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Probability Density Functions from the Fisher Information Metric
[article]

2015
*
arXiv
*
pre-print

We show a general relation between

arXiv:1504.03184v1
fatcat:6zximcrbnfe4zpzzrkp3cpbh24
*the*spatially disjoint product of*probability**density**functions*and*the*sum of their*Fisher**information**metric*tensors. ... We then utilise this result to give a method for constructing*the**probability**density**functions*for an arbitrary Riemannian*Fisher**information**metric*tensor. ... Suppose we desire a family of*probability**density**functions*whose*Fisher**information**metric*is*the**metric*tensor of S 2 . ...##
###
Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

2010
*
Physics Letters A
*

By putting these two aspects together, we show that

doi:10.1016/j.physleta.2010.10.005
fatcat:efih6blxwzhjformbo3srk2drm
*the**Fisher**information**metric*, both classical and quantum, can be described by means of*the*Hermitian tensor on*the*manifold of pure states. ...*The*tomographic picture of quantum mechanics has brought*the*description of quantum states closer to that of classical*probability*and statistics. ... In classical*probability*theory*the**Fisher**information**metric*can be used to characterize*the*distance between*probability*distributions. ...##
###
A study on some geometrical and statistical properties of the continuous power-law distribution with a comparison of similar properties of a particular exponential distribution

2021
*
Journal of the National Science Foundation of Sri Lanka
*

A continuous real random variable x with a power-law distribution has a

doi:10.4038/jnsfsr.v49i1.9710
fatcat:7z65gzt7yfcz5ilotzg3uoxypa
*probability*p(x) of taking a value in*the*interval*from*x to x + dx, where, 2 by 〈 〉 . ... Finally, an example of an exponential distribution having*the*same*information*divergence and*Fisher**information*as that of power-law distributions is given, thus having*the*same lower bound in*the*Cramer-Rao ... We also hope that*the*same*Fisher**information*for power-law and exponential distributions we have obtained will definitely be helpful to understand*the*geometry of such networks. ...##
###
Quantum and Fisher information from the Husimi and related distributions

2006
*
Journal of Mathematical Physics
*

In

doi:10.1063/1.2168125
fatcat:cgrmknrtanhq3clsw27mh5zpui
*the*Petz-Sudar work (completing a program of Chentsov),*the*quantum analogue of*the*(classically unique)*Fisher**information*(montone)*metric*of a*probability*simplex was extended to define an uncountable ... We also investigate*the**Fisher**information**metrics*corresponding to*the*escort Husimi, positive-P and certain Gaussian*probability*distributions, as well as, in some sense,*the*discrete Wigner pseudoprobability ... ACKNOWLEDGMENTS*The*author expresses gratitude to*the*Kavli Institute for Theoretical Physics ͑KITP͒ for computational support in this research and to C. ...##
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The Brody-Hughston Fisher Information Metric
[article]

2003
*
arXiv
*
pre-print

We study

arXiv:quant-ph/0304029v2
fatcat:wdwcoujxbnhznfyp5zah4fxmay
*the*interrelationships between*the**Fisher**information**metric*recently introduced, on*the*basis of maximum entropy considerations, by Brody and Hughston (quant-ph/9906085) and*the*monotone*metrics*... is less noninformative than those obtained*from*any of*the*monotone*metrics*, even*the*minimal monotone (Bures)*metric*. ... BH indicated how to associate a*Fisher**information**metric*to their family of*density**functions*(i. e.,*probability*distributions), each distribution, of course, corresponding to a*density*matrix. ...##
###
Information metric from a linear sigma model

2012
*
Physical Review E
*

*The*idea that a spacetime

*metric*emerges as a

*Fisher*-Rao '

*information*

*metric*' of instanton moduli space has been examined in several field theories such as

*the*Yang-Mills theories and nonlinear sigma models ... In this brief paper, we report that

*the*flat Euclidean or Minkowskian

*metric*, rather than an anti-de Sitter

*metric*that generically emerges

*from*instanton moduli spaces, can be obtained as

*the*

*Fisher*-Rao ... Fund of

*the*Ministry of Education, Culture, Sports, Science and Technology, Japan (Young Scientists (B) 22740176). ...

##
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Extending the Fisher metric to density matrices
[article]

2001
*
arXiv
*
pre-print

Chentsov studied Riemannian

arXiv:quant-ph/0102132v1
fatcat:kqhcluvtsnbhheoewl65ko73iq
*metrics*on*the*set of*probability*measures*from**the*point of view of decision theory. ... He proved that up to a constant factor*the**Fisher**information*is*the*only*metric*which is monotone under stochastic transformations. ... Without some restrictions this would be pointless,*the*emphasis is put on statisticaly relevant*metrics*which on*the*submanifold of*probability*distributions recover*the**Fisher**information**metric*. 2 Chentsov's ...##
###
Hydrodynamical formulation of quantum mechanics, Kahler structure, and Fisher information
[article]

1999
*
arXiv
*
pre-print

*the*

*Fisher*

*information*

*metric*. ...

*The*Schrodinger equation can be derived using

*the*minimum

*Fisher*

*information*principle. ... CROSS-ENTROPY AND

*FISHER*

*INFORMATION*Let P (y i ) be a

*probability*

*density*which is a

*function*of n continuous coordinates y i , and let P (y i + ∆y i ) be

*the*

*density*that results

*from*a small change ...

##
###
The information metric on the moduli space of instantons with global symmetries

2016
*
Physics Letters B
*

In this note we revisit Hitchin's prescription Hitchin of

doi:10.1016/j.physletb.2015.12.044
fatcat:ogwcm7rfffezfdq6rs7tp7usnu
*the**Fisher**metric*as a natural measure on*the*moduli space of instantons that encodes*the*space-time symmetries of a classical field theory. ... Motivated by*the*idea of*the*moduli space of supersymmetric instantons as an emergent space in*the*sense of*the*gauge/gravity duality, we extend*the*prescription to encode also global symmetries of*the*... In addition we are grateful for insight*from*Tslil Clingman, Johanna Erdmenger, Hiroaki Matsueda, Andrew Singleton, Koenraad Schalm and David Tong. ...##
###
Information geometry in quantum field theory: lessons from simple examples
[article]

2020
*
arXiv
*
pre-print

By studying their

arXiv:2001.02683v2
fatcat:hxs4kom33zduxepet3cvuotrie
*Fisher**metrics*, we derive some general lessons that may have important implications for*the*application of*information*geometry in holography. ... We then investigate what*information**the**Fisher**metric*retains about*the*physics of*the*underlying theory by studying*the*geometry for both*the*classical 2d Ising model and*the*corresponding 1d free fermion ... By*the**Fisher**metric*here, we mean*the*generalization of*the*definition of*the**Fisher**metric*in which*the*real-valued*probability*distribution p is simply replaced with a*density*matrix ρ and*the*integral ...##
###
Bankruptcy analysis with self-organizing maps in learning metrics

2001
*
IEEE Transactions on Neural Networks
*

Kiviluoto for his valuable backround

doi:10.1109/72.935102
pmid:18249924
fatcat:zuyrxbunyzbotamcv6v42xceeq
*information*on bankruptcy analysis and his help regarding*the*interpretation*the*data, and*the*Academy of Finland for financial support. ... ACKNOWLEDGMENT*The*authors would like to thank Finnvera Ltd. and particularly P. Bergius for*the*data set, K. ...*The**metric*is based on*the**Fisher**information*matrix, which results*from*a local approximation of*the*Kullback-Leibler divergence between*the*posterior*densities*at close-by points in*the*primary data ...##
###
Fisher information metric and Poisson kernels

2008
*
Differential geometry and its applications
*

We show that this map is embedding and

doi:10.1016/j.difgeo.2007.11.027
fatcat:djuoyazscrf45fefh2z2vcduza
*the*pull-back*metric*of*the**Fisher**information**metric*by this embedding coincides with*the*original*metric*of X up to constant provided X is a rank one symmetric ... A complete Riemannian manifold X with negative curvature satisfying −b 2 K X −a 2 < 0 for some constants a, b, is naturally mapped in*the*space of*probability*measures on*the*ideal boundary ∂X by assigning ...*The*authors would also like to thank to a referee for useful comments. ...##
###
A novel information geometry method for estimating parameters of the Weibull wind speed distribution

2018
*
Proceedings of the Estonian Academy of Sciences
*

Non-Euclidean geometry and

doi:10.3176/proc.2018.1.01
fatcat:6ebbs76sibdvrfneyisvkwydhm
*the*Riemannian*metric*called*the**Fisher**metric*or*the**information**metric*are used in this approach. ... Differential equations derived*from**the**Fisher**information*matrix are solved for*the*Weibull statistical manifold by*the*shooting method. ... ACKNOWLEDGEMENT*The*publication costs of this article were partially covered by*the*Estonian Academy of Sciences. ...##
###
A new distribution metric for image segmentation

2008
*
Medical Imaging 2008: Image Processing
*

Moreover, we briefly provide a theoretical comparison between

doi:10.1117/12.769010
dblp:conf/miip/SandhuGT08
fatcat:heh366uvtvdvnl5rqqcvidu4de
*the*popular*Fisher**Information**metric*,*from*which*the*Bhattacharyya distance originates, with*the*newly proposed similarity*metric*. ... Forming a natural geodesic, our*metric*quantifies "distance" for two*density**functionals*as*the*standard deviation of*the*difference between logarithms of those distributions. ...*Information*on*the*National Centers for Biomedical Computing can be obtained*from*http://nihroadmap.nih.gov/bioinformatics. ...##
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Information Geometry and Classical Cramér-Rao Type Inequalities
[article]

2021
*
arXiv
*
pre-print

We examine

arXiv:2104.01061v3
fatcat:augyhh34xjfjpawc6ia62am53m
*the*role of*information*geometry in*the*context of classical Cramér-Rao (CR) type inequalities. ...*The*classical deterministic CR inequality is derived*from*Kullback-Leibler (KL)-divergence. ... M. acknowledges support*from**the*National Academies of Sciences, Engineering, and Medicine via Army Research Laboratory Harry Diamond Distinguished Postdoctoral Fellowship. ...
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