Differential-Geometrical Methods in Statistics

Advances in computational and statistical diffusion MRI

O’Donnell, L. J., Daducci, A., Wassermann, D., & Lenglet, C. (2017) · NMR in Biomedicine · doi:10.1002/nbm.3805 · Cited by 32

Quasi-homogeneous black hole thermodynamics

Quevedo, H., Quevedo, M. N., & Sánchez, A. (2019) · The European Physical Journal C · doi:10.1140/epjc/s10052-019-6745-0 · Cited by 32

Projective Power Entropy and Maximum Tsallis Entropy Distributions

Eguchi, S., Komori, O., & Kato, S. (2011) · Entropy · doi:10.3390/e13101746 · Cited by 32

Geometry and thermodynamic fluctuations of the Ising model on a Bethe lattice

Dolan, B. P. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0274 · Cited by 32

Preferred Point Geometry and Statistical Manifolds

Critchley, F., Marriott, P. K., & Salmon, M. H. (1993) · The Annals of Statistics · doi:10.1214/aos/1176349258 · Cited by 32

Statistical Inference for Generative Models with Maximum Mean DiscrepancyPreprint

Briol, F., Barp, A., Duncan, A., & Girolami, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.05944 · Cited by 32

New results on mixture and exponential models by Orlicz spaces

Santacroce, M., Siri, P., & Trivellato, B. (2016) · PORTO Publications Open Repository TOrino (Politecnico di Torino) · Cited by 31

An introduction to variational inference in geophysical inverse problems

Zhang, X., Nawaz, M. A., Zhao, X., & Curtis, A. (2021) · Advances in geophysics · doi:10.1016/bs.agph.2021.06.003 · Cited by 31

The Last-Step Minimax Algorithm

Takimoto, E., & Warmuth, M. K. (2000) · Lecture notes in computer science · doi:10.1007/3-540-40992-0_21 · Cited by 31

Information Geometry Approach to Verification of Dynamic Models in Power Systems

Transtrum, M. K., Sarić, A. T., & Stanković, A. M. (2017) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2017.2692523 · Cited by 31

Fisher information under restriction of Shannon information in multi-terminal situations

Амари, Ш.-И. (1989) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00057730 · Cited by 31

Learning the Information Divergence

Dikmen, O., Yang, Z., & Erkki Oja, A. (2014) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2014.2366144 · Cited by 30

Generalized normalized $$\varvec{\delta }$$ δ -Casorati curvature for statistical submanifolds in quaternion Kaehler-like statistical space forms

Aquib, M., & Shahid, M. H. (2018) · Journal of Geometry · doi:10.1007/s00022-018-0418-2 · Cited by 30

Detection of image structures using the Fisher information and the Rao metric

Maybank, S. J. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.122 · Cited by 30

A tracking algorithm for infrared images based on reduced sufficient statistics

Anderson, K. L., & Iltis, R. A. (1997) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/7.575884 · Cited by 30

Non-Commutative Extension of the Information Geometry

Hasegawa, H. (1995) · Springer eBooks · doi:10.1007/978-1-4899-1391-3_31 · Cited by 30

A bayes‐closed approximation of recursive non‐linear estimation

Kulhavý, R. (1990) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.4480040404 · Cited by 30

Dual connections in nonparametric classical information geometry

Grasselli, M. R. (2008) · Annals of the Institute of Statistical Mathematics · doi:10.1007/s10463-008-0191-3 · Cited by 29

Probability density function in the log-law region of low Reynolds number turbulent boundary layer

Tsuji, Y., & Nakamura, I. (1999) · Physics of Fluids · doi:10.1063/1.869936 · Cited by 29

Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds

Sıddıquı, A. N., Chen, B., & Bahadır, O. (2019) · Mathematics · doi:10.3390/math7090797 · Cited by 29

Absolute Continuity of Poisson Random Fields

Takahashi, Y. (1990) · Publications of the Research Institute for Mathematical Sciences · doi:10.2977/prims/1195170849 · Cited by 29

Criteria for global minimum of sum of squares in nonlinear regression

Demidenko, E. (2006) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2006.06.015 · Cited by 29

Nuisance parameter problem in quantum estimation theory: tradeoff relation and qubit examples

Suzuki, J. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab8672 · Cited by 33

Geometry of color perception. Part 1: structures and metrics of a homogeneous color space

Provenzi, E. (2020) · The Journal of Mathematical Neuroscience · doi:10.1186/s13408-020-00084-x · Cited by 28

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

Schulz, A., Hinder, F., & Hammer, B. (2020) · PUB – Publications at Bielefeld University (Bielefeld University) · Cited by 27

Principle of Learning Metrics for Exploratory Data Analysis

Samuel Kaski, A., & Sinkkonen, J. (2004) · The Journal of VLSI Signal Processing Systems for Signal Image and Video Technology · doi:10.1023/b:vlsi.0000027483.39774.f8 · Cited by 28

Bayesian invariant measurements of generalization

Zhu, H., & Rohwer, R. (1995) · Neural Processing Letters · doi:10.1007/bf02309013 · Cited by 28

ON LOCALLY DUALLY FLAT FINSLER METRICS

Cheng, X., Shen, Z., & ZHOU, Y. (2010) · International Journal of Mathematics · doi:10.1142/s0129167x10006616 · Cited by 28

EEG signal classification based on a Riemannian distance measure

Li, Y., Wong, K. M., & deBruin, H. (2009) · IEEE Toronto International Conference Science and Technology for Humanity · doi:10.1109/tic-sth.2009.5444491 · Cited by 28

Estimating Functions for Blind Separation when Sources Have Variance-Dependencies

Kawanabe, M., & Müller, K. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-30110-3_18 · Cited by 28

Conformal-Projective Geometry of Statistical Manifolds

Kurose, T. (2002) · Interdisciplinary Information Sciences · doi:10.4036/iis.2002.89 · Cited by 28

Geometry of quantum states: dual connections and divergence functions

Jenčová, A. (2001) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(01)90008-4 · Cited by 28

A gas of Brownian particles in statistical dynamics

Streater, R. F. (1997) · Journal of Statistical Physics · doi:10.1007/bf02508479 · Cited by 28

Model Dependence in Quantification of Spike Interdependence by Joint Peri-Stimulus Time Histogram

Ito, H., & Tsuji, S. (2000) · Neural Computation · doi:10.1162/089976600300015952 · Cited by 28

Quantum estimation and the quantum central limit theorem

Hayashi, M. (2009) · Translations - American Mathematical Society/Translations · doi:10.1090/trans2/227/05 · Cited by 34

Bayesian inference for latent variable models

Paquet, U. (2021) · CL Technical Reports · doi:10.48456/tr-724 · Cited by 28

Disentangled behavioral representationsPreprint

Dezfouli, A., Ashtiani, H., Ghattas, O., Nock, R., Dayan, P., & Ong, C. S. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/658252 · Cited by 27

On the Geometry of Covariance Matrices

Ning, L., Jiang, X., & Georgiou, T. T. (2013) · IEEE Signal Processing Letters · doi:10.1109/lsp.2013.2266273 · Cited by 27

New results on mixture and exponential models by Orlicz spaces

Santacroce, M., Siri, P., & Trivellato, B. (2016) · Bernoulli · doi:10.3150/15-bej698 · Cited by 27

Electroencephalogram signals classification for sleep-state decision – a Riemannian geometry approach

Li, Y., Wong, K. M., & de Bruin, H. (2012) · IET Signal Processing · doi:10.1049/iet-spr.2011.0234 · Cited by 27

Volume of the quantum mechanical state space

Andai, A. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/44/003 · Cited by 27

Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

Caticha, A. (2018) · Annalen der Physik · doi:10.1002/andp.201700408 · Cited by 33

On generalized m-th root finsler metrics

Tayebi, A., Nia, M. S., & Peyghan, E. (2012) · Linear Algebra and its Applications · doi:10.1016/j.laa.2012.02.025 · Cited by 27

DIFFERENTIAL GEOMETRY OF ARMA MODELS

Равишанкер, Н., Melnick, E. L., & Tsai, C. (1990) · Journal of Time Series Analysis · doi:10.1111/j.1467-9892.1990.tb00057.x · Cited by 27

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/cvprw.2009.5206843 · Cited by 27

Geometry and Dynamics for Markov Chain Monte Carlo

Barp, A., Briol, F., Kennedy, A. D., & Girolami, M. (2017) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-031017-100141 · Cited by 25

Riemannian Optimization and Approximate Joint Diagonalization for Blind Source Separation

Bouchard, F., Malick, J., & Congedo, M. (2018) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2018.2795539 · Cited by 26

Recent developments in Wintgen inequality and Wintgen ideal submanifolds

Chen, B. (2021) · International Electronic Journal of Geometry · doi:10.36890/iejg.838446 · Cited by 26

Bayesian sensitivity analysis with the Fisher–Rao metric

Kurtek, S., & Bharath, K. (2015) · Biometrika · doi:10.1093/biomet/asv026 · Cited by 26

A dually flat structure on the space of escort distributions

Ohara, A., Matsuzoe, H., & Амари, Ш.-И. (2010) · Journal of Physics Conference Series · doi:10.1088/1742-6596/201/1/012012 · Cited by 26

Gradient systems associated with probability distributions

Nakamura, Y. (1994) · Japan Journal of Industrial and Applied Mathematics · doi:10.1007/bf03167211 · Cited by 26

Fisher information matrix and hyperbolic geometry

Costa, S. I. R., Santos, S. A., & Strapasson, J. E. (2005) · IEEE Information Theory Workshop (ITW) · doi:10.1109/itw.2005.1531851 · Cited by 26

Information geometry of statistical inference - an overview

Амари, Ш.-И. (2003) · IEEE Information Theory Workshop (ITW) · doi:10.1109/itw.2002.1115423 · Cited by 26

Displacement convexity of generalized relative entropies. II

Ohta, S.-I., & Takatsu, A. (2013) · Communications in Analysis and Geometry · doi:10.4310/cag.2013.v21.n4.a1 · Cited by 26

Efficient Image Retrieval with Statistical Color Descriptors

Tran, L. V. (2003) · Cited by 26

Entropies of the EEG: The effects of general anaesthesia

Sleigh, J. W., Olofsen, E., Dahan, A., de Goede, J., & Steyn‐Ross, D. A. (2001) · Research Commons (University of Waikato) · Cited by 26

On parabolic geometry and irreversible macroscopic time

Ingarden, R. S., & Tamássy, L. (1993) · Reports on Mathematical Physics · doi:10.1016/0034-4877(93)90069-q · Cited by 26

The geometry of case deletion and the assessment of influence in nonlinear regression

Ross, W. H. (1987) · Canadian Journal of Statistics · doi:10.2307/3315198 · Cited by 26

Algebraic Information Geometry for Learning Machines with Singularities

Watanabe, S. (2000) · Cited by 26

AlphaNet: Improved Training of Supernets with Alpha-DivergencePreprint

Wang, D., Gong, C., Li, M., Liu, Q., & Chandra, V. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.07954 · Cited by 32

Bayesian quantum thermometry based on thermodynamic length

Jørgensen, M. R., Kołodyński, J., Mehboudi, M., Perarnau-Llobet, M., & Brask, J. B. (2022) · Physical Review A · doi:10.1103/physreva.105.042601 · Cited by 26

Einstein-Maxwell-dilaton phantom black holes: Thermodynamics and geometrothermodynamics

Quevedo, H., Quevedo, M. N., & Sánchez, A. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.024057 · Cited by 25

Differential Geometry of Special Mappings

Mikeš, J. (2019) · doi:10.5507/prf.19.24455365 · Cited by 25

Linear Models Based on Noisy Data and the Frisch Scheme

Ning, L., Georgiou, T. T., Tannenbaum, A., & Boyd, S. (2015) · SIAM Review · doi:10.1137/130921179 · Cited by 22

Affine Scaling Algorithm

Tsuchiya, T. (1996) · Applied optimization · doi:10.1007/978-1-4613-3449-1_2 · Cited by 25

Rho–tau embedding and gauge freedom in information geometry

Naudts, J., & Zhang, J. (2018) · Information Geometry · doi:10.1007/s41884-018-0004-6 · Cited by 25

Differential Geometric Least Angle Regression: A Differential Geometric Approach to Sparse Generalized Linear Models

Augugliaro, L., Mineo, A. M., & Wit, E. C. (2013) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12000 · Cited by 25

Nonparametric bootstrap prediction

Fushiki, T., Komaki, F., & Aihara, K. (2005) · Bernoulli · doi:10.3150/bj/1116340296 · Cited by 25

Dual differential geometry associated with the Kullbaek-Leibler information on the Gaussian distributions and its 2-parameter deformations

Yoshizawa, S., & Tanabe, K. (1999) · SUT Journal of Mathematics · doi:10.55937/sut/991985432 · Cited by 25

On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric

Dittmann, J. (2000) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(00)00130-0 · Cited by 25

Duality of Maximum Entropy and Minimum Divergence

Eguchi, S., Komori, O., & Ohara, A. (2014) · Entropy · doi:10.3390/e16073552 · Cited by 24

Nonlinear filtering via stochastic PDE projection on mixture manifolds in $$L^2$$ L 2 direct metric

Armstrong, J., & Brigo, D. (2015) · Mathematics of Control Signals and Systems · doi:10.1007/s00498-015-0154-1 · Cited by 24

Information geometry on the space of equilibrium states of black holes in higher derivative theories

Vetsov, T. (2019) · The European Physical Journal C · doi:10.1140/epjc/s10052-019-6553-6 · Cited by 24

Geometry of contrast functions and conformal geometry

Matsuzoe, H. (1999) · Hiroshima Mathematical Journal · doi:10.32917/hmj/1206125160 · Cited by 24

Riemannian Manifold Hamiltonian Monte Carlo

Girolami, M., Calderhead, B., & Chin, S. (2009) · Cambridge University Engineering Department Publications Database · doi:10.48550/arxiv.0907.1100 · Cited by 24

A Computational Approach to Fisher Information Geometry with Applications to Image Analysis

Mio, W., Badlyans, D., & Liu, X. (2005) · Lecture notes in computer science · doi:10.1007/11585978_2 · Cited by 24

Asymptotic expansions for the ability estimator in item response theory

Ogasawara, H. (2011) · Computational Statistics · doi:10.1007/s00180-011-0282-0 · Cited by 24

Averaging entropy

Campbell, L. L. (1995) · IEEE Transactions on Information Theory · doi:10.1109/18.370086 · Cited by 24

Geometrical Methods in Thermodynamics

Mrugała, R. (2000) · Springer eBooks · doi:10.1007/978-1-4612-1286-7_10 · Cited by 24

Symbolic computation of Fisher information matrices for parametrized state-space systems

Peeters, R., & Hanzon, B. (1999) · Automatica · doi:10.1016/s0005-1098(99)00004-7 · Cited by 24

CONNECTIONS ON STATISTICAL MANIFOLDS OF DENSITY OPERATORS BY GEOMETRY OF NONCOMMUTATIVE Lp-SPACES

Gibilisco, P., & Isola, T. (1999) · Infinite Dimensional Analysis Quantum Probability and Related Topics · doi:10.1142/s0219025799000096 · Cited by 24

On the conditions for the existence of ancillary statistics in a curved exponential family

Kumon, M. (2008) · Statistical Methodology · doi:10.1016/j.stamet.2008.11.003 · Cited by 23

Characterizing Pure High-Order Entanglements in Lexical Semantic Spaces via Information Geometry

Hou, Y., & Song, D. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-00834-4_20 · Cited by 24

Fisher Information of Wavefunctions: Classical and Quantum

Shun-Long, L. (2006) · Chinese Physics Letters · doi:10.1088/0256-307x/23/12/001 · Cited by 23

Graphical Models and Message-Passing Algorithms: Some Introductory Lectures

Wainwright, M. J. (2015) · Lecture notes in mathematics · doi:10.1007/978-3-319-16967-5_3 · Cited by 23

Geometric Science of Information

Combe, N., Combe, P., & Nencka, H. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-80209-7 · Cited by 23

Detecting and mitigating mode-collapse for flow-based sampling of lattice field theories

Nicoli, K. A., Anders, C. J., Hartung, T., Jansen, K., Kessel, P., & Nakajima, S. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.114501 · Cited by 23

Information Divergence Geometry and the Application to Statistical Machine Learning

Eguchi, S. (2008) · Information Theory and Statistical Learning · doi:10.1007/978-0-387-84816-7_13 · Cited by 23

On dual-projectively flat affine connections

Ivanov, S. P. (1995) · Journal of Geometry · doi:10.1007/bf01224043 · Cited by 23

Chen Inequalities for Statistical Submanifolds of Kähler-Like Statistical Manifolds

Aytimur, H., Kon, M., Mihai, A., Özgür, C., & Takano, K. (2019) · Mathematics · doi:10.3390/math7121202 · Cited by 23

On the geometry of generalized Gaussian distributions

Andai, A. (2008) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2008.08.007 · Cited by 23

Affine Moments of a Random Vector

Lutwak, E., Lv, S., Yang, D., & Zhang, G. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2258457 · Cited by 23

Legendre structure of κ-thermostatistics revisited in the framework of information geometry

Scarfone, A. M., & Wada, T. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/27/275002 · Cited by 23

Fast ICA by a fixed-point algorithm that maximizes non-Gaussianity

Hyvärinen, A. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148.003 · Cited by 23

Life-space foam: A medium for motivational and cognitive dynamics

Ivancevic, V., & Aidman, E. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.04.025 · Cited by 31

The EM Algorithm and Information Geometry in Neural Network Learning

Амари, Ш.-И. (1995) · Neural Computation · doi:10.1162/neco.1995.7.1.13 · Cited by 23

Invariant Bayesian estimation on manifolds

Jermyn, I. H. (2005) · The Annals of Statistics · doi:10.1214/009053604000001273 · Cited by 23

Metric-Free Natural Gradient for Joint-Training of Boltzmann MachinesPreprint

Desjardins, G., Pascanu, R., Courville, A. C., & Bengio, Y. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1301.3545 · Cited by 29

Nonlinear-Dynamical Attention Allocation via Information Geometry

Iklé, M., & Goertzel, B. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-22887-2_7 · Cited by 22

On Monotone Embedding in Information Geometry

Zhang, J. (2015) · Entropy · doi:10.3390/e17074485 · Cited by 22

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)