The DOI matches its Crossref record.
Estimating mutual information
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“The information-theoretic neuroscience literature has long recognized the importance of correcting for the limited-sampling bias and has provided effective tools for correcting the Shannon information sampling bias.24,25,26,27,28”
From Sampling bias corrections for discrete and Gaussian partial information decompositions (2026) · cites this paper as [28]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
No references could be resolved yet.
Research works printed but not linked: 36
- T. M. Cover, 1991, Elements of Information Theory, 10.1002/0471200611 · DOI
- A. Renyi, 1971, Probability Theory
- 2001, Independent Component Analysis: Principles and Practice
- A. Hyvärinen, 2001, Independent Component Analysis, 10.1002/0471221317 · DOI
- 10.1103/PhysRevE.52.2318 · DOI
- R. Steuer, 2002, Bioinformatics, 18, S231, 10.1093/bioinformatics/18.suppl_2.S231 · DOI · Paper page
- 10.1103/PhysRevA.33.1134 · DOI
- 10.1109/18.761290 · DOI
- 10.1016/0375-9601(88)90193-4 · DOI
- 10.1016/S0167-2789(98)00269-3 · DOI
- R. L. Dobrushin, 1958, Theor. Probab. Appl., 3, 462
- O. Vasicek, 1976, J. R. Stat. Soc. Ser. B. Methodol., 38, 54, 10.1111/j.2517-6161.1976.tb01566.x · DOI
- 10.1016/S0167-2789(02)00432-3 · DOI
- E. S. Dudewicz, 1981, J. Am. Stat. Assoc., 76, 967, 10.1080/01621459.1981.10477750 · DOI
- B. van Es, 1992, Scand. J. Stat., 19, 61
- 10.1016/0167-7152(94)90046-9 · DOI
- J. C. Correa, 1995, Commun. Stat: Theory Meth., 24, 2439, 10.1080/03610929508831626 · DOI
- A. B. Tsybakov, 1996, Scand. J. Stat., 23, 75
- R. Wieczorkowski, 1999, Commun. Stat.-Simul. Comput., 28, 541, 10.1080/03610919908813564 · DOI
- L. F. Kozachenko, 1987, Probl. Inf. Transm., 23, 95
- 10.1016/0375-9601(85)90724-8 · DOI
- R. L. Somorjai, 1986, Methods for Estimating the Intrinsic Dimensionality of High-Dimensional Point Sets, 10.1007/978-3-642-71001-8_17 · DOI
- 10.1103/PhysRevE.66.051903 · DOI
- 10.1109/18.825848 · DOI
- W. H. Press, 1993, Numerical Recipes
- 10.1016/0375-9601(90)90577-B · DOI
- 10.1016/S0167-9473(99)00020-1 · DOI
- G. A. Darbellay, 1999, 3rd IEEE European Workshop on Computer-intensive Methods in Control and Data Processing, Prague, 1998
- 10.1016/S0092-8674(00)00015-5 · DOI
- B. W. Silverman, 1986, Density Estimation for Statistics and Data Analysis, 10.1007/978-1-4899-3324-9 · DOI
- 10.1109/TBME.2002.805480 · DOI
- J.-F. Cardoso, 1998, Multidimensional Independent Component Analysis, Proceedings of ICASSP ’98
- J.-F. Cardoso, 1993, IEE Proc. F, Radar Signal Process., 140, 362, 10.1049/ip-f-2.1993.0054 · DOI
- A. Ziehe, 1998, An Efficient Algorithm for Blind Separation Using Time Structure
- 10.1109/51.731318 · DOI
- 10.1103/PhysRevE.62.3096 · DOI
Cited by
Sorted by citations
Representational similarity analysis-connecting the branches of systems neuroscience
Kriegeskorte, N. (2008) · Frontiers in Systems Neuroscience · doi:10.3389/neuro.06.004.2008 · Cited by 3,355
Detecting and quantifying causal associations in large nonlinear time series datasets
Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., & Sejdinovic, D. (2019) · Science Advances · doi:10.1126/sciadv.aau4996 · Cited by 979
Equitability, mutual information, and the maximal information coefficient
Kinney, J. B., & Atwal, G. S. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1309933111 · Cited by 667
Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures
Chan, T. E., Stumpf, M. P. H., & Babtie, A. C. (2017) · Cell Systems · doi:10.1016/j.cels.2017.08.014 · Cited by 578
MIFS-ND: A mutual information-based feature selection method
Hoque, N., Bhattacharyya, D. K., & Kalita, J. K. (2014) · Expert Systems with Applications · doi:10.1016/j.eswa.2014.04.019 · Cited by 442
A New Coefficient of Correlation
Chatterjee, S. (2021) · Journal of the American Statistical Association · doi:10.1080/01621459.2020.1758115 · Cited by 374
Practical Measures of Integrated Information for Time-Series Data
Barrett, A. B., & Seth, A. K. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1001052 · Cited by 225
Dai, Y., & Zhao, P. (2020) · Applied Energy · doi:10.1016/j.apenergy.2020.115332 · Cited by 202
Inferring Causal Gene Regulatory Networks from Coupled Single-Cell Expression Dynamics Using Scribe
Qiu, X., Rahimzamani, A., Wang, L., Ren, B., Mao, Q., Durham, T., McFaline-Figueroa, J. L., Saunders, L., Trapnell, C., & Kannan, S. (2020) · Cell Systems · doi:10.1016/j.cels.2020.02.003 · Cited by 185
Roux, F., Wibral, M., Singer, W., Aru, J., & Uhlhaas, P. J. (2013) · The Journal of Neuroscience · doi:10.1523/jneurosci.5778-12.2013 · Cited by 169
A Theory of Usable Information Under Computational Constraints
Xu, Y., Zhao, S., Song, J., Stewart, R., & Ermon, S. (2020) · arXiv · doi:10.48550/arxiv.2002.10689 · Cited by 142
Measuring integrated information: comparison of candidate measures in theory and simulation
Mediano, P., Seth, A., & Barrett, A. (2018) · Entropy · doi:10.3390/e21010017 · Cited by 145
Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines
Cheng, S., Chen, J., & Wang, L. (2018) · Entropy · doi:10.3390/e20080583 · Cited by 104
Information transfer by leaky, heterogeneous, protein kinase signaling systems
Voliotis, M., Perrett, R. M., McWilliams, C., McArdle, C. A., & Bowsher, C. G. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1314446111 · Cited by 98
Root-Cause Metric Location for Microservice Systems via Log Anomaly Detection
Wang, L., Zhao, N., Chen, J., Li, P., Zhang, W., & Sui, K. (2020) · 2020 IEEE International Conference on Web Services (ICWS) · doi:10.1109/icws49710.2020.00026 · Cited by 84
Dopamine promotes head direction plasticity during orienting movements
Fisher, Y. E., Marquis, M., D’Alessandro, I., & Wilson, R. I. (2022) · Nature · doi:10.1038/s41586-022-05485-4 · Cited by 67
Distributed selection of continuous features in multilabel classification using mutual information
Gonzalez-Lopez, J., Ventura, S., & Cano, A. (2019) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2019.2944298 · Cited by 60
Averaging Is Probably Not the Optimum Way of Aggregating Parameters in Federated Learning
Xiao, P., Cheng, S., Stankovic, V., & Vukobratovic, D. (2020) · Entropy · doi:10.3390/e22030314 · Cited by 54
“By using two methods, one is base on the MI derivative formula under the multi-dimensional Gaussian distribution assumption, and another is a continuous-continuous MI estimator based on k-nearest neighbor (KNN) distances described in [21].”
BackgroundMethodInfluentialAn Information-Theoretic Perspective on Intrinsic Motivation in Reinforcement Learning: A Survey
Aubret, A., Matignon, L., & Hassas, S. (2023) · Entropy · doi:10.3390/e25020327 · Cited by 52
Breakdown of local information processing may underlie isoflurane anesthesia effects
Wollstadt, P., Sellers, K. K., Rudelt, L., Priesemann, V., Hutt, A., Fröhlich, F., & Wibral, M. (2017) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1005511 · Cited by 49
Chan, J. S., Wibral, M., Stawowsky, C., Brandl, M., Helbling, S., Naumer, M. J., Kaiser, J., & Wollstadt, P. (2021) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2021.631599 · Cited by 49
Network control principles for identifying personalized driver genes in cancer
Guo, W.-F., Zhang, S.-W., Zeng, T., Akutsu, T., & Chen, L. (2020) · Briefings in Bioinformatics · doi:10.1093/bib/bbz089 · Cited by 44
Wu, S., Luo, H., Jiang, Y., Zhang, J., Tian, J., & Yin, S. (2024) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2023.3331546 · Cited by 26
Detection of long-range concerted motions in protein by a distance covariance
Roy, A., & Post, C. B. (2012) · Journal of Chemical Theory and Computation · doi:10.1021/ct300565f · Cited by 21
Brodski‐Guerniero, A., Naumer, M. J., Moliadze, V., Chan, J., Althen, H., Ferreira‐Santos, F., Lizier, J. T., Schlitt, S., Kitzerow, J., Schütz, M., et al. (2018) · Human Brain Mapping · doi:10.1002/hbm.24072 · Cited by 23
Variable time delay estimation in continuous industrial processes
Cattaldo, M., Ferrer, A., & Måge, I. (2024) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2024.105082 · Cited by 18
An interpretable deep learning framework identifies proteomic drivers of Alzheimer’s disease
Panizza, E., & Cerione, R. A. (2024) · Frontiers in Cell and Developmental Biology · doi:10.3389/fcell.2024.1379984 · Cited by 11
Sampling bias corrections for discrete and Gaussian partial information decompositions
Lorenz, G. M., Engel, N. M., Koçillari, L., Celotto, M., Orsenigo, D., Curreli, S., Malerba, S. B., Engel, A. K., Kayser, C., Fellin, T., et al. (2026) · Patterns · doi:10.1016/j.patter.2026.101619 · Cited by 9
Generating Fair Universal Representations using Adversarial Models
Kairouz, P., Liao, J., Huang, C., Vyas, M., Welfert, M., & Sankar, L. (2019) · arXiv · doi:10.48550/arxiv.1910.00411 · Cited by 19
A Deep Model Framework for Morphological Trait Imputation Across Taxonomic Groups
Wang, Y., Shi, X., Bai, Y., Zhu, H., Yin, X., Song, P., Ergu, D., Zhang, T., Pan, S., Gu, Z., et al. (2026) · Integrative Zoology · doi:10.1111/1749-4877.70178
Metadata
- Authors
- Kraskov, A., Stögbauer, H., & Grassberger, P.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2004-06-23
- Volume
- 69
- Issue
- 6
- ISSN
- 1539-3755
- 1550-2376
- Cited by
- 3,512
- References
- 0
- Language
- en
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review