Differential-Geometrical Methods in Statistics

On mean scaled insurance risk models

Hürlimann, W. (1998) · Blätter der DGVFM · doi:10.1007/bf02808288 · Cited by 5

Marginal information for expectation parameters

Hudson, S., & Vos, P. W. (2000) · Canadian Journal of Statistics · doi:10.2307/3315922 · Cited by 5

Bogoliubov’s metric as a global characteristic of the family of metrics in the Hilbert algebra of observables

Rudoy, Y. G. (2009) · Theoretical and Mathematical Physics · doi:10.1007/s11232-009-0108-1 · Cited by 5

Application of the Fisher-Rao Metric to Structure Detection

Maybank, S. J. (2006) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-006-4533-6 · Cited by 5

On large deviation asymptotics of some tests in time series

Taniguchi, M. (2001) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(00)00353-0 · Cited by 5

Relative curvature measures of nonlinearity for time series models

Ravishankar, N. (1994) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610919408813178 · Cited by 5

Generalized Jensen difference divergence measures and Fisher measure of information

Pardo, L., Morales, D., & Taneja, I. J. (1995) · Kybernetes · doi:10.1108/03684929510083066 · Cited by 5

Monte carlo comparison of wald's, likelihood ratio and rao's tests

Sutradhar, B. C., & Bartlett, R. F. (1993) · Journal of Statistical Computation and Simulation · doi:10.1080/00949659308811490 · Cited by 5

Dimension Reduction with Linear Discriminant Functions Based on an Odds Ratio Parameterization

van der Linde, A. (2003) · International Statistical Review · doi:10.1111/j.1751-5823.2003.tb00218.x · Cited by 5

The Use of MDL to Select among Computational Models of Cognition

Myung, I. J., Pitt, M. A., Zhang, S., & Balasubramanian, V. (2000) · Cited by 5

Classical typicality of the canonical distribution

Plastino, A. R., & Daffertshofer, A. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/84/30006 · Cited by 5

Information Theory Related Learning

Villmann, T., Príncipe, J. C., & Cichocki, A. S. (2011) · Cited by 5

Channel identification and tracking using alternating projections

Zia, A., Reilly, J. P., & Shirani, S. (2004) · IEEE Statistical Signal Processing Workshop (SSP) · doi:10.1109/ssp.2003.1289439 · Cited by 5

Black hole geometric thermodynamics

Udri, C., Ciancio, V., & Ghionea, F. (2007) · Cited by 5

Channel identification and tracking using alternating projections

Zia, A., Reilly, J. P., & Shirani, S. (2003) · Cited by 5

Information geometry for the strongly degenerate ideal Bose–Einstein fluid

López-Picón, J. L., & López-Vega, J. M. (2021) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2021.126144 · Cited by 5

Exponential families admitting almost complex structures

Takano, K. (2010) · SUT Journal of Mathematics · doi:10.55937/sut/1279305629 · Cited by 5

The Information Geometry of Space-Time

Caticha, A. (2019) · International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt) · doi:10.3390/proceedings2019033015 · Cited by 5

Identification method of stochastic nonlinear dynamics using dynamical phase analysis—application to Forsmark data

WATANABE, F., Konno, H., & Kanemoto, S. (2003) · Annals of Nuclear Energy · doi:10.1016/j.anucene.2003.08.004 · Cited by 5

Space-dependency analysis of amplitude and decay ratio based on Forsmark noise data: new approach to contraction of space-dependent information on reactor stability

WATANABE, F., & Konno, H. (2003) · Annals of Nuclear Energy · doi:10.1016/s0306-4549(03)00057-4 · Cited by 5

Minimum cross-entropy estimation with inaccurate side information

Campbell, L. L. (1999) · IEEE Transactions on Information Theory · doi:10.1109/18.796421 · Cited by 5

Information Theoretic Aspects of Fairness Criteria in Network Resource Allocation Problems

Uchida, M. (2007) · International ICST Conference on Performance Evaluation Methodologies and Tools (VALUETOOLS) · doi:10.4108/gamecomm.2007.2039 · Cited by 5

Image processing methods using ICA mixture models

Lee, T.-W., & Lewicki, M. S. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148.010 · Cited by 5

Similarity Measures and Generalized Divergences

Cichocki, A. S., Zdunek, R., Phan, A. H., & Амари, Ш.-И. (2009) · doi:10.1002/9780470747278.ch2 · Cited by 5

On the monotonicity conjecture for the curvature of the Kubo-Mori metricPreprint

Andai, A. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.math-ph/0310064 · Cited by 5

Information Geometry and Statistical ManifoldPreprint

Suzuki, M. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1410.3369 · Cited by 5

Fisher information and model selection for projective transformations of the line

Maybank, S. J. (2003) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2002.1096 · Cited by 5

Coordinate systems and Taylor series in statistics

Murray, M. K. (1988) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1988.0022 · Cited by 5

Information geometry of adaptive systems

Амари, Ш.-И., Ozeki, T., & Park, H. (2002) · IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium (AS-SPCC) · doi:10.1109/asspcc.2000.882438 · Cited by 5

A stochastic natural gradient descent algorithm for blind signal separation

Yang, H. H., & Amari, S. (2002) · Machine learning for signal processing ... · doi:10.1109/nnsp.1996.548373 · Cited by 5

Quantum theory as inductive inferencePreprint

Kostecki, R. P. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1009.2423 · Cited by 5

Survey of Model Selection and Model CombinationPreprint

Xu, M., & Golay, M. W. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1742033 · Cited by 5

Multistability of α -divergence based NMF algorithms

Yang, S., & Ye, M. (2012) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2012.01.010 · Cited by 4

A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle

Hürlimann, W. (2013) · The Scientific World JOURNAL · doi:10.1155/2013/468418 · Cited by 4

Opening the Parallelogram: Considerations on Non-Euclidean Analogies

Murena, P.-A., Cornuéjols, A., & Dessalles, J.-L. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-01081-2_39 · Cited by 4

Bayes Extended Estimators for Curved Exponential Families

Okudo, M., & Komaki, F. (2020) · IEEE Transactions on Information Theory · doi:10.1109/tit.2020.3035027 · Cited by 4

Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Sıddıquı, A. N., AlKhaldi, A. H., & Alqahtani, L. S. (2022) · Mathematics · doi:10.3390/math10101727 · Cited by 4

Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature

Wan, J., & Xie, Z. (2022) · Annali di Matematica Pura ed Applicata (1923 -) · doi:10.1007/s10231-022-01284-w · Cited by 4

Locally product-like statistical submersions

Takano, K., Erkan, E., & Gülbahar, M. (2023) · TURKISH JOURNAL OF MATHEMATICS · doi:10.55730/1300-0098.3397 · Cited by 4

Almost complex parallelizable manifolds: Kodaira dimension and special structures

Cattaneo, A., Nannicini, A., & Томассини, А. (2023) · manuscripta mathematica · doi:10.1007/s00229-023-01496-1 · Cited by 4

Lotka–Volterra model with mutations and generative adversarial networks

Kozyrev, S. V. (2024) · Theoretical and Mathematical Physics · doi:10.1134/s0040577924020077 · Cited by 4

Geometry on Positive Definite Matrices Induced from V-Potential Function

Ohara, A., & Eguchi, S. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-40020-9_69 · Cited by 4

Chapter 17 Geometry of neural networks: Natural gradient for learning

Fukumizu, K. (2001) · Handbook of biological physics · doi:10.1016/s1383-8121(01)80020-8 · Cited by 4

An Information-Geometric Approach to Learning Bayesian Network Topologies from Data

Lauría, E. J. M. (2008) · Studies in computational intelligence · doi:10.1007/978-3-540-85066-3_8 · Cited by 4

Application of iterated Bernstein operators to distribution function and density approximation

Manté, C. (2012) · Applied Mathematics and Computation · doi:10.1016/j.amc.2012.02.073 · Cited by 4

Second-Order Pitman Admissibility and Pitman Closeness: The Multiparameter Case and Stein-Rule Estimators

Ghosh, J. K., Mukerjee, R., & Sen, P. K. (1996) · Journal of Multivariate Analysis · doi:10.1006/jmva.1996.0021 · Cited by 4

A GEOMETRIC STUDY OF SOME EQUATIONS OF MATHEMATICAL PHYSICS

Pitea, A. (2012) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887812500302 · Cited by 4

Information geometry on pruning of neural network

Liu, Y., Luo, S., Li, A., & Yu, H.-B. (2005) · International Conference on Machine Learning and Cybernetics · doi:10.1109/icmlc.2004.1380390 · Cited by 4

Improved Jacobian Eigen-Analysis Scheme for Accelerating Learning in Feedforward Neural Networks

Ampazis, N., Perantonis, S. J., & Drivaliaris, D. (2014) · Cognitive Computation · doi:10.1007/s12559-014-9263-2 · Cited by 4

Improved data visualisation through multiple dissimilarity modelling

Rice, I. (2016) · Information Sciences · doi:10.1016/j.ins.2016.07.073 · Cited by 4

Geometry on the statistical manifold induced by the degradation model with soft failure data

Zhang, F., & Shi, Y. (2019) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2019.06.003 · Cited by 4

ON RANDERS CHANGE OF m-TH ROOT FINSLER METRICS

Tayebi, A., Nia, M. S., & Peyghan, E. (2015) · International Electronic Journal of Geometry · doi:10.36890/iejg.592790 · Cited by 4

On Generalized Kropina Change of Generalized m-th Root Finsler Metrics

Tiwari, B., Kumar, M., & Tayebi, A. (2020) · Proceedings of the National Academy of Sciences India Section A Physical Sciences · doi:10.1007/s40010-020-00681-1 · Cited by 4

Probing the Information-Probabilistic Description

Gogberashvili, M., & Modrekiladze, B. (2022) · International Journal of Theoretical Physics · doi:10.1007/s10773-022-05129-3 · Cited by 5

Tsallis Log-Scale-Location Models. Moments, Gini Index and Some Stochastic Orders

Preda, V., & Catana, L.-I. (2021) · Mathematics · doi:10.3390/math9111216 · Cited by 4

Nonmetricity on Riemann–Cartan–Weyl manifold: Its physical and mathematical meaning and application

Hirano, M., & Nagahama, H. (2022) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887822501535 · Cited by 4

Anti-invariant ξ⊥-cosymplectic-like statistical submersions

Kazan, S. (2022) · Thermal Science · doi:10.2298/tsci2204991k · Cited by 4

Divergence-based tests for the bivariate gamma distribution applied to polarimetric synthetic aperture radar

Nascimento, A. D. C., Ferreira, J. A., & da Silva, A. M. (2022) · Statistical Papers · doi:10.1007/s00362-022-01354-4 · Cited by 4

Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates

Ohga, N., & Ito, S. (2022) · Physical review. E · doi:10.1103/physreve.106.044131 · Cited by 4

Adversarial Robustness with Partial Isometry

Shi-Garrier, L., Bouaynaya, N. C., & Delahaye, D. (2024) · Entropy · doi:10.3390/e26020103 · Cited by 8

A generalized Wintgen inequality in quaternion Kähler geometry

Siddiqi, M. D., Sıddıquı, A. N., & Ahmad, K. (2024) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887824501858 · Cited by 4

On Prior Selection and Covariate Shift of β-Bayesian Prediction Under α-Divergence Risk

Suzuki, T., & Komaki, F. (2010) · Communication in Statistics- Theory and Methods · doi:10.1080/03610920802439146 · Cited by 4

Information-geometrical characterization of statistical models which are statistically equivalent to probability simplexes

Nagaoka, H. (2017) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2017.8006748 · Cited by 4

On the Fisher-Rao Information Metric in the Space of Normal Distributions

Pinele, J., Costa, S. I. R., & Strapasson, J. E. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-26980-7_70 · Cited by 4

New Geometry of Parametric Statistical Models

Zhang, J., & Khan, G. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-26980-7_30 · Cited by 4

High order asymptotic expansion for Wiener functionals

Tudor, C. A., & Yoshida, N. (2023) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2023.07.001 · Cited by 4

Metric Affine Spaces

Паньженский, В. И., Stepanov, S. E., & Sorokina, M. V. (2020) · Journal of Mathematical Sciences · doi:10.1007/s10958-020-04714-3 · Cited by 4

Evaluating Natural Alpha Embeddings on Intrinsic and Extrinsic Tasks

Volpi, R., & Malagò, L. (2020) · Workshop on Representation Learning for NLP (RepL4NLP) · doi:10.18653/v1/2020.repl4nlp-1.9 · Cited by 4

Parameter-free description of the manifold of non-degenerate density matrices

Naudts, J. (2021) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-020-01038-8 · Cited by 4

Exponential arcs in the manifold of vector states on a $$\sigma $$-finite von Neumann algebra

Naudts, J. (2022) · Information Geometry · doi:10.1007/s41884-021-00064-4 · Cited by 4

Dimension Reduction for Mixtures of Exponential Families

Akaho, S. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-87536-9_1 · Cited by 4

Intrinsic Plasticity via Natural Gradient Descent

Neumann, K., & Steil, J. J. (2012) · Cited by 4

The Fisher-Rao metric

Maybank, S. J. (2008) · BIROn (Birkbeck, University of London) · Cited by 4

Thermodynamics and geometrothermodynamics of Born–Infeld black holes with cosmological constant

Quevedo, H., Quevedo, M. N., & Sánchez, A. (2015) · International Journal of Modern Physics D · doi:10.1142/s0218271815500923 · Cited by 4

Natural gradients for deformable registration

Zikic, D., Kamen, A., & Navab, N. (2010) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2010.5540019 · Cited by 4

Curvature form on statistical model manifolds and its application to Bayesian analysis

Tanaka, F. (2012) · Journal of Statistics Applications & Probability · doi:10.12785/jsap/010105 · Cited by 4

Geometry of the log-likelihood ratio statistic in misspecified models

Choi, H.-S., & Kiefer, N. M. (2010) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2010.12.019 · Cited by 4

An Improved EM-method for the Estimation of Transition Probabilities in Multiple Model Switching Systems

Barão, M. S., Marques, J. S., & Lemos, J. M. (2010) · IFAC Proceedings Volumes · doi:10.3182/20100901-3-it-2016.00243 · Cited by 4

Online Bayesian Learning With Natural Sequential Prior Distribution

Nakada, Y., Wakahara, M., & Matsumoto, T. (2013) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2013.2250999 · Cited by 4

Results on nonlinear least squares estimators under nonlinear equality constraints

Pázman, A. (2002) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(01)00234-8 · Cited by 4

Statistics of the RSS estimation algorithm for Gaussian measurement noise

Agate, C. S., & Iltis, R. A. (1999) · IEEE Transactions on Signal Processing · doi:10.1109/78.738236 · Cited by 4

Data compression and statistical inference

Амари, Ш.-И. (1987) · Electronics and Communications in Japan (Part I Communications) · doi:10.1002/ecja.4410701102 · Cited by 4

Information Geometry of Thermodynamics

Ingarden, R. S. (1988) · Springer eBooks · doi:10.1007/978-94-009-3859-5_44 · Cited by 4

Mathematical Foundations of the Self Organized Neighbor Embedding (SONE) for Dimension Reduction and Visualization

Bunte, K., Schleif, F.-M., Haase, S., & Villmann, T. (2011) · University of Groningen research database (University of Groningen / Centre for Information Technology) · Cited by 4

Geometry from information geometry

Caticha, A. (2016) · AIP conference proceedings · doi:10.1063/1.4959050 · Cited by 4

Asymptotic expansions for the estimators of Lagrange multipliers and associated parameters by the maximum likelihood and weighted score methods

Ogasawara, H. (2016) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2015.12.015 · Cited by 4

Discretized Gabor Statistical Models for Face Recognition

Zou, J. X., & Liu, C. (2011) · International Journal of Digital Content Technology and its Applications · doi:10.4156/jdcta.vol5.issue5.19 · Cited by 4

Matrix Constant False Alarm Rate(MCFAR) detector based on information geometry

Ye, L., Qiang, Y., & Wei-bo, D. (2016) · IEEE Information Technology, Networking, Electronic and Automation Control Conference (ITNEC) · doi:10.1109/itnec.2016.7560351 · Cited by 4

A Damped Newton Algorithm for Nonnegative Matrix Factorization Based on Alpha-Divergence

Sano, T., Migita, T., & Takahashi, N. (2019) · International Conference on Systems and Informatics (ICSAI) · doi:10.1109/icsai48974.2019.9010306 · Cited by 4

A New Algebraic Inequality and Some Applications in Submanifold Theory

Mihai, I., & Mihai, R.-I. (2021) · Mathematics · doi:10.3390/math9111175 · Cited by 4

Algebraic Properties of the Information Geometry’s Fourth Frobenius Manifold

Combe, N. C., Combe, P., & Nencka, H. (2022) · Lecture notes in networks and systems · doi:10.1007/978-3-030-98012-2_27 · Cited by 4

Neighbourhoods of Independence for Random Processes via Information Geometry

Arwini, K., & Dodson, C. T. J. (2005) · The Mathematica Journal · Cited by 4

Information geometry of random walk distribution

Abdel-All, N. H., Abd-Ellah, H. N., & Moustafa, H. M. (2003) · Publicationes Mathematicae Debrecen · doi:10.5486/pmd.2003.2630 · Cited by 4

Geometry on Positive Definite Matrices Deformed by V-Potentials and Its Submanifold Structure

Ohara, A., & Eguchi, S. (2014) · Signals and communication technology · doi:10.1007/978-3-319-05317-2_2 · Cited by 4

Latent class and trait models for data classification and visualisation

Girolami, M. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148.011 · Cited by 4

A new model selection criterion based on information geometry

Liu, Y., Siwei, L., Li, A., & Yu, H. (2005) · International Conference on Signal Processing · doi:10.1109/icosp.2004.1441627 · Cited by 4

Distances in Probability Theory

Deza, M. M., & Deza, E. I. (2012) · Springer eBooks · doi:10.1007/978-3-642-30958-8_14 · Cited by 4

Dualistic properties of the manifold of quantum states

Jenčová, A. (2001) · AIP conference proceedings · doi:10.1063/1.1358176 · Cited by 4

Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)

Clevert, D.-A., Unterthiner, T., & Hochreiter, S. (2015) · arXiv · doi:10.48550/arxiv.1511.07289 · Cited by 4,513

Differential-geometrical methods in statistics. Lecture notes in statistics - A. Shun-ichi.

Götze, F. (1987) · Metrika

Diffential-Geometrical Methods in Statistics

Amari, S.-I. (1985)

Chapter 3: Differential and Integral Geometry in Statistical Inference

Barndorff-Nielsen, O. E. (1987) · Lecture notes-monograph series · doi:10.1214/lnms/1215467060 · Cited by 31

Differential geometry and statistics: some mathematical aspects

Barndorff-Nielsen, O. E. (1987) · Cited by 6

Differential geometrical theory of statistics

Barbaresco, F., & Nielsen, F. (2017)