
Cited alongside, same era.
A plug-in approach to support estimation
A. Cuevas and R. Fraiman (1997) · 1997
Cited alongside, same era.
On nonparametric estimation of density level sets
A.B. Tsybakov (1997) · 1997
Cited alongside, same era.
On the asymptotics of Christoffel functions for centrally symmetric weight functions on the ball in ℝ d \mathbb{R}^{d}
L. Bos and B. Della Vecchia and G. Mastroianni (1998) · 1998
Plug-in estimation of general level sets
A. Cuevas and W. González-Manteiga and A.Rodríguez-Casal (2006) · 2006
Later among the works it cites.
The relationship between Precision-Recall and ROC curves
J. Davis and M. Goadrich (2006) · 2006
Later among the works it cites.
Measures with zeros in the inverse of their moment matrix
J.W. Helton, J.B. Lasserre and M. Putinar (2008) · 2008
Later among the works it cites.
Bergman polynomials on an archipelago: estimates, zeros and shape reconstruction
B. Gustafsson, M. Putinar, E. Saff and N. Stylianopoulos (2009) · 2009
Later among the works it cites.
Optimal rates for plug-in estimators of density level sets
P. Rigollet and R. Vert (2009) · 2009
Later among the works it cites.
Adaptive Hausdorff estimation of density level sets
A. Singh, C. Scott and R. Nowak (2009) · 2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
A limit theorem for solutions of inequalities
I.S. Molchanov (1998) · 1998
Cited alongside, same era.
Asymptotics of the Christoffel Functions on a Simplex in ℝ d \mathbb{R}^{d}
Y. Xu (1999) · 1999
Cited alongside, same era.
Set estimation and nonparametric detection
A. Baíllo, A. Cuevas and A. Justel (2000) · 2000
Cited alongside, same era.
An introduction to semialgebraic geometry
M. Coste (2000) · 2000
Cited alongside, same era.
Asymptotics for Christoffel functions for general measures on the real line
V. Totik (2000) · 2000
Cited alongside, same era.
Orthogonal polynomials of several variables
C.F. Dunkl and Y. Xu (2001) · 2001
Cited alongside, same era.
Christoffel functions and universality in the bulk for multivariate orthogonal polynomials
A. Kroò and D. S. Lubinsky (2012) · 2012
Later among the works it cites.
Christoffel functions and universality on the boundary of the ball
A. Kroó and D.S. Lubinsky (2013) · 2013
Later among the works it cites.
UCI Machine Learning Repository, http://archive.ics.uci.edu/ml
M. Lichman (2013) · 2013
Later among the works it cites.
On Poincaré cone property
A. Cholaquidis, A. Cuevas, and R. Fraiman (2014) · 2014
Later among the works it cites.
Multivariate Christoffel functions and hyperinterpolation
S. De Marchi and A. Sommariva and M. Vianello (2014) · 2014
Later among the works it cites.
Level sets and non Gaussian integrals of positively homogeneous functions
J.B. Lasserre (2015) · 2015
Later among the works it cites.
Multiple Instance Learning: Christoffel Function Approach to Distribution Regression Problem
V.G. Malyshkin (2015) · 2015
Later among the works it cites.
Local convex hull support and boundary estimation
C. Aaron and O. Bodart (2016) · 2016
Later among the works it cites.
Sorting out typicality with the inverse moment matrix SOS polynomial,
J.B. Lasserre and E. Pauwels (2016) · 2016
Later among the works it cites.
Adaptation to lowest density regions with application to support recovery
T. Patschkowski and A.Rohde (2016) · 2016
Later among the works it cites.