Open Access
Issue
ESAIM: PS
Volume 28, 2024
Page(s) 132 - 160
DOI https://doi.org/10.1051/ps/2024002
Published online 30 April 2024
  1. F. Cérou and A. Guyader, Nearest neighbor classification in infinite dimension. ESAIM Probab. Stat. 10 (2006) 340–355. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  2. D. Preiss, Dimension of metrics and differentiation of measures. General topology and its relations to modern analysis and algebra, V (Prague, 1981). Heldermann, Berlin. Sigma Ser. Pure Math. 3 (1983) 565–568. [Google Scholar]
  3. J.I. Nagata, On a special metric and dimension. Fund. Math. 55 (1964) 181–194. [CrossRef] [MathSciNet] [Google Scholar]
  4. P.A. Ostrand, A conjecture of J. Nagata on dimension and metrization. Bull. Amer. Math. Soc. 71 (1965) 623–625. [CrossRef] [MathSciNet] [Google Scholar]
  5. B. Collins, S. Kumari and V.G. Pestov, Universal consistency of the k-NN rule in metric spaces and Nagata dimension. ESAIM Probab. Stat. 24 (2020) 914–934. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  6. C. Stone, Consistent nonparametric regression. Ann. Stat. 5 (1977) 595–645. [CrossRef] [Google Scholar]
  7. P. Assouad and T. Quentin de Gromard, Recouvrements, derivation des mesures et dimensions. Rev. Mat. Iberoam. 22 (2006) 893–953. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Korányi and H.M. Reimann, Foundations for the theory of quasiconformal mappings on the Heisenberg group. Adv. Math. 111 (1995) 1–87. [CrossRef] [MathSciNet] [Google Scholar]
  9. E. Sawyer and R.L. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces. Amer. J. Math. 114 (1992) 813–874. [CrossRef] [MathSciNet] [Google Scholar]
  10. L. Devroye and L. Györfi, Nonparametric Density Estimation. The L1 View. John Wiley & Sons, New York (1985). [Google Scholar]
  11. L.C. Zhao, Exponential bounds of mean error for the nearest neighbor estimates of regression functions. J. Multivariate Anal. 21 (1987) 168–178. [CrossRef] [MathSciNet] [Google Scholar]
  12. L. Devroye, L. Györfi and G. Lugosi, A Probabilistic Theory of Pattern Recognition. Springer-Verlag, New York (1996). [CrossRef] [Google Scholar]
  13. S. Kumari, Topics in Random Matrices and Statistical Machine Learning, Ph.D. thesis, Kyoto University, 2018, 125 pp. [Google Scholar]
  14. L. Devroye, L. Györfi A. Krzyżak and G. Lugosi, On the strong universal consistency of nearest neighbor regression function estimates. Ann. Statist. 22 (1994) 1371–1385. [MathSciNet] [Google Scholar]
  15. D.H. Fremlin, Measure Theory. Vol. 2. Broad Foundations, corrected second printing of the 2001 original, Torres Fremlin, Colchester (2003) 563+12 pp. (errata). [Google Scholar]
  16. D. Preiss, Invalid Vitali theorems, in Abstracta. 7th Winter School on Abstract Analysis. Czechoslovak Academy of Sciences (1979) 58–60. [Google Scholar]
  17. L. Devroye, Necessary and sufficient conditions for the pointwise convergence of nearest neighbor regression function estimates. Z. Wahrsch. Verw. Gebiete 61 (1982) 467–481. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. de Groot, On a metric that characterizes dimension. Can. J. Math. 9 (1957) 511–514. [CrossRef] [Google Scholar]
  19. J. Cygan, Subadditivity of homogeneous norms on certain nilpotent Lie groups. Proc. Amer. Math. Soc. 83 (1981) 69–70. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms. Trans. Amer. Math. Soc. 258 (1980) 147–153. [CrossRef] [MathSciNet] [Google Scholar]
  21. E. Le Donne, A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries. Anal. Geom. Metr. Spaces 5 (2017) 116–137. [Google Scholar]
  22. R.A. Martínez Muñoz, Novas regras de aprendizagem supervisionada utilizando a estrutura dos números p-ádicos [New supervised learning rules using the p-adic numbers structure (in Portuguese)], Ph.D. thesis, Federal University of Santa Catarina, Florianópolis, Brazil, November 2023, 189 pp., https://repositorio.ufsc.br/handle/123456789/103512. [Google Scholar]

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