Fisher metric is a metric appearing in information geometry, see there for more information and references. There are also several quantum versions. One is the Bures metric and another is quantum Fisher information matrix.

- wikipedia quantum information, Bures metric

Most references about Fisher metric are at information geometry, here we add few on quantum and $C^*$-algebraic analogues.

- P. Facchi, R. Kulkarni, V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, F. Ventriglia,
*Classical and quantum Fisher information in the geometrical formulation of quantum mechanics*, Physics Letters A 374 pp. 4801 (2010)doi

There is an analogue in free probability

- D.-V. Voiculescu,
*The analogues of entropy and of Fisher’s information measure in free probability theory. V: Noncommutative Hilbert transforms*, Invent. Math. 132:1 (1998) 189–227.

For singular statistical models (including those arising in machine learning) one needs more version of Fisher metric beyond manifolds; one possibility is in the framework of diffeologies,

- Hông Vân Lê,
*Diffeological statistical models and diffeological Hausdorff measures*, video yt, slides pdf - Hông Vân Lê, Alexey A. Tuzhilin,
*Nonparametric estimations and the diffeological Fisher metric*, arXiv:2011.13418 - Hông Vân Lê,
*Diffeological statistical models,the Fisher metric and probabilistic mappings*, Mathematics 2020, 8(2),167, arXiv:1912.02090

Last revised on August 16, 2021 at 06:56:04. See the history of this page for a list of all contributions to it.