Differential-Geometrical Methods in Statistics

Expected lengths of confidence intervals based on empirical discrepancy statistics

Fang, K., & Mukerjee, R. (2005) · Biometrika · doi:10.1093/biomet/92.2.499 · Cited by 12

Convergence analysis of the information potential criterion in Adaline training

Deniz Erdogmus, B., & Príncipe, J. C. (2002) · Machine learning for signal processing ... · doi:10.1109/nnsp.2001.943117 · Cited by 12

Prior knowledge and preferential structures in gradient descent learning algorithms

Mahony, R. E., & Williamson, R. C. (2001) · ANU Open Research (Australian National University) · doi:10.1162/153244301753683735 · Cited by 12

Characterization of the Bayes estimator and the MDL estimator for exponential families

Takeuchi, J. (1997) · IEEE Transactions on Information Theory · doi:10.1109/18.605579 · Cited by 12

Entropic Priors

Caticha, A. (2004) · AIP conference proceedings · doi:10.1063/1.1751380 · Cited by 12

Physical Information and the Derivation of Electron Physics

Frieden, B. R. (1994) · Advances in imaging and electron physics · doi:10.1016/s1076-5670(08)70084-3 · Cited by 12

Semiparametric model and superefficiency in blind deconvolution

Zhang, L.-Q., Амари, Ш.-И., & Cichocki, A. S. (2001) · Signal Processing · doi:10.1016/s0165-1684(01)00146-3 · Cited by 12

Variational Inference with Rényi Divergence.Preprint

Li, Y., & Turner, R. E. (2016) · arXiv (Cornell University) · Cited by 12

Nonparametric Information GeometryPreprint

Pistone, G. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1306.0480 · Cited by 12

Length-preserving biconnection gravity and its cosmological implications

Csillag, L., Hama, R., Józsa, M., Harko, T., & Sabău, S. V. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/12/034 · Cited by 12

Dually flat geometries of the deformed exponential family

Harsha, K. V., & Subrahamanian Moosath, K. S. (2015) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2015.03.023 · Cited by 11

Natural Option Critic

Tiwari, S., & Thomas, P. S. (2019) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v33i01.33015175

A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

Mikeš, J., & Stepanova, E. (2013) · Annals of Global Analysis and Geometry · doi:10.1007/s10455-013-9390-0 · Cited by 11

On parameter orthogonality to the mean

Hürlimann, W. (1992) · Statistical Papers · doi:10.1007/bf02925313 · Cited by 11

Stochastic Divergence Minimization for Online Collapsed Variational Bayes Zero Inference of Latent Dirichlet Allocation

Sato, I., & Nakagawa, H. (2015) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/2783258.2783355 · Cited by 11

Geometrical expansions for the distributions of the score vector and the maximum likelihood estimator

Mora, M. (1992) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00048670 · Cited by 11

Geometry of quantum group invariant systems

Ubriaco, M. R. (2012) · Physics Letters A · doi:10.1016/j.physleta.2012.10.042 · Cited by 11

Dual scaling of comparison and reference stimuli in multi-dimensional psychological space

Zhang, J. (2004) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2004.09.001 · Cited by 11

Geometry of exponential family with competing risks and censored data

Zhang, F., & Shi, Y. (2015) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2015.12.003 · Cited by 11

Geometry of the Fisher–Rao metric on the space of smooth densities on a compact manifold

Bruveris, M., & Michor, P. W. (2018) · Mathematische Nachrichten · doi:10.1002/mana.201600523 · Cited by 11

The physical significance of geometrothermodynamic metrics

Pineda, V., Quevedo, H., Quevedo, M. N., Sánchez, A., & Valdés, E. (2019) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887819501688 · Cited by 11

From Hessian to Weitzenböck: manifolds with torsion-carrying connections

Zhang, J., & Khan, G. (2019) · Information Geometry · doi:10.1007/s41884-019-00018-x · Cited by 11

Riemann–Langevin Particle Filtering in Track-Before-Detect

Garcia, F. J. I., Mandal, P. K., Bocquel, M., & Marques, A. G. (2018) · IEEE Signal Processing Letters · doi:10.1109/lsp.2018.2841507 · Cited by 11

Conformally-projectively flat trans-Sasakian statistical manifolds

Kazan, A. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.122441 · Cited by 11

Classification and evolution of galaxies according to the dynamical state of host clusters and galaxy luminosities

Morell, D. F., Ribeiro, A. L. B., de Carvalho, R. R., Rembold, S. B., Lopes, P. A. A., & Costa, A. P. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa881 · Cited by 11

The Information-Geometric Perspective of Compositional Data Analysis

Erb, I., & Ay, N. (2021) · Springer eBooks · doi:10.1007/978-3-030-71175-7_2 · Cited by 11

When optimal transport meets information geometry

Khan, G., & Zhang, J. (2022) · Information Geometry · doi:10.1007/s41884-022-00066-w · Cited by 11

On dually flat (α,β) -metrics

Yu, C. (2013) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2013.11.004 · Cited by 11

Wasserstein geometry of porous medium equation

Takatsu, A. (2011) · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · doi:10.1016/j.anihpc.2011.10.003 · Cited by 11

Continuity of the Maximum-Entropy Inference

Weis, S. (2014) · Communications in Mathematical Physics · doi:10.1007/s00220-014-2090-1 · Cited by 13

Fisher Score Based Naive Bayesian Classifier

Shi, Z., Huang, Y., & Zhang, S. (2006) · International Conference on Neural Networks and Brain · doi:10.1109/icnnb.2005.1614941 · Cited by 11

Doubly warped product Finsler manifolds with some non-Riemannian curvature properties

Peyghan, E., Tayebi, A., & Najafi, B. (2012) · Annales Polonici Mathematici · doi:10.4064/ap105-3-6 · Cited by 11

Alpha divergence minimization in multi-class Gaussian process classification

Villacampa-Calvo, C., & Hernández-Lobato, D. (2019) · Neurocomputing · doi:10.1016/j.neucom.2019.09.090 · Cited by 11

Equi-convergence Algorithm for Blind Separation of Sources with Arbitrary Distributions

Zhang, L.-Q., Амари, Ш.-И., & Cichocki, A. S. (2001) · Lecture notes in computer science · doi:10.1007/3-540-45723-2_100 · Cited by 11

Bayesian ying-yang theory for empirical learning, regularization and model selection: general formulation

Xu, L. (2003) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.1999.831557 · Cited by 11

Using relative entropy to find optimal approximations: An application to simple fluids

Tseng, C., & Caticha, A. (2008) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2008.08.035 · Cited by 11

Transformation Techniques for Partial Differential Equations on Projectively Flat Manifolds

Simon, U. (1995) · Results in Mathematics · doi:10.1007/bf03322279 · Cited by 11

The Kullback-Leibler risk of the Stein estimator and the conditional MLE

Yanagimoto, T. (1994) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00773590 · Cited by 11

On metric of quantum channel spacesPreprint

Matsumoto, K. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1006.0300 · Cited by 11

Finite Information Geometry

Ay, N., Jost, J., Lê, H. V., & Schwachhöfer, L. (2017) · Ergebnisse der Mathematik und ihrer Grenzgebiete · doi:10.1007/978-3-319-56478-4_2 · Cited by 10

Entropic Regularization of Markov Decision Processes

Belousov, B., & Peters, J. (2019) · Technischen Universität Darmstadt · Cited by 10

Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Chen, B., Decu, S., & Vîlcu, G. (2021) · Entropy · doi:10.3390/e23111399 · Cited by 10

On a constant curvature statistical manifold

Kobayashi, S., & Ohno, Y. (2022) · Information Geometry · doi:10.1007/s41884-022-00065-x · Cited by 10

Information Topologies on Non-Commutative State Spaces

Weis, S. (2014) · Journal of convex analysis · doi:10.68381/jca21019 · Cited by 11

Fast Curvature Matrix-Vector Products

Schraudolph, N. N. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44668-0_4 · Cited by 10

Empirical geodesic graphs and CAT(k) metrics for data analysis

Kobayashi, K., & Wynn, H. P. (2019) · Statistics and Computing · doi:10.1007/s11222-019-09855-3 · Cited by 10

Exploiting Information Geometry to Improve the Convergence of Nonparametric Active Contours

Pereyra, M., Batatia, H., & McLaughlin, S. (2014) · IEEE Transactions on Image Processing · doi:10.1109/tip.2014.2383318 · Cited by 10

Locally dually flat Finsler metrics with special curvature properties

Cheng, X., & Tian, Y. (2011) · Differential Geometry and its Applications · doi:10.1016/j.difgeo.2011.04.014 · Cited by 10

Riemannian geometry of the space of volume preserving immersions

Bauer, M., Michor, P. W., & Müller, O. (2016) · Differential Geometry and its Applications · doi:10.1016/j.difgeo.2016.07.002 · Cited by 10

Thermodynamic geometry of strongly interacting matter

Castorina, P., Imbrosciano, M., & Lanteri, D. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.096006 · Cited by 10

Affine Natural Proximal Learning

Li, W., Lin, A. T., & Montúfar, G. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-26980-7_73 · Cited by 10

A review of tests for exponentiality with Monte Carlo comparisons

Ossai, E. O., Madukaife, M. S., & Oladugba, A. V. (2020) · Journal of Applied Statistics · doi:10.1080/02664763.2020.1854202 · Cited by 10

From Statistical Distances to Minimally Dissipative Processes

Diósi, L., & Salamon, P. (2000) · Springer eBooks · doi:10.1007/978-1-4612-1286-7_11 · Cited by 10

Scalar curvature of systems with fractal distribution functions

Ubriaco, M. R. (2012) · Physics Letters A · doi:10.1016/j.physleta.2012.07.023 · Cited by 10

Decomposition of Kullback–Leibler risk and unbiasedness for parameter-free estimators

Wu, Q., & Vos, P. W. (2012) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2012.01.002 · Cited by 10

The geometric structure of the inverse gamma distribution.

Li, T., Peng, L., & Sun, H. (2008) · Cited by 10

On Mixture and Exponential Connection by Open Arcs

Santacroce, M., Siri, P., & Trivellato, B. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-68445-1_67 · Cited by 10

COMPARISON OF TESTS IN THE PRESENCE OF A NUISANCE PARAMETER

Mukerjee, R. (1989) · Elsevier eBooks · doi:10.1016/b978-0-444-88029-1.50017-4 · Cited by 10

Hybrid IMM/SVM approach for wavelet-domain probabilistic model based texture classification

Chen, L., & Man, H. (2005) · IEE Proceedings - Vision Image and Signal Processing · doi:10.1049/ip-vis:20045030 · Cited by 10

The geometry of prior selection

Snoussi, H. (2005) · Neurocomputing · doi:10.1016/j.neucom.2004.11.038 · Cited by 10

Geometric aspects of Fleming-Viot and Dawson-Watanabe processes

Schied, A. (1997) · The Annals of Probability · doi:10.1214/aop/1024404509 · Cited by 10

SOME GEOMETRICAL ASPECTS OF DATA ANALYSIS AND STATISTICS

Oller, J. M. (1989) · Elsevier eBooks · doi:10.1016/b978-0-444-88029-1.50009-5 · Cited by 10

A geometric approach to the thermodynamics of the van der Waals systemPreprint

Quevedo, H., & Ramírez, A. D. J. T. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1205.3544 · Cited by 10

Geometric methods for estimation of structured covariancesPreprint

Ning, L., Jiang, X., & Georgiou, T. T. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1110.3695 · Cited by 10

Intrinsic constraints in space-time filtering: a new approach to representing uncertainty in low-level vision

Jasinchi, R. S. (1992) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.120330 · Cited by 10

Recent Developments on Chen–Ricci Inequalities in Differential Geometry

Chen, B., & Blaga, A. M. (2024) · Infosys science foundation series · doi:10.1007/978-981-99-9750-3_1 · Cited by 9

Self-stabilized deep neural network

Ghahremani, P., & Droppo, J. (2016) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2016.7472719 · Cited by 9

Information Geometric Approach to Recursive Update in Nonlinear Filtering

Li, Y., Cheng, Y., Li, X., Hua, X., & Qin, Y. (2017) · Entropy · doi:10.3390/e19020054 · Cited by 9

Tomographic reconstruction of quantum metrics

Laudato, M., Marmo, G., Mele, F. M., Ventriglia, F., & Vitale, P. (2017) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa9e61 · Cited by 9

Einstein statistical warped product manifolds

Aytimur, H., & Özgür, C. (2018) · Filomat · doi:10.2298/fil1811891a · Cited by 9

Higher Order Automatic Differentiation of Higher Order Functions

Huot, M., Staton, S., & Vákár, M. (2022) · Logical Methods in Computer Science · doi:10.46298/lmcs-18(1:41)2022 · Cited by 9

B.-Y. Chen's Inequality for Kähler-like Statistical Submersions

Sıddıquı, A. N., Uddin, S., & Shahid, M. H. (2022) · International Electronic Journal of Geometry · doi:10.36890/iejg.1006287 · Cited by 9

Anti-invariant Holomorphic Statistical Submersions

Kazan, S., & Takano, K. (2023) · Results in Mathematics · doi:10.1007/s00025-023-01904-8 · Cited by 9

Natural Gradient Learning in NLDA Networks

Dorronsoro, J. R., González, A. M., & Cruz, C. S. (2001) · Lecture notes in computer science · doi:10.1007/3-540-45720-8_50 · Cited by 9

Application of the Fisher-Rao Metric to Ellipse Detection

Maybank, S. J. (2006) · International Journal of Computer Vision · doi:10.1007/s11263-006-9033-z · Cited by 9

Foliations and divergences of flat statistical manifolds

Uohashi, K., Ohara, A., & Fujii, T. (2000) · Hiroshima Mathematical Journal · doi:10.32917/hmj/1206124606 · Cited by 9

Classical and Quasi-Newton Methods for a Meteorological Parameters Prediction Boundary Value Problem

Famelis, I. T., Galanis, G. N., Ehrhardt, M., & Triantafyllou, D. S. (2014) · Applied Mathematics & Information Sciences · doi:10.12785/amis/080604 · Cited by 9

Information geometry for model identification and parameter estimation in renewable energy – DFIG plant case

Sarić, A. T., Transtrum, M. K., & Stanković, A. M. (2017) · IET Generation Transmission & Distribution · doi:10.1049/iet-gtd.2017.0606 · Cited by 9

Fisher–Rao geometry and Jeffreys prior for Pareto distribution

Li, M., Sun, H., & Peng, L. (2020) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2020.1771593 · Cited by 9

Information Geometry of the Probability Simplex: A Short Course

Pistone, G. (2020) · Nonlinear Phenomena in Complex Systems · doi:10.33581/1561-4085-2020-23-2-221-242 · Cited by 9

Projection Filtering With Observed State Increments With Applications in Continuous-Time Circular Filtering

Kutschireiter, A., Rast, L. I., & Drugowitsch, J. (2022) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2022.3143471 · Cited by 10

On Statistical and Semi-Weyl Manifolds Admitting Torsion

Blaga, A. M., & Nannicini, A. (2022) · Mathematics · doi:10.3390/math10060990 · Cited by 9

A Precise Bare Simulation Approach to the Minimization of Some Distances. I. Foundations

Broniatowski, M., & Stummer, W. (2022) · IEEE Transactions on Information Theory · doi:10.1109/tit.2022.3215496 · Cited by 9

Information Trajectory of Optimal Learning

Belavkin, R. V. (2010) · Springer optimization and its applications · doi:10.1007/978-1-4419-5689-7_2 · Cited by 9

Kalman filter and state-space approach to blind deconvolution

Zhang, L.-Q., Cichocki, A. S., & Амари, Ш.-И. (2002) · Machine learning for signal processing ... · doi:10.1109/nnsp.2000.889435 · Cited by 9

Voronoi diagrams by divergences with additive weights

Sadakane, K., Imai, H., Onishi, K., Inaba, M., Takeuchi, F., & Imai, K. (1998) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/276884.276929 · Cited by 9

A Fisher-Rao Metric for Paracatadioptric Images of Lines

Maybank, S. J., Ieng, S.-H., & Benosman, R. B. (2012) · International Journal of Computer Vision · doi:10.1007/s11263-012-0523-x · Cited by 9

Information geometric similarity measurement for near-random stochastic processes

Dodson, C. T. J., & Scharcanski, J. (2003) · IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans · doi:10.1109/tsmca.2003.809185 · Cited by 9

The Mathematics of Divergence Based Online Learning in Vector Quantization

Villmann, T., Haase, S., Schleif, F.-M., Hammer, B., & Biehl, M. L. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-12159-3_10 · Cited by 9

Classification of Totally Umbilical CR-Statistical Submanifolds in Holomorphic Statistical Manifolds with Constant Holomorphic Curvature

Boyom, M. N., Sıddıquı, A. N., Othman, W. A. M., & Shahid, M. H. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-68445-1_93 · Cited by 9

How the Hawking radiation affect quantum Fisher information of Dirac particles in the background of a Schwarzschild black hole

Huang, C., Ma, W., Wang, D., & Ye, L. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1779-4 · Cited by 9

Memories of the Future. Predictable and Unpredictable Information in Fractional Flipping a Biased Coin

Volchenkov, D. (2019) · Entropy · doi:10.3390/e21080807 · Cited by 9

Measure of the density of quantum states in information geometry and quantum multiparameter estimation

Xing, H., & Fu, L. (2020) · Physical Review A · doi:10.1103/physreva.102.062613 · Cited by 9

Information metric on instanton moduli spaces in nonlinear σ models

Yahikozawa, S. (2004) · Physical Review E · doi:10.1103/physreve.69.026122 · Cited by 9

Harmonic Bayesian Prediction Under $\alpha$ -Divergence

Maruyama, Y., Matsuda, T., & Ohnishi, T. (2019) · IEEE Transactions on Information Theory · doi:10.1109/tit.2019.2915245 · Cited by 9

Ideal quantum gases: A geometrothermodynamic approach

Zaldivar, S. A., & Quevedo, H. (2023) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2023.104837 · Cited by 9

Variable selection for structural models

Kano, Y. (2002) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(02)00277-x · Cited by 9

On the Applicability of the Energy Level Dynamics for the Hamiltonian Systems in the Transition Region between Integrability and Chaos

Hasegawa, H. H., & Robnik, M. (1993) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/23/3/003 · Cited by 9

Quantum Statistical Inference

Silver, R. N. (1993) · Springer eBooks · doi:10.1007/978-94-017-2217-9_22 · Cited by 9

NOTE ON THE UNIVERSAL BASES OF A PAIR OF POLYMATROIDS

Murota, K. (1988) · Journal of the Operations Research Society of Japan · doi:10.15807/jorsj.31.565 · Cited by 9

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)