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BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 50 Sayı: 4, 1140 - 1154, 06.08.2021
https://doi.org/10.15672/hujms.645070

Öz

Kaynakça

  • [1] M.T.K. Abbassi and M. Sarih, On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Diff. Geom. Appl. 22, 19–47, 2005.
  • [2] S. Amari, Information geometry of the EM and em algorithms for neural networks, Neural Networks, 8 (9), 1379–1408, 1995.
  • [3] F. Asgari and H.R. Salimi Moghaddam, On the Riemannian geometry of tangent Lie groups, Rend. Circ. Mat. Palermo, II. Ser. 67 (2), 185–195, 2018.
  • [4] V. Balan, E. Peyghan and E. Sharahi, Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric, Hacet. J. Math. Stat. 49 (1), 120–135, 2020.
  • [5] M. Belkin, P. Niyogi and V. Sindhwani, Manifold regularization: a geometric framework for learning from labeled and unlabeled examples, J. Mach. Learn. Res. 7, 2399– 2434, 2006.
  • [6] L. Bilen and A. Gezer, Some results on Riemannian g-natural metrics generated by classical lifts on the tangent bundle, Eurasian Math. J. 8 (4), 18–34, 2017.
  • [7] T. Fei and J. Zhang, Interaction of Codazzi couplings with (Para-)Kähler geometry, Result Math. 72 (4), 2037–2056, 2017.
  • [8] S. Gudmundsson and E. Kappos, On the geometry of the tangent bundles, Expo. Math. 20, 1–41, 2002.
  • [9] S. Ianus, Statistical manifolds and tangent bundles, Sci. Bull. Univ. Politechnica of Bucharest Ser. D, 56, 29–34, 1994.
  • [10] S.L. Lauritzen, Statistical manifolds, In: Differential Geometry in Statistical Inferences, IMS Lecture Notes Monogr. Ser. 10, Inst. Math. Statist. Hayward California, 96–163, 1987.
  • [11] H. Matsuzoe and J.I. Inoguchi, Statistical structures on tangent bundles, APPS. Appl.Sci. 5 (1), 55–57, 2003.
  • [12] K. Nomizu and T. Sasaki, Affine Differential Geometry: Geometry of Affine Immersions, vol. 111 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1994.
  • [13] L. Nourmohammadifar, E. Peyghan and S. Uddin, Geometry of almost Kenmotsu Hom-Lie algebras, Quaest. Math. DOI: 10.2989/16073606.2021.1886194.
  • [14] C.R. Rao, Information and accuracy attainable in the estimation of statistical parameters, Bull. Calcutta Math. Soc. 37, 81–91, 1945.
  • [15] A. Schwenk-Schellschmidt and U. Simon, Codazzi-equivalent affine connections, Result Math. 56, 211–229, 2009.
  • [16] K. Sun and S. Marchand-Maillet, An information geometry of statistical manifold learning, (Proceedings of the 31st International Conference on Machine Learning (ICML-14), 1–9, 2014.
  • [17] K. Yano, and S. Ishihara, Tangent and cotangent bundles, Marcel Dekker, Inc., New York 1973.

Statistical structures on tangent bundles and tangent Lie groups

Yıl 2021, Cilt: 50 Sayı: 4, 1140 - 1154, 06.08.2021
https://doi.org/10.15672/hujms.645070

Öz

Let $TM$ be a tangent bundle over a Riemannian manifold $M$ with a Riemannian metric $g$ and $TG$ be a tangent Lie group over a Lie group with a left-invariant metric $g$. The purpose of the paper is two folds. Firstly, we study statistical structures on the tangent bundle $TM$ equipped with two Riemannian $g$-natural metrics and lift connections. Secondly, we define a left-invariant complete lift connection on the tangent Lie group $TG$ equipped with metric $\tilde{g}$ introduced in [F. Asgari and H. R. Salimi Moghaddam, On the Riemannian geometry of tangent Lie groups, Rend. Circ. Mat. Palermo II. Series, 2018] and study statistical structures in this setting.

Kaynakça

  • [1] M.T.K. Abbassi and M. Sarih, On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Diff. Geom. Appl. 22, 19–47, 2005.
  • [2] S. Amari, Information geometry of the EM and em algorithms for neural networks, Neural Networks, 8 (9), 1379–1408, 1995.
  • [3] F. Asgari and H.R. Salimi Moghaddam, On the Riemannian geometry of tangent Lie groups, Rend. Circ. Mat. Palermo, II. Ser. 67 (2), 185–195, 2018.
  • [4] V. Balan, E. Peyghan and E. Sharahi, Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric, Hacet. J. Math. Stat. 49 (1), 120–135, 2020.
  • [5] M. Belkin, P. Niyogi and V. Sindhwani, Manifold regularization: a geometric framework for learning from labeled and unlabeled examples, J. Mach. Learn. Res. 7, 2399– 2434, 2006.
  • [6] L. Bilen and A. Gezer, Some results on Riemannian g-natural metrics generated by classical lifts on the tangent bundle, Eurasian Math. J. 8 (4), 18–34, 2017.
  • [7] T. Fei and J. Zhang, Interaction of Codazzi couplings with (Para-)Kähler geometry, Result Math. 72 (4), 2037–2056, 2017.
  • [8] S. Gudmundsson and E. Kappos, On the geometry of the tangent bundles, Expo. Math. 20, 1–41, 2002.
  • [9] S. Ianus, Statistical manifolds and tangent bundles, Sci. Bull. Univ. Politechnica of Bucharest Ser. D, 56, 29–34, 1994.
  • [10] S.L. Lauritzen, Statistical manifolds, In: Differential Geometry in Statistical Inferences, IMS Lecture Notes Monogr. Ser. 10, Inst. Math. Statist. Hayward California, 96–163, 1987.
  • [11] H. Matsuzoe and J.I. Inoguchi, Statistical structures on tangent bundles, APPS. Appl.Sci. 5 (1), 55–57, 2003.
  • [12] K. Nomizu and T. Sasaki, Affine Differential Geometry: Geometry of Affine Immersions, vol. 111 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1994.
  • [13] L. Nourmohammadifar, E. Peyghan and S. Uddin, Geometry of almost Kenmotsu Hom-Lie algebras, Quaest. Math. DOI: 10.2989/16073606.2021.1886194.
  • [14] C.R. Rao, Information and accuracy attainable in the estimation of statistical parameters, Bull. Calcutta Math. Soc. 37, 81–91, 1945.
  • [15] A. Schwenk-Schellschmidt and U. Simon, Codazzi-equivalent affine connections, Result Math. 56, 211–229, 2009.
  • [16] K. Sun and S. Marchand-Maillet, An information geometry of statistical manifold learning, (Proceedings of the 31st International Conference on Machine Learning (ICML-14), 1–9, 2014.
  • [17] K. Yano, and S. Ishihara, Tangent and cotangent bundles, Marcel Dekker, Inc., New York 1973.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Esmaeil Peyghan 0000-0002-2713-6253

Davood Seifipour Bu kişi benim 0000-0003-1622-3914

Aydın Gezer 0000-0001-7505-0385

Yayımlanma Tarihi 6 Ağustos 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 4

Kaynak Göster

APA Peyghan, E., Seifipour, D., & Gezer, A. (2021). Statistical structures on tangent bundles and tangent Lie groups. Hacettepe Journal of Mathematics and Statistics, 50(4), 1140-1154. https://doi.org/10.15672/hujms.645070
AMA Peyghan E, Seifipour D, Gezer A. Statistical structures on tangent bundles and tangent Lie groups. Hacettepe Journal of Mathematics and Statistics. Ağustos 2021;50(4):1140-1154. doi:10.15672/hujms.645070
Chicago Peyghan, Esmaeil, Davood Seifipour, ve Aydın Gezer. “Statistical Structures on Tangent Bundles and Tangent Lie Groups”. Hacettepe Journal of Mathematics and Statistics 50, sy. 4 (Ağustos 2021): 1140-54. https://doi.org/10.15672/hujms.645070.
EndNote Peyghan E, Seifipour D, Gezer A (01 Ağustos 2021) Statistical structures on tangent bundles and tangent Lie groups. Hacettepe Journal of Mathematics and Statistics 50 4 1140–1154.
IEEE E. Peyghan, D. Seifipour, ve A. Gezer, “Statistical structures on tangent bundles and tangent Lie groups”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 4, ss. 1140–1154, 2021, doi: 10.15672/hujms.645070.
ISNAD Peyghan, Esmaeil vd. “Statistical Structures on Tangent Bundles and Tangent Lie Groups”. Hacettepe Journal of Mathematics and Statistics 50/4 (Ağustos 2021), 1140-1154. https://doi.org/10.15672/hujms.645070.
JAMA Peyghan E, Seifipour D, Gezer A. Statistical structures on tangent bundles and tangent Lie groups. Hacettepe Journal of Mathematics and Statistics. 2021;50:1140–1154.
MLA Peyghan, Esmaeil vd. “Statistical Structures on Tangent Bundles and Tangent Lie Groups”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 4, 2021, ss. 1140-54, doi:10.15672/hujms.645070.
Vancouver Peyghan E, Seifipour D, Gezer A. Statistical structures on tangent bundles and tangent Lie groups. Hacettepe Journal of Mathematics and Statistics. 2021;50(4):1140-54.