Wasserstein information matrix

Amari, S.: Differential-geometrical methods in statistics. Number 28 in Lecture Notes in Statistics. Springer, Berlin; New York, corr. 2nd print edition (1990)

Amari, S.: Natural gradient works efficiently in learning. Neural Comput. 10(2), 251–276 (1998)

Amari, S.: Information Geometry and Its Applications. Number volume 194 in Applied mathematical sciences. Springer, Japan (2016)

Amari, S., Matsuda, T.: Wasserstein statistics in one-dimensional location-scale model. Ann. Inst. Stat. Math. 74, 33–47 (2022)

Arbel, M., Gretton, A., Li, W., Montufar, G.: Kernelized wasserstein natural gradient. Int. Conf. Learn. Represent. (2020)

Ay, N., Jost, J., Vân Lê, H., Schwachhöfer, L.: Information Geometry, volume 64. Springer (2017)

Bernton, E., Jacob, P.E., Gerber, M., Robert, C.P.: On parameter estimation with the Wasserstein distance. Inform. Inference A J. IMA 8(4), 657–676 (2019)

Blanchet, J., Murthy, K., Nguyen, V.A.: Statistical analysis of Wasserstein distributionally robust estimators. In: Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications, pp 227–254. INFORMS (2021)

Briol, F.-X., Barp, A., Duncan, A.B., Girolami, M.: Statistical inference for generative models with maximum mean discrepancy (2019). arXiv preprint arXiv:1906.05944

Casella, G., Berger, R.L.: Statistical Inference, vol. 2. Duxbury, Pacific Grove (2002)

Chen, Y., Li, W.: Optimal transport natural gradient for statistical manifolds with continuous sample space. Inform. Geom. 3, 1–32 (2020)

Cover, T.M., Thomas, J.A.: Elements of information theory. Wiley-Interscience, Hoboken, N.J, 2nd ed edition (2006)

Kriegl, A., Michor, P.W.: The convenient setting of global analysis, volume 53. American Mathematical Soc (1997)

Lafferty, J.D.: The density manifold and configuration space quantization. Trans. Am. Math. Soc. 305(2), 699–741 (1988)

Li, W.: Transport information geometry: Riemannian calculus on probability simplex. Inform. Geom. 5, 161–207 (2022)

Li, W., Montúfar, G.: Natural gradient via optimal transport. Inform. Geom. 1, 181–214 (2018)

Li, W., Montúfar, G.: Ricci curvature for parametric statistics via optimal transport. Inform. Geom. 3, 89–117 (2020)

Li, W., Liu, S., Zha, H., Zhou, H.; Parametric fokker-planck equation. Geom. Sci. Inform., 715–724 (2019)

Li, W., Lin, A.T., Montúfar, G.: Affine natural proximal learning. Geomet. Sci. Inform., 705–714 (2019)

Lin, A.T., Li, W., Osher, S., Montufar, G.: Wasserstein proximal of GANs. Geom. Sci. Inform., 524-533 (2021)

Lott, J.: Some geometric calculations on Wasserstein space. Commun. Math. Phys. 277, 423–437 (2008)

Mallasto, A., Haije, T.D., Feragen, A.: A formalization of the natural gradient method for general similarity measures. Geom. Sci. Inform, 599-607 (2019)

Nielsen, F.: On voronoi diagrams on the information-geometric Cauchy manifolds. Entropy 22(7), 713 (2020)

Ollivier, Y.: Online natural gradient as a Kalman filter. Electron. J. Stat. 12(2), 2930–2961 (2018)

Otto, F.: The geometry of dissipative evolution equations the porous medium equation. Commun. Part. Differ. Equ. 26(1–2), 101–174 (2001)

Otto, F., Villani, C.: Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173(2), 361–400 (2000)

Petersen, A., Müller, H.-G.: Wasserstein covariance for multiple random densities. Biometrika 106(2), 339–351 (2019)

Villani, C.: Topics in optimal transportation. Number 58. American Mathematical Soc., (2003)

Villani, C.: Optimal transport: old and new, volume 338. Springer (2008)

Wong, T.-K.L.: Logarithmic divergences from optimal transport and Rényi geometry. Inform. Geom. 1(1), 39–78 (2018)

Zozor, S., Brossier, J.-M.: Debruijn identities: from shannon, Kullback–Leibler and Fisher to generalized $$\varphi $$-entropies, $$\varphi $$-divergences and $$\varphi $$-fisher informations. In: AIP Conference Proceedings 1641, 522–529. AIP (2015)