Advanced mean field methods: theory and practice

Manfred Opper (Editor), David Saad (Editor)

Research output: Book/ReportBook


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.
Original languageEnglish
Place of PublicationCambridge, Massachusetts (US)
Number of pages287
ISBN (Print)0262150549
Publication statusPublished - Feb 2001

Publication series

NameNeural Information Processing
PublisherMassachusetts Institute of Technology Press (MIT Press)


  • probabilistic modeling
  • multivariate probability distributions
  • efficient approximate computations
  • TAP approach


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  • The TAP approach to intensive and extensive connectivity systems

    Kabashima, Y. & Saad, D., Feb 2001, Advanced mean field methods: Theory and practice. Opper, M. & Saad, D. (eds.). Cambridge, US: MIT, p. 51-65 15 p. (Neural Information Processing).

    Research output: Chapter in Book/Published conference outputChapter

    Open Access

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