Statistical Inference for Probabilistic Functions of Finite State Markov Chains
Open accessThe 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
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?
The Baum-Welch algorithm was proposed in the mid-1960s to learn the conditional probabilities between hidden states and visible outputs.
“The Baum-Welch algorithm [41] was proposed in the mi-1960s to learn those conditional probabilities.”
From A comprehensive survey on machine learning for networking: Evolution, applications and research opportunities (2018) · cites this paper as [41]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Doob, J. L., & Doob, J. L. (1953) · CERN Document Server (European Organization for Nuclear Research) · Cited by 8,964 · see citing works
Statistical Inference for Markov Processes
Pyke, R., & Billingsley, P. (1963) · Technometrics · doi:10.2307/1266351 · Cited by 561 · see citing works
The Lindeberg-Lévy theorem for martingales
Billingsley, P. (1961) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1961-0126871-x · Cited by 276 · see citing works
Some Theorems on Distribution Functions
Cramér, H., & Wold, H. (1936) · Journal of the London Mathematical Society · doi:10.1112/jlms/s1-11.4.290 · Cited by 275 · see citing works
On the Identifiability Problem for Functions of Finite Markov Chains
Blackwell, D., & Koopmans, L. H. (1957) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177706802 · Cited by 119 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
A tutorial on hidden Markov models and selected applications in speech recognition
Rabiner, L. R. (1989) · Proceedings of the IEEE · doi:10.1109/5.18626 · Cited by 22,743 · see citing works
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570 · see citing works
Ahmed, Z., Mohamed, K., Zeeshan, S., & Dong, X. (2020) · Database · doi:10.1093/database/baaa010 · Cited by 1,035 · see citing works
Boutaba, R., Salahuddin, M. A., Limam, N., Ayoubi, S., Shahriar, N., Estrada-Solano, F., & Caicedo, O. M. (2018) · Journal of Internet Services and Applications · doi:10.1186/s13174-018-0087-2 · Cited by 1,036 · see citing works
The hierarchical hidden Markov model: Analysis and applications
Fine, S., Singer, Y., & Tishby, N. (1998) · Machine Learning · doi:10.1023/a:1007469218079 · Cited by 906 · see citing works
Memory Fusion Network for Multi-view Sequential Learning
Zadeh, A., Liang, P. P., Mazumder, N., Poria, S., Cambria, E., & Morency, L.-P. (2018) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v32i1.12021 · Cited by 855 · see citing works
Zitnik, M., Nguyen, F., Wang, B., Leskovec, J., Goldenberg, A., & Hoffman, M. M. (2019) · Information Fusion · doi:10.1016/j.inffus.2018.09.012 · Cited by 675 · see citing works
Recurrent Neural Network Model for Constructive Peptide Design
Müller, A. T., Hiss, J. A., & Schneider, G. (2018) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.7b00414 · Cited by 270 · see citing works
Multimodal Language Analysis with Recurrent Multistage Fusion
Liang, P. P., Liu, Z., Bagher Zadeh, A., & Morency, L.-P. (2018) · Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing · doi:10.18653/v1/d18-1014 · Cited by 230 · see citing works
Estimation of dynamic functional connectivity using multiplication of temporal derivatives
Shine, J. M., Koyejo, O., Bell, P. T., Gorgolewski, K. J., Gilat, M., & Poldrack, R. A. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2015.07.064 · Cited by 166 · see citing works
Al-Nasheri, A., Muhammad, G., Alsulaiman, M., Ali, Z., Malki, K. H., Mesallam, T. A., & Farahat Ibrahim, M. (2018) · IEEE Access · doi:10.1109/access.2017.2696056 · Cited by 174 · see citing works
BILMES, J. A. (2006) · IEICE Transactions on Information and Systems · doi:10.1093/ietisy/e89-d.3.869 · Cited by 172 · see citing works
TAPAS: An Open-Source Software Package for Translational Neuromodeling and Computational Psychiatry
Frässle, S., Aponte, E. A., Bollmann, S., Brodersen, K. H., Do, C. T., Harrison, O. K., Harrison, S. J., Heinzle, J., Iglesias, S., Kasper, L., et al. (2021) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2021.680811 · Cited by 169 · see citing works
Gobert, J. D., Sao Pedro, M. A., Baker, R. S. J. D., Toto, E., & Montalvo, O. (2012) · Zenodo · doi:10.5281/zenodo.3554645 · Cited by 122 · see citing works
Deep learning versus traditional machine learning methods for aggregated energy demand prediction
Paterakis, N. G., Mocanu, E., Gibescu, M., Stappers, B., & van Alst, W. (2017) · 2017 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe) · doi:10.1109/isgteurope.2017.8260289 · Cited by 118 · see citing works
Principles and Practice of Explainable Machine Learning
Belle, V., & Papantonis, I. (2021) · Frontiers in Big Data · doi:10.3389/fdata.2021.688969 · Cited by 99 · see citing works
A subcortical switchboard for perseverative, exploratory and disengaged states
Ahmadlou, M., Shirazi, M. Y., Zhang, P., Rogers, I. L. M., Dziubek, J., Young, M., & Hofer, S. B. (2025) · Nature · doi:10.1038/s41586-025-08672-1 · Cited by 25 · see citing works
Barnes, S. J. (2021) · Computers in Human Behavior · doi:10.1016/j.chb.2021.106967 · Cited by 23 · see citing works
“…which is required to calculate the maximum likelihood of model parameters in equation (1), is determined using Lystig and Hughes (2002) adaption of the forward-backward algorithm (Baum & Petrie, 1966; Rabiner, 1989), which enables the calculation of both gradients and log-likelihoods concurrently.”
MethodYe, X., & Han, M.-M. (2022) · Information & Computer Security · doi:10.1108/ics-12-2019-0142 · Cited by 16 · see citing works
Machine Generated Text: A Comprehensive Survey of Threat Models and Detection Methods
Crothers, E., Japkowicz, N., & Viktor, H. (2022) · arXiv · doi:10.48550/arxiv.2210.07321 · Cited by 196 · see citing works
- Authors
- Baum, L. E., & Petrie, T.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1966-12
- Volume
- 37
- Issue
- 6
- Pages
- 1554-1563
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2007321142
- Cited by
- 2,775
- References
- 5
- Citations by year
- 2026: 60 · 2025: 89 · 2024: 132 · 2023: 133 · 2022: 128 · 2021: 139 · 2020: 152 · 2019: 159 · 2018: 153 · 2017: 146 · 2016: 113 · 2015: 144 · 2014: 151 · 2013: 125 · 2012: 90
- FWCI
- 0.74
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Locations
- The Annals of Mathematical Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Keywords
- finite Markov chains, statistical inference, ergodic theory
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
