Cited by 1,673Probability and Statistical ResearchAdvanced Differential Geometry ResearchStatistical Methods and Applications

The DOI matches its Crossref record.

Differential-Geometrical Methods in Statistics

Amari, Shun-ichi·1985·Lecture Notes in Statistics

DOI 10.1007/978-1-4612-5056-2

Open this paper in CoChat — free account

Integrity signals

Registry

Crossref · 10.1007/978-1-4612-5056-2

Cites

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Still being checked.

Sorted by citations

Items 701–800 of 999

Instantons and the Information Metric
Groisser, D., & Murray, M. K. (1997) · Annals of Global Analysis and Geometry · doi:10.1023/a:1006560802410 · Cited by 9
Reconstruction of complex signals using minimum Rényi information
Frieden, B. R., & Bajkova, A. T. (1995) · Applied Optics · doi:10.1364/ao.34.004086 · Cited by 9
A CRITICAL COMPARISON OF THREE INFORMATION-BASED APPROACHES TO PHYSICS
Frieden, B. R., & Soffer, B. H. (2000) · Foundations of Physics Letters · doi:10.1023/a:1007725804670 · Cited by 9
On Formulas for the Distribution of Nonlinear L.S. Estimates
Pázman, A. (1987) · Statistics · doi:10.1080/02331888708801983 · Cited by 9
Erratum: Second-order approximation of the entropy in nonlinear least-squares estimation
Luc Pronzato, B., & Pázman, A. (1994) · Czech digital mathematics library · Cited by 9
Kernelized Wasserstein Natural GradientPreprint
Arbel, M., Gretton, A., Li, W., & Montúfar, G. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.09652 · Cited by 9
Group Invariance of Information Geometry on q-Gaussian Distributions Induced by Beta-Divergence
Ohara, A., & Eguchi, S. (2013) · Entropy · doi:10.3390/e15114732 · Cited by 8
Extremities for statistical submanifolds in Кenmotsu statistical manifolds
Sıddıquı, A. N., Suh, Y. J., & Bahadır, O. (2021) · Filomat · doi:10.2298/fil2102591s · Cited by 8
Thermodynamics and Geometry of Strange Quark Matter
Gholizade, H., Altaibayeva, A., & Myrzakulov, R. (2014) · International Journal of Theoretical Physics · doi:10.1007/s10773-014-2417-x · Cited by 8
Immunophenotypic signatures of benign and dysplastic granulopoiesis by cytomic profiling
Finn, W. G., Harrington, A. M., Carter, K. M., Raich, R., Kroft, S. H., & Hero, A. O. (2011) · Cytometry Part B Clinical Cytometry · doi:10.1002/cyto.b.20592 · Cited by 8
F-Geometry and Amari’s α-Geometry on a Statistical Manifold
Harsha, K. V., & Subrahamanian, S. (2014) · Entropy · doi:10.3390/e16052472 · Cited by 8
On locally dually flat (α, β)-metrics with isotropic S-curvature
Tayebi, A., Peyghan, E., & Sadeghi, H. (2012) · Indian Journal of Pure and Applied Mathematics · doi:10.1007/s13226-012-0031-2 · Cited by 8
Welcome to Riemannian Computing in Computer Vision
Srivastava, A., & Turaga, P. K. (2015) · Springer eBooks · doi:10.1007/978-3-319-22957-7_1 · Cited by 8
Asymptotic Expansions for Stochastic Processes
Yoshida, N. (2016) · Springer eBooks · doi:10.1007/978-3-319-30190-7_2 · Cited by 8
Entropic Regularization of Markov Decision Processes
Belousov, B., & Peters, J. (2019) · Entropy · doi:10.3390/e21070674 · Cited by 13
Relations between Extrinsic and Intrinsic Invariants of Statistical Submanifolds in Sasaki-Like Statistical Manifolds
Aytimur, H., Mihai, A., & Özgür, C. (2021) · Mathematics · doi:10.3390/math9111285 · Cited by 8
Chen Inequalities for Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms
Decu, S., & Haesen, S. (2022) · Mathematics · doi:10.3390/math10030330 · Cited by 8
On an intrinsic analysis of statistical estimation
Oller, J. M. (1993) · Elsevier eBooks · doi:10.1016/b978-0-444-81531-6.50030-1 · Cited by 8
An information geometry algorithm for distribution control
Zhong, F., Sun, H., & Zhang, Z. (2008) · Bulletin of the Brazilian Mathematical Society New Series · doi:10.1007/s00574-008-0068-3 · Cited by 8
Natural Gradient Descent for Training Stochastic Complex-Valued Neural Networks
Nitta, T. (2014) · International Journal of Advanced Computer Science and Applications · doi:10.14569/ijacsa.2014.050729 · Cited by 8
Using Entropy Leads to a Better Understanding of Biological Systems
Tseng, C., & Tuszyński, J. A. (2010) · Entropy · doi:10.3390/e12122450 · Cited by 8
Universal connection and curvature for statistical manifold geometry
Arwini, K., Riego, L. D., & Dodson, C. T. J. (2007) · MIMS EPrints (University of Southampton) · Cited by 8
Ranking evaluation of institutions based on a Bayesian network having a latent variable
Jun-Seong, K., & Jun, C. (2013) · Knowledge-Based Systems · doi:10.1016/j.knosys.2013.05.010 · Cited by 8
Functional Data and Elastic Registration
Srivastava, A., & Klassen, E. P. (2016) · Springer series in statistics · doi:10.1007/978-1-4939-4020-2_4 · Cited by 8
Generalized Wintegen Type Inequality for Lagrangian Submanifolds in Holomorphic Statistical Space Forms
Boyom, M. N., Aquib, M., Shahid, M. H., & Jamali, M. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-68445-1_19 · Cited by 8
An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information
Ali, S. A., Cafaro, C., Gassner, S., & Giffin, A. (2018) · Advances in Mathematical Physics · doi:10.1155/2018/2048521 · Cited by 8
Geometry of Lightlike Hypersurfaces of a Statistical Manifold
Bahadır, O., & Tripathi, M. M. (2023) · WSEAS TRANSACTIONS ON MATHEMATICS · doi:10.37394/23206.2023.22.52 · Cited by 8
On the geometry of lightlike submanifolds of indefinite statistical manifolds
Jain, V., Singh, A. P., & Kumar, R. (2020) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887820500991 · Cited by 8
Information Geometry of α-Projection in Mean Field Approximation
Амари, Ш.-И., Ikeda, S., & Shimokawa, H. (2004) · Cited by 8
A Study of Kenmotsu-like Statistical Submersions
Siddiqi, M. D., Sıddıquı, A. N., Mofarreh, F., & Aytimur, H. (2022) · Symmetry · doi:10.3390/sym14081681 · Cited by 8
Data Visualization and Analysis with Self-Organizing Maps in Learning Metrics
Samuel Kaski, A., Sinkkonen, J., & Peltonen, J. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44801-2_17 · Cited by 8
Sparse Super Symmetric Tensor Factorization
Cichocki, A. S., Jankovic, M. V., Zdunek, R., & Амари, Ш.-И. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-69158-7_81 · Cited by 8
Stochastic Processes Having Fractional Order Nonlinearity Associated with Hyper Gamma Distribution
Konno, H., & Lomdahl, P. S. (2004) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.73.573 · Cited by 8
Asymptotically optimal tests for parametric functions against ordered functional alternatives
Tsai, M.-T., & Sen, P. K. (2004) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2004.07.002 · Cited by 8
Minimumα‐divergence estimation for arch models
Chandra, S. A., & Taniguchi, M. (2006) · Journal of Time Series Analysis · doi:10.1111/j.1467-9892.2005.00444.x · Cited by 8
A geometric approach to statistical estimation
Kulhavý, R. (2002) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.1995.480237 · Cited by 8
Statistics for the LHC: Progress, Challenges, and Future
Cranmer, K. S. (2008) · CERN Document Server (European Organization for Nuclear Research) · doi:10.5170/cern-2008-001.47 · Cited by 8
Separation of non-stationary sources: algorithms and performance
Cardoso, J.-F., & Pham, D.-T. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148.007 · Cited by 8
On the Riemannian Interpretation of the Gauss-Newton Algorithm
Hanzon, B., & Peeters, R. (1993) · Springer eBooks · doi:10.1007/978-1-4615-2968-2_7 · Cited by 8
Geometrical interpretation of iterative turbo decoding
Muquet, B., Duhamel, P., & Courville, A. (2003) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2002.1023414 · Cited by 8
Extensions of the conjugate prior through the Kullback–Leibler separators
Yanagimoto, T., & Ohnishi, T. (2003) · Journal of Multivariate Analysis · doi:10.1016/s0047-259x(03)00133-7 · Cited by 8
Image and Audio Distances
Deza, M. M., & Deza, E. I. (2014) · Springer eBooks · doi:10.1007/978-3-662-44342-2_21 · Cited by 8
Bayesian asymptotics under misspecification
Kleijn, B. (2004) · Digital Academic REpository of VU University Amsterdam (Vrije Universiteit Amsterdam) · Cited by 8
Almost exact distributions of estimators ii- hat nonlinear regression models
Pázman, A. (1990) · Statistics · doi:10.1080/02331889008802222 · Cited by 8
f-GANs in an Information Geometric NutshellPreprint
Nock, R., Cranko, Z., Menon, A. K., Qu, L., & Williamson, R. C. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1707.04385 · Cited by 8
Kählerian information geometry for signal processingPreprint
Choi, J., Andrew, & Mullhaupt, P. (2016) · Cited by 8
Bayesian Robustness: A New Look from Geometry
Rodríguez, C. C. (1996) · Springer eBooks · doi:10.1007/978-94-015-8729-7_5 · Cited by 8
Distances on Strings and Permutations
Deza, M. M., & Deza, E. I. (2014) · Springer eBooks · doi:10.1007/978-3-662-44342-2_11 · Cited by 8
Lifts of a Semi-Symmetric Metric Connection from Sasakian Statistical Manifolds to Tangent Bundle
Kumar, R., Shenawy, S., Turki, N. B., Colney, L., & De, U. C. (2024) · Mathematics · doi:10.3390/math12020226 · Cited by 7
Information Geometry Under Monotone Embedding. Part I: Divergence Functions
Zhang, J., & Naudts, J. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-68445-1_24 · Cited by 7
Weighted Relative Group Entropies and Associated Fisher Metrics
Hirica, I.-E., Pripoae, C.-L., Pripoae, G.-T., & Preda, V. (2022) · Entropy · doi:10.3390/e24010120 · Cited by 7
DIFFERENTIAL GEOMETRY OFARFIMAPROCESSES
Равишанкер, Н. (2001) · Communication in Statistics- Theory and Methods · doi:10.1081/sta-100105703 · Cited by 7
Eidetic Reduction of Information Geometry Through Legendre Duality of Koszul Characteristic Function and Entropy: From Massieu–Duhem Potentials to Geometric Souriau Temperature and Balian Quantum Fisher Metric
Barbaresco, F. (2014) · Signals and communication technology · doi:10.1007/978-3-319-05317-2_7 · Cited by 7
Maximum likelihood estimators uniformly minimize distribution variance among distribution unbiased estimators in exponential families
Vos, P. W., & Wu, Q. (2015) · Bernoulli · doi:10.3150/14-bej637 · Cited by 7
Second-Order Powers of a Class of Tests in the Presence of a Nuisance Parameter
Kakizawa, Y. (2012) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2011.564743 · Cited by 7
Improved data visualisation through nonlinear dissimilarity modelling
Rice, I. (2017) · Pattern Recognition · doi:10.1016/j.patcog.2017.07.016 · Cited by 7
The influence of the dynamic state of galaxy clusters on segregation phenomena and velocity dispersion profiles
Nascimento, R. S., Lopes, P. A. A., Ribeiro, A. L. B., Costa, A. P., & Morell, D. F. (2018) · Monthly Notices of the Royal Astronomical Society Letters · doi:10.1093/mnrasl/sly229 · Cited by 7
Entropic Dynamics of Exchange Rates and Options
Abedi, M., & Bartolomeo, D. (2019) · Entropy · doi:10.3390/e21060586 · Cited by 7
Information geometry of scaling expansions of non-exponentially growing configuration spaces
Korbel, J., Hanel, R., & Stefan Thurner, A. (2020) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2020-900190-x · Cited by 7
Optimizations on Statistical Hypersurfaces with Casorati Curvatures
Sıddıquı, A. N., & Shahid, M. H. (2021) · Kragujevac Journal of Mathematics · doi:10.46793/kgjmat2103.449s · Cited by 7
Minimum-entanglement protocols for function estimation
Ehrenberg, A., Bringewatt, J., & Gorshkov, A. V. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.033228 · Cited by 8
Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection
Decu, S., & Vîlcu, G. (2022) · Entropy · doi:10.3390/e24060800 · Cited by 7
Optimal projection filters with information geometry
Armstrong, J., Brigo, D., & Hanzon, B. (2023) · Information Geometry · doi:10.1007/s41884-023-00108-x · Cited by 7
Remarks on Invariance in the Primary Visual Systems of Mammals
Bennequin, D. (2014) · Lecture notes in morphogenesis · doi:10.1007/978-3-642-34444-2_7 · Cited by 7
Gradients on matrix manifolds and their chain rule
Theis, F. J. (2005) · University of Regensburg Publication Server (University of Regensburg) · Cited by 7
Bayesian Information Geometry: Application to Prior Selection on Statistical Manifolds
Snoussi, H. (2007) · Advances in imaging and electron physics · doi:10.1016/s1076-5670(06)46003-1 · Cited by 7
Some properties of m-th root Finsler metrics
Tayebi, A., Nankali, A., & Peyghan, E. (2014) · Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) · doi:10.3103/s1068362314040049 · Cited by 7
A Riemannian manifold analysis of endothelial cell monolayer impedance parameter precision
English, A. E., Plaut, C., & Moy, A. B. (2007) · Journal of Mathematical Biology · doi:10.1007/s00285-007-0103-9 · Cited by 7
DATA SET MODELS AND EXPONENTIAL FAMILIES IN STATISTICAL PHYSICS AND BEYOND
Naudts, J., & Anthonis, B. (2012) · Modern Physics Letters B · doi:10.1142/s0217984912500625 · Cited by 7
Quantum Fisher Information andq-Deformed Relative Entropies
Hasegawa, H. (2006) · Progress of Theoretical Physics Supplement · doi:10.1143/ptps.162.183 · Cited by 7
Computational Information Geometry in Statistics: Foundations
Anaya‐Izquierdo, K., Critchley, F., Marriott, P. K., & Vos, P. W. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-40020-9_33 · Cited by 7
Intrinsic Losses Based on Information Geometry and Their Applications
Rong, Y., Tang, M., & Zhou, J. (2017) · Entropy · doi:10.3390/e19080405 · Cited by 7
Geometry of Chen invariants in statistical warped product manifolds
Al-Solamy, F. R., Bansal, P., Chen, B., Murathan, C., & Shahid, M. H. (2020) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887820500814 · Cited by 7
Thermodynamic geometry for binary mixtures: A constrained approach
Jaramillo-Gutiérrez, J., López-Picón, J. L., & Torres-Arenas, J. (2020) · Journal of Molecular Liquids · doi:10.1016/j.molliq.2020.114213 · Cited by 7
Differential Geometrical Theory of Statistics
Barbaresco, F., & Nielsen, F. (2017) · MDPI eBooks · doi:10.3390/books978-3-03842-425-3 · Cited by 7
Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures
Lee, C. W., & Lee, J. W. (2018) · Mathematics · doi:10.3390/math6110259 · Cited by 7
Learning metrics for exploratory data analysis
Samuel Kaski, A. (2002) · Machine learning for signal processing ... · doi:10.1109/nnsp.2001.943110 · Cited by 7
The Information Metric on Rational Maps
Murray, M. K. (1993) · Experimental Mathematics · doi:10.1080/10586458.1993.10504568 · Cited by 7
Improving Path Trimming in a Network Algorithm for Fisher's Exact Test in Two-way Contingency Tables
Aoki, S. (2002) · Journal of Statistical Computation and Simulation · doi:10.1080/00949650212389 · Cited by 7
Statistical information approaches for the modelling of the epileptic brain
Pardalos, P. M., Sackellares, J. C., Iasemidis, L. D., Yatsenko, V., Yang, M. C. K., Shiau, D., & Chaovalitwongse, W. A. (2003) · Computational Statistics & Data Analysis · doi:10.1016/s0167-9473(02)00152-4 · Cited by 7
Convex foundations for generalized MaxEnt models
Frongillo, R., & Reid, M. D. (2014) · AIP conference proceedings · doi:10.1063/1.4903703 · Cited by 7
A geometric look at nuisance parameter effect of local powers in testing hypothesis
Eguchi, S. (1991) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00118634 · Cited by 7
Generalized Relative Entropies as Contrast Functionals on Density Matrices
Jenčová, A. (2004) · International Journal of Theoretical Physics · doi:10.1023/b:ijtp.0000048809.54756.84 · Cited by 7
Divergence Based Online Learning in Vector Quantization
Villmann, T., Haase, S., Schleif, F.-M., & Hammer, B. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-13208-7_60 · Cited by 7
Mathematical Aspects of Divergence Based Vector Quantization Using Fr´ echet-Derivatives - Extended and revised version -
Villmann, T., & Haase, S. (2010) · Cited by 7
Can Approximate Bayesian Estimation be Consistent with the Ideal Solution? *
Kulhavý, R. (1993) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)48274-7 · Cited by 7
Differential Geometric Structures of Stable State Feedback Systems with Dual Connections
Ohara, A., & Амари, Ш.-И. (1992) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)49745-x · Cited by 7
Nonlinear ICA
Karhunen, J. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148.005 · Cited by 7
Towards Real-Time Implementation of Bayesian Parameter Estimation
Kulhavý, R., Nagy, I., & Spousta, J. (1992) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)50709-0 · Cited by 7
Affine connections, duality and divergences for a von Neumann algebraPreprint
Jenčová, A. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.math-ph/0311004 · Cited by 7
Assessing case influence on confidence intervals in nonlinear regression
Dzięciołowski, K., & Ross, W. H. (1990) · Canadian Journal of Statistics · doi:10.2307/3315561 · Cited by 7
SVM that maximizes the margin in the input space
Akaho, S. (2004) · Systems and Computers in Japan · doi:10.1002/scj.10631 · Cited by 7
Algorithmic Information Theoretic Issues in Quantum MechanicsPreprint
Segre, G. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0110018 · Cited by 10
Bayesian geometric theory of learning algorithms
Zhu, H. (2002) · IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks · doi:10.1109/icnn.1997.616171 · Cited by 7
A geometrothermodynamic approach to ideal quantum gases and Bose-Einstein condensatesPreprint
Quevedo, H., & Zaldivar, S. A. (2015) · arXiv (Cornell University) · Cited by 7
DATA EXPLORATION WITH LEARNING METRICS
Peltonen, J. (2004) · Aaltodoc (Aalto University) · Cited by 7
Learning metrics and discriminative clustering
Sinkkonen, J. (2003) · Aaltodoc (Aalto University) · Cited by 7
Differential Geometry of Recursive Nonlinear Estimation
Kulhavý, R. (1990) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)51988-6 · Cited by 7
Monotone Riemannian metrics on density matrices with nonmonotone scalar curvaturePreprint
Andai, A. (2013) · Cited by 7
Towards a Statistical GeometrodynamicsPreprint
Caticha, A. (2003) · Cited by 7

Authors: Amari, S.-I.
Venue: Lecture Notes in Statistics
Publisher: Springer New York
Published: 1985
ISSN: 0930-0325 (ISSN-L)
DOI: 10.1007/978-1-4612-5056-2
OpenAlex: W1520168181
Cited by: 1,673
References: 0
Citations by year: 2026: 26 · 2025: 21 · 2024: 53 · 2023: 55 · 2022: 72 · 2021: 67 · 2020: 57 · 2019: 75 · 2018: 49 · 2017: 55 · 2016: 51 · 2015: 51 · 2014: 80 · 2013: 67 · 2012: 51
FWCI: 8.33
Type: book
Language: en
Open access: closed
Licence: www.springer.com/tdm (tdm)
Locations: Lecture notes in statistics (publishedVersion)
CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords: differential geometry, statistical inference, statistical manifolds, information geometry

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Differential-Geometrical Methods in Statistics

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks