Differential-Geometrical Methods in Statistics

Statistical Inference for the Population Landscape via Moment-Adjusted Stochastic Gradients

Liang, T., & Su, W. (2019) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12313 · Cited by 17

Generalization and maximum likelihood from small data sets

Byrne, B. (2002) · Machine learning for signal processing ... · doi:10.1109/nnsp.1993.471869 · Cited by 17

Geometry of f-divergence

Vos, P. W. (1991) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00053370 · Cited by 17

Active contour model with adaptive weighted function for robust image segmentation under biased conditions

Joshi, A., Khan, M. S., Niaz, A., Akram, F., Song, H. C., & Choi, K. N. (2021) · Expert Systems with Applications · doi:10.1016/j.eswa.2021.114811 · Cited by 16

Unified representation of homogeneous and quasi-homogenous systems in geometrothermodynamics

Quevedo, H., & Quevedo, M. N. (2023) · Physics Letters B · doi:10.1016/j.physletb.2023.137678 · Cited by 16

The Krylov-proportionate normalized least mean fourth approach: Formulation and performance analysis

Sayin, M. O., Yılmaz, Y., Demir, A., & Kozat, S. S. (2014) · Signal Processing · doi:10.1016/j.sigpro.2014.10.015 · Cited by 16

Investigation of Possible Neural Architectures Underlying Information-Geometric Measures

Tatsuno, M., & Okada, M. (2004) · Neural Computation · doi:10.1162/089976604322860686 · Cited by 16

The Chen's first inequality for submanifolds of statistical warped product manifolds

Sıddıquı, A. N., Murathan, C., & Siddiqi, M. D. (2021) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2021.104344 · Cited by 16

An Information Geometrical View of Stationary Subspace Analysis

Kawanabe, M., Samek, W., von Bünau, P., & Meinecke, F. C. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-21738-8_51 · Cited by 16

Flat connections and Wigner-Yanase-Dyson metrics

Jenčová, A. (2003) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(03)80033-2 · Cited by 16

Geodesic regression on orientation distribution functions with its application to an aging study

Du, J. T., Goh, A., Kushnarev, S., & Qiu, A. (2013) · NeuroImage · doi:10.1016/j.neuroimage.2013.06.081 · Cited by 16

Intelligence Science

Shi, Z. (2011) · WORLD SCIENTIFIC eBooks · doi:10.1142/8211 · Cited by 16

Total bregman divergence, a robust divergence measure, and its applications

Vemuri, B. C., & Liu, M. (2011) · Cited by 16

On dually flat Randers metrics

Yu, C. (2013) · Nonlinear Analysis · doi:10.1016/j.na.2013.09.008 · Cited by 16

Inspecting adversarial examples using the fisher information

Martin, J., & Elster, C. (2019) · Neurocomputing · doi:10.1016/j.neucom.2019.11.052 · Cited by 16

Geometry of Hessian Structures

Shima, H. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-40020-9_4 · Cited by 16

Statistical inference: learning in artificial neural networks

Yang, H. H., Murata, N., & Amari, S. (1998) · Trends in Cognitive Sciences · doi:10.1016/s1364-6613(97)01114-5 · Cited by 16

Beyond second-order statistics for learning: A pairwise interaction model for entropy estimation

Deniz Erdogmus, B., Príncipe, J. C., & Hild, K. E. (2002) · Natural Computing · doi:10.1023/a:1015064029375 · Cited by 16

The Metrics Induced by the Kullback Number

Rodríguez, C. C. (1989) · Springer eBooks · doi:10.1007/978-94-015-7860-8_43 · Cited by 16

Field Theoretical Analysis of On-Line Learning of Probability Distributions

Aida, T. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3554 · Cited by 16

Geometric Science of Information

Nielsen, F., & Barbaresco, F. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-38271-0 · Cited by 15

Geometric methods for sampling, optimization, inference, and adaptive agents

Barp, A., Costa, L. D., França, G., Friston, K. J., Girolami, M., Jordan, M. I., & Pavliotis, G. A. (2022) · Handbook of statistics · doi:10.1016/bs.host.2022.03.005 · Cited by 24

Natural gradient, fitness modelling and model selection: A unifying perspective

Malagò, L., Matteucci, M., & Pistone, G. (2013) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec.2013.6557608 · Cited by 15

Path Connectedness on a Space of Probability Density Functions

Eguchi, S., & Komori, O. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-25040-3_66 · Cited by 15

Sketching Information Divergences

Guha, S., Indyk, P., & McGregor, A. (2007) · Springer eBooks · doi:10.1007/978-3-540-72927-3_31 · Cited by 15

Exploiting Information Geometry to Improve the Convergence Properties of Variational Active Contours

Pereyra, M., Batatia, H., & McLaughlin, S. (2013) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2013.2258136 · Cited by 15

Asymptotic Expansions of the Distributions of the Polyserial Correlation Coefficients

Ogasawara, H. (2011) · Behaviormetrika · doi:10.2333/bhmk.38.153 · Cited by 15

Bayesian prediction based on a class of shrinkage priors for location-scale models

Komaki, F. (2007) · Annals of the Institute of Statistical Mathematics · doi:10.1007/s10463-006-0102-4 · Cited by 15

Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures

Scarfone, A. M., Matsuzoe, H., & Wada, T. (2018) · Entropy · doi:10.3390/e20060436 · Cited by 15

Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection

Kazan, A., & Kazan, S. (2018) · Universal Journal of Mathematics and Applications · doi:10.32323/ujma.439013 · Cited by 15

Detection of syntonies between multiple spike trains using a coarse-grain binarization of spike count distributions

Prete, V. D., Martignon, L. F., & Villa, A. E. P. (2004) · Network Computation in Neural Systems · doi:10.1088/0954-898x_15_1_002 · Cited by 15

Lagrangian and Hamiltonian dynamics for probabilities on the statistical bundle

Chirco, G., Malagò, L., & Pistone, G. (2022) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887822502140 · Cited by 15

Information Geometry of Neural Networks — An Overview —

Амари, Ш.-И. (1997) · Operations research, computer science. Interface series · doi:10.1007/978-1-4615-6099-9_2 · Cited by 15

Hooke’s law in statistical manifolds and divergences

Henmi, M., & Kobayashi, R. (2000) · Nagoya Mathematical Journal · doi:10.1017/s002776300000739x · Cited by 15

Natural gradient‐projection algorithm for distribution control

Zhang, Z., Sun, H., & Zhong, F. (2008) · Optimal Control Applications and Methods · doi:10.1002/oca.874 · Cited by 15

Minimum f-divergence estimators and quasi-likelihood functions

Vos, P. W. (1992) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00058640 · Cited by 15

On the converse theorem in statistical hypothesis testing

Nakagawa, K., & Kanaya, F. (1993) · IEEE Transactions on Information Theory · doi:10.1109/18.212293 · Cited by 15

A distributed bearings-only tracking algorithm using reduced sufficient statistics

Anderson, K. L., & Iltis, R. A. (1996) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/7.481273 · Cited by 15

AN ON-LINE ADAPTATION ALGORITHM FOR ADAPTIVE SYSTEM TRAINING WITH MINIMUM ERROR ENTROPY: STOCHASTIC INFORMATION GRADIENT

Deniz Erdogmus, B., & Príncipe, J. C. (2001) · Cited by 15

Thermodynamic Metrics and Black Hole Physics

Åman, J. E., Bengtsson, I., & Pidokrajt, N. (2015) · Entropy · doi:10.3390/e17096503 · Cited by 14

Stability and anyonic behavior of systems with M -statistics

Ubriaco, M. R. (2013) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2013.06.062 · Cited by 14

Kinetic derivation of the Hessian geometric structure in chemical reaction networks

Kobayashi, T. J., Loutchko, D., Kamimura, A., & Sughiyama, Y. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033066 · Cited by 14

Comparative study of FeedForward and Radial Basis Function Neural Networks for solving an Environmental Boundary Value Problem

Famelis, I. T., Donas, A., & Galanis, G. N. (2022) · Results in Applied Mathematics · doi:10.1016/j.rinam.2022.100344 · Cited by 14

The geometric structures of the Weibull distribution manifold and the generalized exponential distribution manifold

Cao, L., Sun, H., & Wang, X. (2008) · Tamkang Journal of Mathematics · doi:10.5556/j.tkjm.39.2008.44 · Cited by 14

Theq-exponential family in statistical physics

Naudts, J. (2010) · Journal of Physics Conference Series · doi:10.1088/1742-6596/201/1/012003 · Cited by 14

Towards an Informational Pragmatic Realism

Caticha, A. (2013) · Minds and Machines · doi:10.1007/s11023-013-9322-6 · Cited by 14

Geometric description of chemical reactions

Quevedo, H., & Tapias, D. (2013) · Journal of Mathematical Chemistry · doi:10.1007/s10910-013-0250-8 · Cited by 14

Vanishing largest Lyapunov exponent and Tsallis entropy

Kalogeropoulos, N. (2013) · QScience Connect · doi:10.5339/connect.2013.26 · Cited by 14

Lie groupoids in information geometry

Grabowska, K., Grabowski, J., Kuś, M., & Marmo, G. (2019) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab542e · Cited by 14

On Cosymplectic-Like Statistical Submersions

Aytimur, H., & Özgür, C. (2019) · Mediterranean Journal of Mathematics · doi:10.1007/s00009-019-1332-z · Cited by 14

On the Relationship between α Connections and the Asymptotic Properties of Predictive Distributions

Corcuera, J. M., Giummolè, F., Corcuera, J. M., & Giummolè, F. (1999) · Bernoulli · doi:10.2307/3318617 · Cited by 14

Intrinsic Cramer-Rao bounds and subspace estimation accuracy

Smith, S. T. (2002) · IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM) · doi:10.1109/sam.2000.878057 · Cited by 14

A Characterization of Monotone and Regular Divergences

Corcuera, J. M., & Giummolè, F. (1998) · Annals of the Institute of Statistical Mathematics · doi:10.1023/a:1003569210573 · Cited by 14

On Parametric Bootstrapping and Bayesian Prediction

Fushiki, T., Komaki, F., & Aihara, K. (2004) · Scandinavian Journal of Statistics · doi:10.1111/j.1467-9469.2004.02_127.x · Cited by 14

A differential geometric approach to nonlinear filtering: the projection filter

Brigo, D., Hanzon, B., & Gland, F. L. (2002) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.1995.479232 · Cited by 14

DUALITY, MONOTONICITY AND THE WIGNER–YANASE–DYSON METRICS

Grasselli, M. R. (2004) · Infinite Dimensional Analysis Quantum Probability and Related Topics · doi:10.1142/s021902570400161x · Cited by 14

A Geometric Approach to Detecting Influential Cases

Vos, P. W. (1991) · The Annals of Statistics · doi:10.1214/aos/1176348262 · Cited by 14

The Expectation of the Likelihood Ratio Criterion

Ross, W. H. (1987) · International Statistical Review · doi:10.2307/1403408 · Cited by 14

Semi-symmetric non-metric connections on statistical manifolds

Yıldırım, M. (2022) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2022.104505 · Cited by 13

Orthogonal parametric non-negative matrix tri-factorization with α -divergence for co-clustering

Hoseinipour, S., Aminghafari, M., & Mohammadpour, A. (2023) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.120680 · Cited by 13

EM Algorithm : Application to Clustering and Recent Development

Akaho, S. (2000) · Journal of Japan Society for Fuzzy Theory and Intelligent Informatics · doi:10.3156/jfuzzy.12.5_2 · Cited by 13

Amplifying Inter-Message Distance: On Information Divergence Measures in Big Data

She, R., Liu, S., & Fan, P. (2017) · IEEE Access · doi:10.1109/access.2017.2768385 · Cited by 13

Lower Bounds on Statistical Submersions with vertical Casorati curvatures

Sıddıquı, A. N., Siddiqi, M. D., AlKhaldi, A. H., & Ali, A. (2021) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s021988782250044x · Cited by 13

Symplectic and Kähler Structures on Statistical Manifolds Induced from Divergence Functions

Zhang, J., & Li, F. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-40020-9_66 · Cited by 13

What does intrinsic mean in statistical estimation

García, G. H., & Oller, J. M. (2006) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · Cited by 13

Iterative Approximation of Statistical Distributions and Relation to Information Geometry

Dodson, C. T. J., & Wang, H. (2001) · Statistical Inference for Stochastic Processes · doi:10.1023/a:1012289028897 · Cited by 13

On Kropina Change for mth Root Finsler Metrics

Tayebi, A., Tabatabaeifar, T., & Peyghan, E. (2014) · Ukrainian Mathematical Journal · doi:10.1007/s11253-014-0919-6 · Cited by 13

Conjugate connections on statistical manifolds

Stepanov, S. E., Stepanova, E. S., & Shandra, I. G. (2007) · Russian Mathematics · doi:10.3103/s1066369x07100052 · Cited by 13

Adaptive Improved Natural Gradient Algorithm for Blind Source Separation

Liu, J., Feng, D., & Zhang, W. (2008) · Neural Computation · doi:10.1162/neco.2008.07-07-562 · Cited by 13

Almost cosympletic statistical manifolds

Erken, İ. K., Murathan, C., & Yazla, A. (2019) · Quaestiones Mathematicae · doi:10.2989/16073606.2019.1576069 · Cited by 13

When Geometry Meets Psycho-Physics and Quantum Mechanics: Modern Perspectives on the Space of Perceived Colors

Berthier, M., & Provenzi, E. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-26980-7_64 · Cited by 13

An Information Geometry Approach to Robustness Analysis for the Uncertainty Quantification of Computer Codes

Gauchy, C., Stenger, J., Sueur, R., & Iooss, B. (2021) · Technometrics · doi:10.1080/00401706.2021.1905072 · Cited by 13

Invariant tests based onM-estimators, estimating functions, and the generalized method of moments

Dufour, J., Trognon, A., & Tuvaandorj, P. (2016) · Econometric Reviews · doi:10.1080/07474938.2015.1114285 · Cited by 13

Hypothesis testing: a model selection approach

Cubedo, M., & Oller, J. M. (2002) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(02)00267-7 · Cited by 13

On Tests for Global Maximum of the Log-Likelihood Function

Blatt, D., & Hero, A. O. (2007) · IEEE Transactions on Information Theory · doi:10.1109/tit.2007.899537 · Cited by 13

Multivariate density estimation with optimal marginal parzen density estimation and gaussianization

Deniz Erdogmus, B., Jenssen, R., Rao, Y. N., & Príncipe, J. C. (2005) · Machine learning for signal processing ... · doi:10.1109/mlsp.2004.1422961 · Cited by 13

Algorithms for blind signal separation and recovery in static and dynamic environments

Gharbi, A. B., & Salam, F. M. (2002) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.1997.608970 · Cited by 13

Perspectives on cognitive informatics

Shi, Z., & Shi, J. T. (2004) · IEEE International Conference on Cognitive Informatics · doi:10.1109/coginf.2003.1225970 · Cited by 13

Effect of initial values in simple perception

Raudys, Š., & Amari, S. (2002) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.1998.686004 · Cited by 13

Computational Information Geometry in Statistics: Theory and Practice

Critchley, F., & Marriott, P. K. (2014) · Entropy · doi:10.3390/e16052454 · Cited by 12

Geometry of the q -exponential distribution with dependent competing risks and accelerated life testing

Zhang, F., Shi, Y., & Wang, R. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.10.069 · Cited by 12

Statistical mirror symmetry

Zhang, J., & Khan, G. (2020) · Differential Geometry and its Applications · doi:10.1016/j.difgeo.2020.101678 · Cited by 12

Generalized geometry of Norden manifolds

Nannicini, A. (2015) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2015.10.011 · Cited by 12

Third order asymptotic efficiency of the sequential maximum likelihood estimation procedure

Akahira, M., & Takeuchi, K. (1989) · Sequential Analysis · doi:10.1080/07474948908836186 · Cited by 12

Bayesian influence analysis of generalized partial linear mixed models for longitudinal data

Tang, N., & Duan, X. (2014) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2013.12.005 · Cited by 12

Semiparametric estimation of shifts on compact Lie groups for image registration

Bigot, J., Loubes, J., & Vimond, M. (2010) · Probability Theory and Related Fields · doi:10.1007/s00440-010-0327-2 · Cited by 12

Information geometry of the power inverse Gaussian distribution

Zhang, Z., Sun, H., & Zhong, F. (2007) · Cited by 12

Quantum process tomography via optimal design of experiments

Gazit, Y., Ng, H. K., & Suzuki, J. (2019) · Physical Review A · doi:10.1103/physreva.100.012350 · Cited by 12

F‐Manifolds and geometry of information

Combe, N. C., & Manin, Y. I. (2020) · Bulletin of the London Mathematical Society · doi:10.1112/blms.12411 · Cited by 12

Projective Nonnegative Matrix Factorization with α-Divergence

Yang, Z., & Erkki Oja, A. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-04274-4_3 · Cited by 12

Logarithm Versus Square Root: Comparing Quantum Fisher Information

Shun-Long, L. (2007) · Communications in Theoretical Physics · doi:10.1088/0253-6102/47/4/005 · Cited by 12

Comparison of test statistics via expected lengths of associated confidence intervals

Mukerjee, R., & Reid, N. M. (2001) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(00)00350-5 · Cited by 12

An Extension of Least Angle Regression Based on the Information Geometry of Dually Flat Spaces

Hirose, Y., & Komaki, F. (2010) · Journal of Computational and Graphical Statistics · doi:10.1198/jcgs.2010.09064 · Cited by 12

Invited discussion paper small-sample distributional properties of nonlinear regression estimators (a geometric approach)

Pizman, A. (1990) · Statistics · doi:10.1080/02331889008802249 · Cited by 12

A Nonlinear Filtering Approach to Changepoint Detection Problems: Direct and Differential-Geometric Methods

Vellekoop, M., & Clark, J. M. C. (2003) · SIAM Journal on Control and Optimization · doi:10.1137/s0363012900375950 · Cited by 12

Harmonicity of gradient mappings of level surfaces in a real affine space

Shima, H. (1995) · Geometriae Dedicata · doi:10.1007/bf01267641 · Cited by 12

Fast Approximate Joint Diagonalization of Positive Definite Hermitian Matrices

Todros, K., & Tabrikian, J. (2007) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2007.367101 · Cited by 12

Local mixture models of exponential families

Anaya-Izquierdo, K., & Marriott, P. (2007) · Bernoulli · doi:10.3150/07-bej6170 · Cited by 12

On the Search Algorithm for the Output Distribution That Achieves the Channel Capacity

Nakagawa, K., Watabe, K., & Sabu, T. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2636847 · Cited by 12

Large Deformation Diffeomorphic Metric Mapping of Orientation Distribution Functions

Du, J. T., Goh, A., & Qiu, A. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-22092-0_37 · Cited by 12

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)