Differential-Geometrical Methods in Statistics

Informative barycentres in statistics

Bruno Pelletier, B. (2005) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf02915437 · Cited by 22

The geometric structures and instability of entropic dynamical models

Peng, L., Sun, H., Sun, D., & Yi, J. (2011) · Advances in Mathematics · doi:10.1016/j.aim.2011.02.002 · Cited by 22

Geometric study for the Legendre duality of generalized entropies and its application to the porous medium equation

Ohara, A. (2009) · The European Physical Journal B · doi:10.1140/epjb/e2009-00170-y · Cited by 22

Homogeneity and thermodynamic identities in geometrothermodynamics

Quevedo, H., Quevedo, M. N., & Sánchez, A. (2017) · The European Physical Journal C · doi:10.1140/epjc/s10052-017-4739-3 · Cited by 22

Some Quantum Mechanical Properties of the Wolfram Model

Gorard, J. (2020) · Complex Systems · doi:10.25088/complexsystems.29.2.537 · Cited by 23

Direct approach to quantum extensions of Fisher information

Chen, P., & Luo, S. (2007) · Frontiers of Mathematics · doi:10.1007/s11464-007-0023-4 · Cited by 22

Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?

Cafaro, C., & Ali, S. A. (2008) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2008.09.010 · Cited by 21

Information measures based on Tsallis’ entropy and geometric considerations for thermodynamic systems

Portesi, M., Plastino, A. R., & Pennini, F. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.01.034 · Cited by 22

Reference Priors for the Orbit in a Group Model

Chang, T., & Eaves, D. M. (1990) · The Annals of Statistics · doi:10.1214/aos/1176347868 · Cited by 22

Influence Analysis Based on the Case Sensitivity Function

Critchley, F., Atkinson, R. A., Lu, G., & Biazi, E. (2001) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00287 · Cited by 22

Thermodynamics of boson systems related to Dunkl differential–difference operators

Ubriaco, M. R. (2014) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2014.06.087 · Cited by 21

Bayesian Learning

Theodoridis, S. (2015) · Elsevier eBooks · doi:10.1016/b978-0-12-801522-3.00013-6 · Cited by 20

Robust Subspace Detectors Based on α-Divergence With Application to Detection in Imaging

Rekavandi, A. M., Seghouane, A., & Evans, R. J. (2021) · IEEE Transactions on Image Processing · doi:10.1109/tip.2021.3077139 · Cited by 21

Generalized t-SNE Through the Lens of Information Geometry

Kimura, M. (2021) · IEEE Access · doi:10.1109/access.2021.3113397 · Cited by 21

Self-similar profile of probability density functions in zero-pressure gradient turbulent boundary layers

Tsuji, Y., Lindgren, B., & Johansson, A. V. (2005) · Fluid Dynamics Research · doi:10.1016/j.fluiddyn.2005.06.003 · Cited by 21

A distance between elliptical distributions based in an embedding into the Siegel group

Calvo, M., & Oller, J. M. (2002) · Journal of Computational and Applied Mathematics · doi:10.1016/s0377-0427(01)00584-2 · Cited by 21

Sketching information divergences

Guha, S., Indyk, P., & McGregor, A. (2008) · Machine Learning · doi:10.1007/s10994-008-5054-x · Cited by 21

Information Geometry of Generalized Bayesian Prediction Using $\alpha$ -Divergences as Loss Functions

Zhang, F., Shi, Y., Ng, H. K. T., & Ruibing, W. (2017) · IEEE Transactions on Information Theory · doi:10.1109/tit.2017.2774820 · Cited by 21

Mis-specification analysis of Wiener degradation models by using f-divergence with outliers

Zhang, F., Ng, H. K. T., & Shi, Y. (2019) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2019.106751 · Cited by 21

Information geometry

Амари, Ш.-И. (2021) · Japanese journal of mathematics · doi:10.1007/s11537-020-1920-5 · Cited by 21

Wave height characteristics in the north Atlantic ocean: a new approach based on statistical and geometrical techniques

Galanis, G. N., Chu, P. C., Kallos, G., Kuo, Y.-H., & Dodson, C. T. J. (2011) · Stochastic Environmental Research and Risk Assessment · doi:10.1007/s00477-011-0540-2 · Cited by 21

Dually Flat Manifolds and Global Information Geometry

Ay, N., & Tuschmann, W. (2002) · Open Systems & Information Dynamics · doi:10.1023/a:1015604927654 · Cited by 21

Fractional Brownian Motion and Rao Geodesic Distance for Bone X-Ray Image Characterization

Hassouni, M. E., Tafraouti, A., Toumi, H., Lespessailles, É., & Jennane, R. (2016) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2016.2619420 · Cited by 21

A nonparametric Riemannian framework for processing high angular resolution diffusion images (HARDI)

Goh, A., Lenglet, C., Thompson, P. M., & Vidal, R. (2009) · 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.2009.5206843 · Cited by 21

Approximated Moment-Matching Dynamics for Basket-Options SimulationPreprint

Brigo, D., Mercurio, F., Rapisarda, F., & Scotti, R. (2001) · SSRN Electronic Journal · doi:10.2139/ssrn.268433 · Cited by 21

Dualistic Structures on Twisted Product ManifoldsPreprint

Diallo, A. S., & Todjihounde, L. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1408.3450 · Cited by 21

Correspondence between thermodynamics and inference

LaMont, C., & Wiggins, P. A. (2019) · Physical review. E · doi:10.1103/physreve.99.052140 · Cited by 19

Quantum-limited estimation of continuous spontaneous localization

McMillen, S., Brunelli, M., Carlesso, M., Bassi, A., Ulbricht, H., Paris, M. G. A., & Paternostro, M. (2017) · Physical Review A · doi:10.1103/physreva.95.012132 · Cited by 22

Gradient solitons on statistical manifolds

Blaga, A. M., & Chen, B. (2021) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2021.104195 · Cited by 20

Sublinear estimation of entropy and information distances

Guha, S., McGregor, A., & Venkatasubramanian, S. (2009) · ACM Transactions on Algorithms · doi:10.1145/1597036.1597038 · Cited by 20

Geometrical properties of Pareto distribution

Abdel-All, N. H., Mahmoud, M. A. W., & Abd-Ellah, H. N. (2003) · Applied Mathematics and Computation · doi:10.1016/s0096-3003(02)00490-3 · Cited by 20

Reexamination of an information geometric construction of entropic indicators of complexity

Cafaro, C., Giffin, A., Ali, S. A., & Kim, D.-H. (2010) · Applied Mathematics and Computation · doi:10.1016/j.amc.2010.08.028 · Cited by 20

Information Geometry and Its Applications

Ay, N., Gibilisco, P., & Matúš, F. (2018) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-97798-0 · Cited by 22

Connecting Information Geometry and Geometric Mechanics

Leok, M. B.-T., & Zhang, J. (2017) · Entropy · doi:10.3390/e19100518 · Cited by 20

Measurements of Generalisation Based on Information Geometry

Zhu, H., & Rohwer, R. (1997) · Operations research, computer science. Interface series · doi:10.1007/978-1-4615-6099-9_69 · Cited by 20

Dimensionality Reduction and Clustering on Statistical Manifolds

Lee, S.-M., Abbott, A. L., & Araman, P. A. (2007) · 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.2007.383408 · Cited by 20

The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Mihai, A., & Mihai, I. (2020) · Entropy · doi:10.3390/e22020164 · Cited by 20

Differential geometry of nonequilibrium processes

Obata, T., Hara, H., & Endo, K. (1992) · Physical Review A · doi:10.1103/physreva.45.6997 · Cited by 20

Temperature as Order Parameter of Broken Scale Invariance

Ojima, I. (2004) · Publications of the Research Institute for Mathematical Sciences · doi:10.2977/prims/1145475491 · Cited by 20

Change, time and information geometry

Caticha, A. (2001) · AIP conference proceedings · doi:10.1063/1.1381872 · Cited by 20

Information geometry and prior selection

Snoussi, H. (2003) · AIP conference proceedings · doi:10.1063/1.1570549 · Cited by 20

Recursive nonlinear estimation: Geometry of a space of posterior densities

Kulhavý, R. (1992) · Automatica · doi:10.1016/0005-1098(92)90118-y · Cited by 20

Strings, tensorial combinants, and Bartlett adjustments

Barndorff-Nielsen, O. E. (1986) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1986.0069 · Cited by 20

On Best Equivariance and Admissibility of Simultaneous MLE for Mean Direction Vectors of Several Langevin Distributions

SenGupta, A., & Maitra, R. (1998) · Annals of the Institute of Statistical Mathematics · doi:10.1023/a:1003712930390 · Cited by 20

Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and EntropyPreprint

Niven, R. K. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.cond-mat/0512017 · Cited by 20

On Wasserstein geometry of the space of Gaussian measuresPreprint

Takatsu, A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0801.2250 · Cited by 20

Geometrical methods of inference

Krakowski, K. (2002) · UWA Profiles and Research Repository (UWA) · doi:10.26182/5d526805ae757 · Cited by 20

PENROSE VOTING SYSTEM AND OPTIMAL QUOTAPreprint

Wojciech, S. (2006) · arXiv (Cornell University) · Cited by 20

Generalized Variational Inference: Three arguments for deriving new PosteriorsPreprint

Knoblauch, J., Jewson, J., & Damoulas, T. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1904.02063 · Cited by 145

Towards a Revolutionary Info-Geometric Control Theory with Potential Applications of Fokker Planck Kolmogorov(FPK) Equation to System Control, Modelling and Simulation

Mageed, I. A., Zhou, Y., Liu, Y., & Zhang, Q. (2023) · International Conference on Automation and Computing (ICAC) · doi:10.1109/icac57885.2023.10275271 · Cited by 19

Phase transitions, shadows, and microstructure of Reissner-Nordström-Anti-de-Sitter black holes from a geometrothermodynamic perspective

Ladino, J. M., Romero-Figueroa, C. E., & Quevedo, H. (2024) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2024.116734 · Cited by 19

Some inequalities for statistical submanifolds of quaternion Kaehler-like statistical space forms

Aquib, M. (2019) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887819501299 · Cited by 19

DeepView: Visualizing Classification Boundaries of Deep Neural Networks as Scatter Plots Using Discriminative Dimensionality Reduction

Schulz, A., Hinder, F., & Hammer, B. (2020) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2020/319 · Cited by 19

Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences

Nielsen, F. (2022) · Entropy · doi:10.3390/e24030421 · Cited by 19

Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems

Nurbekyan, L., Lei, W., & Yang, Y. (2023) · SIAM Journal on Scientific Computing · doi:10.1137/22m1477805 · Cited by 19

Riemannian geometry of thermodynamics and systems with repulsive power-law interactions

Ruppeiner, G. (2005) · Physical Review E · doi:10.1103/physreve.72.016120 · Cited by 19

A pinching theorem for statistical manifolds with Casorati curvatures

Lee, C. W., Yoon, D. W., & Lee, J. W. (2017) · The Journal of Nonlinear Sciences and Applications · doi:10.22436/jnsa.010.09.31 · Cited by 19

On entropies, divergences, and mean values

Basseville, M., & Cardoso, J.-F. (2002) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.1995.550317 · Cited by 19

DUAL GEOMETRY OF THE WIGNER–YANASE–DYSON INFORMATION CONTENT

Hasegawa, H. (2003) · Infinite Dimensional Analysis Quantum Probability and Related Topics · doi:10.1142/s021902570300133x · Cited by 19

Yokes and symplectic structures

Barndorff-Nielsen, O. E., & Jupp, P. E. (1997) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(97)00006-2 · Cited by 19

Geometrical aspects of a generalized statistical mechanics

Portesi, M., Pennini, F., & Plastino, A. R. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.05.024 · Cited by 19

Gaussianization: An Efficient Multivariate Density Estimation Technique for Statistical Signal Processing

Deniz Erdogmus, B., Jenssen, R., Rao, Y. N., & Príncipe, J. C. (2006) · The Journal of VLSI Signal Processing Systems for Signal Image and Video Technology · doi:10.1007/s11265-006-9772-7 · Cited by 19

ICA, graphical models and variational methods

Attias, H. T. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148.004 · Cited by 19

Strings: mathematical theory and statistical examples

Barndorff-Nielsen, O. E., & Blæsild, P. (1987) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1987.0059 · Cited by 19

Probabilistic design of layered neural networks based on their unified framework

Watanabe, S., & Fukumizu, K. (1995) · IEEE Transactions on Neural Networks · doi:10.1109/72.377974 · Cited by 19

Volume of the quantum mechanical state spacePreprint

Andai, A. (2006) · Cited by 19

Duality versus dual flatness in quantum information geometry

Ay, N., & Tuschmann, W. (2003) · Journal of Mathematical Physics · doi:10.1063/1.1556192 · Cited by 18

Iterative reconstruction for sparse-view X-ray CT using alpha-divergence constrained total generalized variation minimization

Niu, S., Huang, J., Bian, Z., Zeng, D., Chen, W., Yu, G., Liang, Z., & Ma, J. (2017) · Journal of X-Ray Science and Technology · doi:10.3233/xst-16239 · Cited by 18

Geometrothermodynamics of van der Waals systems

Quevedo, H., Quevedo, M. N., & Sánchez, A. (2022) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2022.104495 · Cited by 18

Parameter estimation and uncertainty quantification using information geometry

Sharp, J. A., Browning, A. P., Burrage, K., & Simpson, M. J. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2021.0940 · Cited by 18

Learning Disentangled Textual Representations via Statistical Measures of Similarity

Colombo, P., Staerman, G., Noiry, N., & Piantanida, P. (2022) · Proceedings of the conference - Association for Computational Linguistics. Meeting · doi:10.18653/v1/2022.acl-long.187 · Cited by 20

A Kullback-Leibler distance approach to system identification

Kulhavý, R. (1996) · Annual Reviews in Control · doi:10.1016/s1367-5788(97)00010-2 · Cited by 18

Optimal measures and Markov transition kernels

Belavkin, R. V. (2012) · Journal of Global Optimization · doi:10.1007/s10898-012-9851-1 · Cited by 18

Measuring the Uncertainty of Predictions in Deep Neural Networks with Variational Inference

Steinbrener, J., Posch, K., & Pilz, J. (2020) · Sensors · doi:10.3390/s20216011 · Cited by 52

Local mixture models of exponential families

Anaya‐Izquierdo, K., & Marriott, P. K. (2007) · Open Research Online (The Open University) · Cited by 18

F-manifolds and geometry of information

Combe, N., & Manin, Y. (2020) · MPG.PuRe (Max Planck Society) · Cited by 18

Statistical manifold as an affine space: A functional equation approach

Zhang, J., & Hästö, P. (2005) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2005.08.003 · Cited by 18

Voronoi diagram in statistical parametric space by Kullback-Leibler divergence

Onishi, K., & Imai, H. (1997) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/262839.263084 · Cited by 18

Maximum likelihood separation of constant modulus signals

Leshem, A. (2000) · IEEE Transactions on Signal Processing · doi:10.1109/78.869053 · Cited by 18

ICA: model order selection and dynamic source models

Penny, W. D., Roberts, S., & Everson, R. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148.013 · Cited by 18

On Confidence Intervals Associated With the Usual and Adjusted Likelihoods

Mukerjee, R., & Reid, N. M. (1999) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00212 · Cited by 18

Asymptotic Properties of Bayesian Predictive Densities When the Distributions of Data and Target Variables are Different

Komaki, F. (2015) · Bayesian Analysis · doi:10.1214/14-ba886 · Cited by 18

Information geometry and statistical manifold

Abdel-All, N. H., Abd-Ellah, H. N., & Moustafa, H. M. (2002) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(02)00142-x · Cited by 18

The e-PCA and m-PCA: dimension reduction of parameters by information geometry

Akaho, S. (2005) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2004.1379884 · Cited by 18

Nonparametric approach for discriminant analysis in time series

Zhang, G., & Taniguchi, M. (1995) · Journal of nonparametric statistics · doi:10.1080/10485259508832637 · Cited by 18

Separation of non-stationary natural signals

Parra, L. C., & Spence, C. D. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148.006 · Cited by 18

Mathematical methods of neurocomputing

Амари, Ш.-И. (1993) · Springer eBooks · doi:10.1007/978-1-4899-3099-6_1 · Cited by 18

Are We Cruising a Hypothesis Space?

Rodríguez, C. C. (1999) · Springer eBooks · doi:10.1007/978-94-011-4710-1_14 · Cited by 17

Information-Geometric Measures as Robust Estimators of Connection Strengths and External Inputs

Tatsuno, M., Fellous, J., & Амари, Ш.-И. (2009) · Neural Computation · doi:10.1162/neco.2009.04-08-748 · Cited by 17

A gradient-based algorithm competitive with variational Bayesian EM for mixture of Gaussians

Kuusela, M., Raiko, T., Honkela, A., & Karhunen, J. (2009) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2009.5178726 · Cited by 17

Information Geometry of Interspike Intervals in Spiking Neurons

Ikeda, K. (2005) · Neural Computation · doi:10.1162/089976605774320593 · Cited by 17

Geometry Induced by a Generalization of Rényi Divergence

Souza, D. D., Vigelis, R. F., & Cavalcante, C. C. (2016) · Entropy · doi:10.3390/e18110407 · Cited by 17

Quantum Statistical Manifolds

Naudts, J. (2018) · Entropy · doi:10.3390/e20060472 · Cited by 14

Geometric Approach to Quantum Statistical Inference

Jarzyna, M., & Kolodynski, J. (2020) · IEEE Journal on Selected Areas in Information Theory · doi:10.1109/jsait.2020.3017469 · Cited by 16

Exponential family Fisher vector for image classification

Sánchez, J., & Redolfi, J. A. (2015) · Pattern Recognition Letters · doi:10.1016/j.patrec.2015.03.010 · Cited by 17

CONFORMAL GEOMETRY OF ESCORT PROBABILITY AND ITS APPLICATIONS

Ohara, A., Matsuzoe, H., & Амари, Ш.-И. (2012) · Modern Physics Letters B · doi:10.1142/s0217984912500637 · Cited by 17

Maximum likelihood estimators for generalized Cauchy processes

Konno, H., & WATANABE, F. (2007) · Journal of Mathematical Physics · doi:10.1063/1.2800162 · Cited by 17

Convergence of the Wake-Sleep Algorithm

Ikeda, S., Амари, Ш.-И., & Nakahara, H. (1998) · Cited by 17

The Fisher-Rao Metric for Projective Transformations of the Line

Maybank, S. J. (2005) · International Journal of Computer Vision · doi:10.1007/s11263-005-6877-6 · Cited by 17

Differential Geometric Structures of Stable State Feedback Systems with Dual Connections

Ohara, A., & Амари, Ш.-И. (1992) · Elsevier eBooks · doi:10.1016/b978-0-08-042057-8.50046-x · Cited by 17

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)