Differential-Geometrical Methods in Statistics

Natural Gradient Works Efficiently in Learning

Амари, Ш.-И. (1998) · Neural Computation · doi:10.1162/089976698300017746 · Cited by 2,745 · see citing works

Independent Component Analysis

(2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511624148 · Cited by 1,949 · see citing works

A New Learning Algorithm for Blind Signal Separation

Амари, Ш.-И., Cichocki, A. S., & Yang, H. H. (1995) · Cited by 1,904 · see citing works

Improving predictive inference under covariate shift by weighting the log-likelihood function

Shimodaira, H. (2000) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(00)00115-4 · Cited by 1,678 · see citing works

Nonnegative Matrix and Tensor Factorizations

Cichocki, A. S., Zdunek, R., Phan, A. H., & Амари, Ш.-И. (2009) · Wiley eBooks · doi:10.1002/9780470747278 · Cited by 1,404 · see citing works

Parameter Orthogonality and Approximate Conditional Inference

Cox, D. R., & Reid, N. M. (1987) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1987.tb01422.x · Cited by 1,370 · see citing works

Riemannian geometry in thermodynamic fluctuation theory

Ruppeiner, G. (1995) · Reviews of Modern Physics · doi:10.1103/revmodphys.67.605 · Cited by 855 · see citing works

Foundations of neural networks, fuzzy systems, and knowledge engineering

Kasabov, N. K. (1997) · Choice Reviews Online · doi:10.5860/choice.35-0330 · Cited by 821 · see citing works

Dataset Shift in Machine Learning

(2008) · doi:10.7551/mitpress/9780262170055.001.0001 · Cited by 1,553 · see citing works

Advances in Variational Inference

Zhang, C., Bütepage, J., Kjellström, H., & Mandt, S. (2018) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2018.2889774 · Cited by 676 · see citing works

Shape Analysis of Elastic Curves in Euclidean Spaces

Srivastava, A., Klassen, E., Joshi, S. H., & Jermyn, I. H. (2011) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2010.184 · Cited by 683 · see citing works

Neural Networks and Related Methods for Classification

Ripley, B. D. (1994) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1994.tb01990.x · Cited by 627 · see citing works

Information Theory and Statistics: A Tutorial

Csiszár, I., & Shields, P. C. (2004) · now publishers, Inc. eBooks · doi:10.1561/9781933019543 · Cited by 606 · see citing works

Monotone metrics on matrix spaces

Petz, D. (1996) · Linear Algebra and its Applications · doi:10.1016/0024-3795(94)00211-8 · Cited by 585 · see citing works

Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations

Cichocki, A. S., & Phan, A. H. (2009) · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · doi:10.1587/transfun.e92.a.708 · Cited by 576 · see citing works

A First Course in Information Theory

Yeung, R. W. (2002) · Information technology: transmission, processing and storage · doi:10.1007/978-1-4419-8608-5 · Cited by 524 · see citing works

Blind separation of instantaneous mixtures of nonstationary sources

Pham, D.-T., & Cardoso, J.-F. (2001) · IEEE Transactions on Signal Processing · doi:10.1109/78.942614 · Cited by 507 · see citing works

Toward a method of selecting among computational models of cognition.

Pitt, M. A., Myung, I. J., & Zhang, S. (2002) · Psychological Review · doi:10.1037/0033-295x.109.3.472 · Cited by 506 · see citing works

Information Theoretic Learning

Deniz Erdogmus, B., & Príncipe, J. C. (2009) · IGI Global eBooks · doi:10.4018/978-1-59904-849-9.ch133 · Cited by 536 · see citing works

Adaptive blind signal processing-neural network approaches

Амари, Ш.-И., & Cichocki, A. S. (1998) · Proceedings of the IEEE · doi:10.1109/5.720251 · Cited by 466 · see citing works

Divergence measures and message passing

Minka, T. P. (2005) · Cited by 462 · see citing works

Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities

Cichocki, A. S., & Амари, Ш.-И. (2010) · Entropy · doi:10.3390/e12061532 · Cited by 459 · see citing works

Information Theory and Statistics: A Tutorial

Csiszár, I., & Shields, P. C. (2004) · Foundations and Trends® in Communications and Information Theory · doi:10.1561/0100000004 · Cited by 424 · see citing works

Large sample theory of intrinsic and extrinsic sample means on manifolds

Bhattacharya, R. N., & Patrangenaru, V. (2003) · The Annals of Statistics · doi:10.1214/aos/1046294456 · Cited by 402 · see citing works

Information geometry on hierarchy of probability distributions

Амари, Ш.-И. (2001) · IEEE Transactions on Information Theory · doi:10.1109/18.930911 · Cited by 403 · see citing works

An error-entropy minimization algorithm for supervised training of nonlinear adaptive systems

Deniz Erdogmus, B., & Príncipe, J. C. (2002) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2002.1011217 · Cited by 353 · see citing works

Saddlepoint Methods and Statistical Inference

Reid, N. M. (1988) · Statistical Science · doi:10.1214/ss/1177012906 · Cited by 338 · see citing works

Information geometry of the EM and em algorithms for neural networks

Амари, Ш.-И. (1995) · Neural Networks · doi:10.1016/0893-6080(95)00003-8 · Cited by 326 · see citing works

Strong converse and Stein's lemma in quantum hypothesis testing

Nagaoka, H., & Ogawa, T. (2000) · IEEE Transactions on Information Theory · doi:10.1109/18.887855 · Cited by 307 · see citing works

Analysis and Design of Echo State Networks

Ozturk, M. C., Xu, D., & Príncipe, J. C. (2006) · Neural Computation · doi:10.1162/neco.2007.19.1.111 · Cited by 311 · see citing works

Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of Distributions

Azoury, K. S., & Warmuth, M. K. (2001) · Machine Learning · doi:10.1023/a:1010896012157 · Cited by 298 · see citing works

Support Vector Machines with Applications

Moguerza, J. M., & Muñoz, A. (2006) · Statistical Science · doi:10.1214/088342306000000493 · Cited by 297 · see citing works

Nonlinear analysis of EEG signals at different mental states

Natarajan, K., Acharya, U. R., Alias, F., Tiboleng, T., & Puthusserypady, S. K. (2004) · BioMedical Engineering OnLine · doi:10.1186/1475-925x-3-7 · Cited by 293 · see citing works

Stability Analysis of Learning Algorithms for Blind Source Separation

Амари, Ш.-И., Chen, T., & Cichocki, A. S. (1997) · Neural Networks · doi:10.1016/s0893-6080(97)00039-7 · Cited by 293 · see citing works

Support Vector Machines Applications

Ma, Y., & Guo, G. (2014) · Springer eBooks · doi:10.1007/978-3-319-02300-7 · Cited by 286 · see citing works

Csiszár’s Divergences for Non-negative Matrix Factorization: Family of New Algorithms

Cichocki, A. S., Zdunek, R., & Амари, Ш.-И. (2006) · Lecture notes in computer science · doi:10.1007/11679363_5 · Cited by 275 · see citing works

Robust parameter estimation with a small bias against heavy contamination

Fujisawa, H., & Eguchi, S. (2008) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2008.02.004 · Cited by 267 · see citing works

Fast Curvature Matrix-Vector Products for Second-Order Gradient Descent

Schraudolph, N. N. (2002) · Neural Computation · doi:10.1162/08997660260028683 · Cited by 265 · see citing works

Divergence measures for statistical data processing—An annotated bibliography

Basseville, M. (2012) · Signal Processing · doi:10.1016/j.sigpro.2012.09.003 · Cited by 249 · see citing works

Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds

Smith, S. T. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2005.845428 · Cited by 245 · see citing works

Blind source separation-semiparametric statistical approach

Амари, Ш.-И., & Cardoso, J.-F. (1997) · IEEE Transactions on Signal Processing · doi:10.1109/78.650095 · Cited by 244 · see citing works

Generalized information potential criterion for adaptive system training

Deniz Erdogmus, B., & Príncipe, J. C. (2002) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2002.1031936 · Cited by 237 · see citing works

Statistical Inference, Occam's Razor, and Statistical Mechanics on the Space of Probability Distributions

Balasubramanian, V. (1997) · Neural Computation · doi:10.1162/neco.1997.9.2.349 · Cited by 236 · see citing works

Geometries of quantum states

Petz, D., & Sudár, C. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531535 · Cited by 234 · see citing works

New Algorithms for Non-Negative Matrix Factorization in Applications to Blind Source Separation

Cichocki, A. S., Zdunek, R., & Амари, Ш.-И. (2006) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2006.1661352 · Cited by 223 · see citing works

An Elementary Introduction to Information Geometry

Nielsen, F. (2020) · Entropy · doi:10.3390/e22101100 · Cited by 238 · see citing works

Statistical inference under multiterminal data compression

Han, T. S., & Амари, Ш.-И. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.720540 · Cited by 216 · see citing works

Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization

Cichocki, A. S., Cruces, S., & Амари, Ш.-И. (2011) · Entropy · doi:10.3390/e13010134 · Cited by 213 · see citing works

The Geometry of Asymptotic Inference

Kass, R. E. (1989) · Statistical Science · doi:10.1214/ss/1177012480 · Cited by 212 · see citing works

Algebraic Analysis for Nonidentifiable Learning Machines

Watanabe, S. (2001) · Neural Computation · doi:10.1162/089976601300014402 · Cited by 211 · see citing works

Wigner-Yanase skew information vs. quantum Fisher information

Luo, S. (2003) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-03-07175-2 · Cited by 201 · see citing works

Stochastic Learning

Bottou, L. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-28650-9_7 · Cited by 201 · see citing works

Information geometry of Boltzmann machines

Амари, Ш.-И., Kurata, K., & Nagaoka, H. (1992) · IEEE Transactions on Neural Networks · doi:10.1109/72.125867 · Cited by 189 · see citing works

Parallel Cortico-Basal Ganglia Mechanisms for Acquisition and Execution of Visuomotor Sequences—A Computational Approach

Nakahara, H., Doya, K., & Hikosaka, O. (2001) · Journal of Cognitive Neuroscience · doi:10.1162/089892901750363208 · Cited by 192 · see citing works

Interpreting Kullback–Leibler divergence with the Neyman–Pearson lemma

Eguchi, S., & Copas, J. B. (2006) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2006.03.007 · Cited by 190 · see citing works

Information Geometry of U-Boost and Bregman Divergence

Murata, N., Takenouchi, T., Kanamori, T., & Eguchi, S. (2004) · Neural Computation · doi:10.1162/089976604323057452 · Cited by 172 · see citing works

Geometric derivation of the quantum speed limit

Jones, P. J., & Kok, P. (2010) · Physical Review A · doi:10.1103/physreva.82.022107 · Cited by 172 · see citing works

Counting probability distributions: Differential geometry and model selection

Myung, I. J., Balasubramanian, V., & Pitt, M. A. (2000) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.170283897 · Cited by 163 · see citing works

Hypothesis testing with multiterminal data compression

Han, T. S. (1987) · IEEE Transactions on Information Theory · doi:10.1109/tit.1987.1057383 · Cited by 161 · see citing works

Revisiting Natural Gradient for Deep NetworksPreprint

Pascanu, R., & Bengio, Y. (2014) · Cited by 159 · see citing works

Bayesian neural networks: An introduction and survey

Goan, E., & Fookes, C. (2020) · QUT ePrints (Queensland University of Technology) · Cited by 162 · see citing works

INTRODUCTION TO QUANTUM FISHER INFORMATION

Petz, D., & GHINEA, C. (2011) · doi:10.1142/9789814338745_0015 · Cited by 153 · see citing works

Four Types of Learning Curves

Амари, Ш.-И., Fujita, N., & Shinomoto, S. (1992) · Neural Computation · doi:10.1162/neco.1992.4.4.605 · Cited by 144 · see citing works

Wasserstein geometry of Gaussian measures

Takatsu, A. (2011) · Osaka City University (Osaka City University) · doi:10.18910/4973 · Cited by 147 · see citing works

The Concept of Morphospaces in Evolutionary and Developmental Biology: Mathematics and Metaphors

Mitterœcker, P., & Huttegger, S. M. (2009) · Biological Theory · doi:10.1162/biot.2009.4.1.54 · Cited by 148 · see citing works

Neural Learning in Structured Parameter Spaces - Natural Riemannian Gradient

Амари, Ш.-И. (1997) · Cited by 147 · see citing works

Non-negative matrix factorization with α-divergence

Cichocki, A. S., Lee, H.-K., Kim, Y., & Choi, S. (2008) · Pattern Recognition Letters · doi:10.1016/j.patrec.2008.02.016 · Cited by 145 · see citing works

Markov blankets, information geometry and stochastic thermodynamics

Parr, T., Da Costa, L., & Friston, K. (2020) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2019.0159 · Cited by 141 · see citing works

Identifiability of hidden Markov information sources and their minimum degrees of freedom

Ito, H., Амари, Ш.-И., & Kobayashi, K. (1992) · IEEE Transactions on Information Theory · doi:10.1109/18.119690 · Cited by 141 · see citing works

Bankruptcy analysis with self-organizing maps in learning metrics

Samuel Kaski, A., Sinkkonen, J., & Peltonen, J. (2001) · IEEE Transactions on Neural Networks · doi:10.1109/72.935102 · Cited by 139 · see citing works

Information-Geometric Measure for Neural Spikes

Nakahara, H., & Амари, Ш.-И. (2002) · Neural Computation · doi:10.1162/08997660260293238 · Cited by 138 · see citing works

Covariance and Fisher information in quantum mechanics

Petz, D. (2002) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/35/4/305 · Cited by 132 · see citing works

Symmetric Positive-Definite Matrices: From Geometry to Applications and Visualization

Moakher, M., & Batchelor, P. G. (2006) · Mathematics and visualization · doi:10.1007/3-540-31272-2_17 · Cited by 136 · see citing works

Relative Loss Bounds for Multidimensional Regression Problems

Kivinen, J., & Warmuth, M. K. (2001) · Machine Learning · doi:10.1023/a:1017938623079 · Cited by 135 · see citing works

Statistical Theory of Learning Curves under Entropic Loss Criterion

Амари, Ш.-И., & Murata, N. (1993) · Neural Computation · doi:10.1162/neco.1993.5.1.140 · Cited by 134 · see citing works

CramÉr–Rao and Moment-Entropy Inequalities for Renyi Entropy and Generalized Fisher Information

Lutwak, E., Yang, D., & Zhang, G. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2004.840871 · Cited by 133 · see citing works

Dropout Inference in Bayesian Neural Networks with Alpha-divergencesPreprint

Li, Y.-Z., & Gal, Y. (2017) · International Conference on Machine Learning · doi:10.48550/arxiv.1703.02914 · Cited by 246 · see citing works

On asymptotic properties of predictive distributions

Komaki, F. (1996) · Biometrika · doi:10.1093/biomet/83.2.299 · Cited by 129 · see citing works

Learning the Similarity of Documents: An Information-Geometric Approach to Document Retrieval and Categorization

Hofmann, T. (1999) · Cited by 126 · see citing works

THE ONTOGENETIC TRAJECTORY OF THE PHENOTYPIC COVARIANCE MATRIX, WITH EXAMPLES FROM CRANIOFACIAL SHAPE IN RATS AND HUMANS

Mitterœcker, P., & Bookstein, F. L. (2008) · Evolution · doi:10.1111/j.1558-5646.2008.00587.x · Cited by 123 · see citing works

Geometry of minimum contrast

Eguchi, S. (1992) · Hiroshima Mathematical Journal · doi:10.32917/hmj/1206128508 · Cited by 122 · see citing works

Extended SMART Algorithms for Non-negative Matrix Factorization

Cichocki, A. S., Амари, Ш.-И., Zdunek, R., Kompass, R., Hori, G., & He, Z. (2006) · Lecture notes in computer science · doi:10.1007/11785231_58 · Cited by 120 · see citing works

Contact geometry and thermodynamics

Bravetti, A. (2018) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887819400036 · Cited by 119 · see citing works

Hellinger Versus Kullback–Leibler Multivariable Spectrum Approximation

Ferrante, A., Pavon, M., & Ramponi, F. (2008) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2008.920238 · Cited by 118 · see citing works

Information-theoretic image formation

O’Sullivan, J. A., Blahut, R. E., & Snyder, D. L. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.720533 · Cited by 118 · see citing works

Maximum entropy and Bayesian data analysis: Entropic prior distributions

Caticha, A., & Preuss, R. (2004) · Physical Review E · doi:10.1103/physreve.70.046127 · Cited by 115 · see citing works

Non-negative Matrix Factorization with Quasi-Newton Optimization

Zdunek, R., & Cichocki, A. S. (2006) · Lecture notes in computer science · doi:10.1007/11785231_91 · Cited by 113 · see citing works

Boosting as entropy projection

Kivinen, J., & Warmuth, M. K. (1999) · Conference on Learning Theory · doi:10.1145/307400.307424 · Cited by 114 · see citing works

Face recognition based on multi-class mapping of Fisher scores

Chen, L., Man, H., & Nefian, A. (2005) · Pattern Recognition · doi:10.1016/j.patcog.2004.11.003 · Cited by 112 · see citing works

Generalized Leverage and its Applications

Wei, B., Hu, Y., & Fung, W. (1998) · Scandinavian Journal of Statistics · doi:10.1111/1467-9469.00086 · Cited by 112 · see citing works

New Developments in Generalized Information Measures

Taneja, I. J. (1995) · Advances in imaging and electron physics · doi:10.1016/s1076-5670(08)70106-x · Cited by 110 · see citing works

Geometry of canonical correlation on the state space of a quantum system

Petz, D. (1994) · Journal of Mathematical Physics · doi:10.1063/1.530611 · Cited by 110 · see citing works

Fundamental equations for statistical submanifolds with applications to the Bartlett correction

Vos, P. W. (1989) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00050660 · Cited by 110 · see citing works

Streaming and Sublinear Approximation of Entropy and Information Distances

Guha, S., McGregor, A., & Venkatasubramanian, S. (2006) · Cited by 110 · see citing works

Dynamical maps beyond Markovian regime

Chruściński, D. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.09.003 · Cited by 110 · see citing works

Asymptotics and the theory of inference

Reid, N. M. (2003) · The Annals of Statistics · doi:10.1214/aos/1074290325 · Cited by 103 · see citing works

Information Geometry on Complexity and Stochastic Interaction

Ay, N. (2015) · Entropy · doi:10.3390/e17042432 · Cited by 100 · see citing works

Stochastic neighbor embedding (SNE) for dimension reduction and visualization using arbitrary divergences

Bunte, K., Haase, S., Biehl, M. L., & Villmann, T. (2012) · Neurocomputing · doi:10.1016/j.neucom.2012.02.034 · Cited by 100 · see citing works

A differential geometric approach to nonlinear filtering: the projection filter

Brigo, D., Hanzon, B., & Gland, F. L. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.661075 · Cited by 100 · see citing works

Approximate Nonlinear Filtering by Projection on Exponential Manifolds of Densities

Brigo, D., Hanzon, B., Gland, F. L., & Gland, F. L. (1999) · Bernoulli · doi:10.2307/3318714 · Cited by 99 · see citing works

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 · see citing works

Differential geometry and statistics: some mathematical aspects

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

Differential geometrical theory of statistics

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