Cited by 3,791Bayesian Modeling and Causal InferenceGaussian Processes and Bayesian InferenceMarkov Chains and Monte Carlo Methods

The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.

An Introduction to Variational Methods for Graphical Models

Open access

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.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1023/a:1007665907178

Cites

2 of 2 references verified0 citation errors · 0 not checkable

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.

A few free checks a day · papers already verified open instantly · results are public

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?

  • A variety of analytic approximations exist which ameliorate, but do not remove, the tradeoff between tractability and flexibility.

    “A variety of analytic approximations exist which ameliorate, but do not remove, this tradeoff”

    From Deep Unsupervised Learning using Nonequilibrium Thermodynamics (2015) · cites this paper as Jordan et al., 1999

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

Flagged first, then by citations

Research works printed but not linked: 59

  1. Bathe, K. J. (1996). Finite element procedures. Englewood Cliffs, NJ: Prentice-Hall.
  2. Baum, L. E., Petrie, T., Soules, G., & Weiss, N. (1970). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. The Annals of Mathematical Statistics, 41, 164–171. · DOI
  3. Bishop, C. M., Lawrence, N., Jaakkola, T. S., & Jordan, M. I. (1998). Approximating posterior distributions in belief networks using mixtures. In M. Jordan, M. Kearns, & S. Solla (Eds.), Advances in neural information processing systems 10, Cambridge MA: MIT Press.
  4. Cover, T., & Thomas, J. (1991). Elements of information theory. New York: John Wiley.
  5. Dagum, P., & Luby, M. (1993). Approximating probabilistic inference in Bayesian belief networks is NP-hard. Artificial Intelligence, 60, 141–153. · DOI
  6. Dayan, P., Hinton, G. E., Neal, R., & Zemel, R. S. (1995). The Helmholtz Machine. Neural Computation, 7, 889–904. · DOI · Paper page
  7. Dean, T., & Kanazawa, K. (1989). A model for reasoning about causality and persistence. Computational Intelligence, 5, 142–150. · DOI · Paper page
  8. Dechter, R. (1999). Bucket elimination: A unifying framework for probabilistic inference. In M. I. Jordan (Ed.), Learning in graphical models. Cambridge, MA: MIT Press.
  9. Draper, D. L., & Hanks, S. (1994). Localized partial evaluation of belief networks. Uncertainty and Artificial Intelligence: Proceedings of the Tenth Conference. San Mateo, CA: Morgan Kaufmann.
  10. Frey, B., Hinton, G. E., & Dayan, P. (1996). Does the wake-sleep algorithm learn good density estimators? In D. S. Touretzky, M. C. Mozer, & M. E. Hasselmo (Eds.), Advances in neural information processing systems 8. Cambridge, MA: MIT Press.
  11. Fung, R. & Favero, B. D. (1994). Backward simulation in Bayesian networks. Uncertainty and Artificial Intelligence: Proceedings of the Tenth Conference. San Mateo, CA: Morgan Kaufmann.
  12. Galland, C. (1993). The limitations of deterministic Boltzmann machine learning. Network, 4, 355–379. · DOI
  13. Ghahramani, Z., & Hinton, G. E. (1996). Switching state-space models. (Technical Report CRG-TR–96–3). Toronto: Department of Computer Science, University of Toronto.
  14. Ghahramani, Z., & Jordan, M. I. (1997). Factorial Hidden Markov models. Machine Learning, 29, 245–273. · DOI · Paper page
  15. Gilks, W., Thomas, A., & Spiegelhalter, D. (1994). A language and a program for complex Bayesian modelling. The Statistician, 43, 169–178. · DOI
  16. Heckerman, D. (1999). A tutorial on learning with Bayesian networks. In M. I. Jordan (Ed.), Learning in graphical models. Cambridge, MA: MIT Press.
  17. Henrion, M. (1991). Search-based methods to bound diagnostic probabilities in very large belief nets. Uncertainty and Artificial Intelligence: Proceedings of the Seventh Conference. San Mateo, CA: Morgan Kaufmann.
  18. Hinton, G. E., & Sejnowski, T. (1986). Learning and relearning in Boltzmann machines. In D. E. Rumelhart & J. L. McClelland (Eds.), Parallel distributed processing (Vol. 1). Cambridge, MA: MIT Press.
  19. Hinton, G. E., Dayan, P., Frey, B., & Neal, R. M. (1995). The wake-sleep algorithm for unsupervised neural networks. Science, 268, 1158–1161. · DOI · Paper page
  20. Hinton, G. E., Sallans, B., & Ghahramani, Z. (1999). A hierarchical community of experts. In M. I. Jordan (Ed.), Learning in graphical models. Cambridge, MA: MIT Press.
  21. Horvitz, E. J., Suermondt, H. J., & Cooper, G. F. (1989). Bounded conditioning: Flexible inference for decisions under scarce resources. Conference on Uncertainty in Artificial Intelligence: Proceedings of the Fifth Conference. Mountain View, CA: Association for UAI.
  22. Jaakkola, T. S., & Jordan, M. I. (1996). Computing upper and lower bounds on likelihoods in intractable networks. Uncertainty and Artificial Intelligence: Proceedings of the Twelth Conference. San Mateo, CA: Morgan Kaufmann.
  23. Jaakkola, T. S. (1997). Variational methods for inference and estimation in graphical models. Unpublished doctoral dissertation, Massachusetts Institute of Technology, Cambridge, MA.
  24. Jaakkola, T. S., & Jordan, M. I. (1997a). Recursive algorithms for approximating probabilities in graphical models. In M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.), Advances in neural information processing systems 9. Cambridge, MA: MIT Press.
  25. Jaakkola, T. S., & Jordan, M. I. (1997b). Bayesian logistic regression: A variational approach. In D. Madigan & P. Smyth (Eds.), Proceedings of the 1997 Conference on Artificial Intelligence and Statistics. Ft. Lauderdale, FL.
  26. Jaakkola, T. S., & Jordan, M. I. (1999a). Improving the mean field approximation via the use of mixture distributions. In M. I. Jordan (Ed.), Learning in graphical models. Cambridge, MA: MIT Press.
  27. Jaakkola, T. S., & Jordan, M. I. (1999b). Variational methods and the QMR-DT database. Journal of Artificial Intelligence Research, 10, 291–322. · DOI
  28. Jensen, C. S., Kong, A., & Kjærulff, U. (1995). Blocking-Gibbs sampling in very large probabilistic expert systems. International Journal of Human-Computer Studies, 42, 647–666. · DOI
  29. Jensen, F. V., & Jensen, F. (1994). Optimal junction trees. Uncertainty and Artificial Intelligence: Proceedings of the Tenth Conference. San Mateo, CA: Morgan Kaufmann.
  30. Jensen, F. V. (1996). An introduction to Bayesian networks. London: UCL Press.
  31. Jordan, M. I. (1994). A statistical approach to decision tree modeling. In M. Warmuth (Ed.), Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory. New York: ACM Press.
  32. Jordan, M. I., Ghahramani, Z., & Saul, L. K. (1997). Hidden Markov decision trees. In M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.), Advances in neural information processing systems 9. Cambridge, MA: MIT Press.
  33. Kanazawa, K., Koller, D., & Russell, S. (1995). Stochastic simulation algorithms for dynamic probabilistic networks. Uncertainty and Artificial Intelligence: Proceedings of the Eleventh Conference. San Mateo, CA: Morgan Kaufmann.
  34. Kjærulff, U. (1990). Triangulation of graphs—Algorithms giving small total state space. (Research Report R–90–09). Department of Mathematics and Computer Science, Aalborg University, Denmark.
  35. Kjærulff, U. (1994). Reduction of computational complexity in Bayesian networks through removal of weak dependences. Uncertainty and Artificial Intelligence: Proceedings of the Tenth Conference. San Mateo, CA: Morgan Kaufmann.
  36. MacKay, D. J. C. (1997). Ensemble learning for hidden Markov models. Unpublished manuscript. Cambridge: Department of Physics, University of Cambridge.
  37. McEliece, R. J., MacKay, D. J. C., & Cheng, J.-F. (1998). Turbo decoding as an instance of Pearl's “belief propagation algorithm.” IEEE Journal on Selected Areas in Communication, 16, 140–152. · DOI
  38. Merz, C. J., & Murphy, P. M. (1996). UCI repository of machine learning databases. Irvine, CA: Department of Information and Computer Science, University of California.
  39. Neal, R. (1992). Connectionist learning of belief networks. Artificial Intelligence, 56, 71–113. · DOI
  40. Neal, R. (1993). Probabilistic inference using Markov chain Monte Carlo methods. (Technical Report CRG-TR–93–1). Toronto: Department of Computer Science, University of Toronto.
  41. Neal, R., & Hinton, G. E. (1999). A view of the EM algorithm that justifies incremental, sparse, and other variants. In M. I. Jordan (Ed.), Learning in graphical models. Cambridge, MA: MIT Press.
  42. Parisi, G. (1988). Statistical field theory. Redwood City, CA: Addison-Wesley.
  43. Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Mateo, CA: Morgan Kaufmannn.
  44. Peterson, C., & Anderson, J. R. (1987). A mean field theory learning algorithm for neural networks. Complex Systems, 1, 995–1019.
  45. Rockafellar, R. (1972). Convex analysis. Princeton University Press.
  46. Rustagi, J. (1976). Variational methods in statistics. New York: Academic Press.
  47. Sakurai, J. (1985). Modern quantum mechanics. Redwood City, CA: Addison-Wesley.
  48. Saul, L. K., & Jordan, M. I. (1994). Learning in Boltzmann trees. Neural Computation, 6, 1173–1183.
  49. Saul, L. K., Jaakkola, T. S., & Jordan, M. I. (1996). Mean field theory for sigmoid belief networks. Journal of Artificial Intelligence Research, 4, 61–76. · DOI
  50. Saul, L. K., & Jordan, M. I. (1996). Exploiting tractable substructures in intractable networks. In D. S. Touretzky, M. C. Mozer, & M. E. Hasselmo (Eds.), Advances in neural information processing systems 8. Cambridge, MA: MIT Press.
  51. Saul, L. K., & Jordan, M. I. (1999). A mean field learning algorithm for unsupervised neural networks. In M. I. Jordan (Ed.), Learning in graphical models. Cambridge, MA: MIT Press.
  52. Seung, S. (1995). Annealed theories of learning. In J.-H. Oh, C. Kwon, S. Cho (Eds.), Neural networks: The statistical mechanics perspectives. Singapore: World Scientific.
  53. Shachter, R. D., Andersen, S. K., & Szolovits, P. (1994). Global conditioning for probabilistic inference in belief networks. Uncertainty and Artificial Intelligence: Proceedings of the Tenth Conference. San Mateo, CA: Morgan Kaufmann.
  54. Shenoy, P. P. (1992). Valuation-based systems for Bayesian decision analysis. Operations Research, 40, 463–484. · DOI
  55. Shwe, M. A., & Cooper, G. F. (1991). An empirical analysis of likelihood—Weighting simulation on a large, multiply connected medical belief network. Computers and Biomedical Research, 24, 453–475. · DOI
  56. Shwe, M. A., Middleton, B., Heckerman, D. E., Henrion, M., Horvitz, E. J., Lehmann, H. P., & Cooper, G. F. (1991). Probabilistic diagnosis using a reformulation of the INTERNIST-1/QMR knowledge base. Meth. Inform. Med., 30, 241–255. · DOI
  57. Smyth, P., Heckerman, D., & Jordan, M. I. (1997). Probabilistic independence networks for hidden Markov probability models. Neural Computation, 9, 227–270. · DOI
  58. Waterhouse, S., MacKay, D. J. C., & Robinson, T. (1996). Bayesian methods for mixtures of experts. In D. S. Touretzky, M. C. Mozer, & M. E. Hasselmo (Eds.), Advances in neural information processing systems 8. Cambridge, MA: MIT Press.
  59. Williams, C. K. I., & Hinton, G. E. (1991). Mean field networks that learn to discriminate temporally distorted strings. In D. S. Touretzky, J. Elman, T. Sejnowski, & G. E. Hinton (Eds.), Proceedings of the 1990 Connectionist Models Summer School. San Mateo, CA: Morgan Kaufmann.

Cited by

Sorted by citations

Metadata

Authors
Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K.
Affiliations
  • University of California, Berkeley (US)
  • Gatsby Computational Neuroscience Unit (GB)
  • Massachusetts Institute of Technology (US)
  • AT&T (United States) (US)
Venue
Machine Learning
Published
1999-11
Volume
37
Issue
2
Pages
183-233
ISSN
  • 0885-6125 (ISSN-L)
  • 1573-0565
OpenAlex
W1516111018
Cited by
3,791
References
2
Citations by year
2026: 148 · 2025: 158 · 2024: 132 · 2023: 137 · 2022: 142 · 2021: 244 · 2020: 315 · 2019: 298 · 2018: 217 · 2017: 182 · 2016: 162 · 2015: 182 · 2014: 151 · 2013: 141 · 2012: 173
FWCI
35.87
Type
journal article
Language
en
Open access
Locations
Machine Learning (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
  • Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
Keywords
variational methods, probabilistic graphical models, Bayesian networks, Markov random fields, approximate inference, convex duality, Boltzmann machine, hidden Markov models, probabilistic learning

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