A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models.Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models.Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.
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"This book provides an extremely valuable treatment of mean field methods and their application to problems in probabilistic inference and learning."--Lawrence Saul, Principal Technical Staff Member, AT&T Labs--Research
About the Author
Manfred Opper is a Reader at the Neural Computing Research Group, School of Engineering and Applied Science, Aston University, UK.
David Saad is Professor, the Neural Computing Research Group, School of Engineering and Applied Science, Aston University, UK
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A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
variational marginals, probabilistic editor, cavity activation distribution, naive mean field approximation, sigmoid belief networks, advanced mean field methods, variational distribution, factor analysers, variational approximation methods, quenched variables, rough energy landscapes, junction tree algorithm, factorized distribution, variational objective, belief propagation, cavity method, information geometry, mean field equations, biased messages, probabilistic graphical models, replica method, directed representation, variational approximations, ensemble learning, low density parity check codes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Neural Information Processing Systems, Neural Computation, David Saad, San Francisco, Mean-field Theory of Learning, Morgan Kaufmann Publishers, New York, World Scientific, Addison Wesley, Cambridge University Press, International Symposium, Introduction Mean, John Wiley, Kluwer Academic Publishers, Lecture Notes, Computational Learning Theory, Oxford University Press, San Mateo, Solid State Phys New!
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A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
variational marginals, probabilistic editor, cavity activation distribution, naive mean field approximation, sigmoid belief networks, advanced mean field methods, variational distribution, factor analysers, variational approximation methods, quenched variables, rough energy landscapes, junction tree algorithm, factorized distribution, variational objective, belief propagation, cavity method, information geometry, mean field equations, biased messages, probabilistic graphical models, replica method, directed representation, variational approximations, ensemble learning, low density parity check codes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Neural Information Processing Systems, Neural Computation, David Saad, San Francisco, Mean-field Theory of Learning, Morgan Kaufmann Publishers, New York, World Scientific, Addison Wesley, Cambridge University Press, International Symposium, Introduction Mean, John Wiley, Kluwer Academic Publishers, Lecture Notes, Computational Learning Theory, Oxford University Press, San Mateo, Solid State Phys New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 25
books:
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4
books
cite this book:
- Learning in Graphical Models (Adaptive Computation and Machine Learning) by Michael I. Jordan on 9 pages
- Statistical Field Theory (Advanced Book Classics) by Giorgio Parisi on 5 pages
- Spin Glass Theory And Beyond: An Introduction To The Replica Method And Its Applications (World Scientific Lecture Notes in Physics) by M Mezard on 4 pages
- Graphical Models for Machine Learning and Digital Communication (Adaptive Computation and Machine Learning) by Brendan J. Frey on page 34, page 82, and page 227
- Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference by Judea Pearl on page 20, page 35, and page 83
See all 25 books this book cites
- Algorithmic Learning Theory: 15th International Conference, ALT 2004, Padova, Italy, October 2-5, 2004. Proceedings (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence) by Shai Ben David in Back Matter
- Probabilistic Models of the Brain: Perception and Neural Function (Neural Information Processing) by Rajesh P. N. Rao in Front Matter
- Learning Theory: 17th Annual Conference on Learning Theory, COLT 2004, Banff, Canada, July 1-4, 2004, Proceedings (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence) by John Shawe-Taylor on page 439
- The Variational Bayes Method in Signal Processing (Signals and Communication Technology) by Václav mídl in Back Matter
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