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## Linear Response for Approximate Inference (2003)

Citations: | 2 - 0 self |

### Citations

1792 | Factor graphs and the sumproduct algorithm,”
- Kschischang, Frey, et al.
- 2001
(Show Context)
Citation Context ... its neighbors are simply N# = {i # #}. Factor graphs are a convenient representation for structured probabilistic models and subsume undirected graphical models and acyclic directed graphical models =-=[3]-=-. Further, there is a simple message passing algorithm for approximate inference that generalizes the belief propagation algorithms on both undirected and acyclic directed graphical models, n i# (x i ... |

474 | Generalized belief propagation. In
- Yedidia, Freeman, et al.
- 2001
(Show Context)
Citation Context ...increased our understanding of the convergence properties and accuracy of the algorithm. In particular, recent developments show that the stable fixed points are local minima of the Bethe free energy =-=[10, 1], which pa-=-ved the way for more accurate "generalized belief propagation" algorithms and convergent alternatives to BP [11, 6]. Despite its success, BP does not provide a prescription to compute joint ... |

137 | CCCP algorithms to minimize the Bethe and Kikuchi free energies: Convergent alternatives to belief propagation.
- Raymond, Yuille
- 2002
(Show Context)
Citation Context ...how that the stable fixed points are local minima of the Bethe free energy [10, 1], which paved the way for more accurate "generalized belief propagation" algorithms and convergent alternati=-=ves to BP [11, 6]-=-. Despite its success, BP does not provide a prescription to compute joint probabilities over pairs of non-neighboring nodes in the graph. When the graph is a tree, there is a single chain connecting ... |

71 | Stable fixed points of loopy belief propagation are minima of the Bethe free energy. In
- Heskes
- 2003
(Show Context)
Citation Context ...increased our understanding of the convergence properties and accuracy of the algorithm. In particular, recent developments show that the stable fixed points are local minima of the Bethe free energy =-=[10, 1], which pa-=-ved the way for more accurate "generalized belief propagation" algorithms and convergent alternatives to BP [11, 6]. Despite its success, BP does not provide a prescription to compute joint ... |

62 | Efficient learning in Boltzmann machines using linear response theory.
- Kappen, Rodriguez
- 1998
(Show Context)
Citation Context ...##k (xk ) by first computing ## i (x i ) #bk (xk ) and then inverting the matrix formed by flattened {i, x i } into a row index and {k, x k } into a column index. This method is a direct extension of =-=[2]-=-. The intuition is that while perturbations in a single # i (x i ) affect the whole system, perturbations in a single b i (x i ) (while keeping the others fixed) affect each subsystem # # A independen... |

50 | The unified propagation and scaling algorithm. In
- Teh, Welling
- 2002
(Show Context)
Citation Context ...how that the stable fixed points are local minima of the Bethe free energy [10, 1], which paved the way for more accurate "generalized belief propagation" algorithms and convergent alternati=-=ves to BP [11, 6]-=-. Despite its success, BP does not provide a prescription to compute joint probabilities over pairs of non-neighboring nodes in the graph. When the graph is a tree, there is a single chain connecting ... |

22 |
Approximate inference in Boltzmann machines
- Welling, Teh
- 2003
(Show Context)
Citation Context ... i )## j (x j ) # # # # #=0 (12) In essence, we can interpret G # (#) as a local convex dual of G BP (b) (by restricting attention to D). Since G BP is an approximation to the exact Gibbs free energy =-=[8]-=-, which is in turn dual to F (#) [4], G # (#) can be seen as an approximation to F (#) for small values of #. For that reason we can take its second derivatives C ij (x i , x j ) as approximations to ... |

20 | Linear response algorithms for approximate inference in graphical models.
- Welling, Teh
- 2004
(Show Context)
Citation Context ...es (20,21,22) form a linear system of equations which can only have one stable fixed point. The existence and stability of this fixed 3 For a more detailed proof of the above two theorems we refer to =-=[9]-=-. point is proven by observing that the first order term is identical to the one obtained from a linear expansion of the BP equations (2) around its stable fixed point. Finally, the SteinRosenberg the... |

14 | From Naive Mean Field Theory to the TAP Equations, Advanced mean field methods: theory and practice
- Opper, Winther
- 2001
(Show Context)
Citation Context ...essence, we can interpret G # (#) as a local convex dual of G BP (b) (by restricting attention to D). Since G BP is an approximation to the exact Gibbs free energy [8], which is in turn dual to F (#) =-=[4]-=-, G # (#) can be seen as an approximation to F (#) for small values of #. For that reason we can take its second derivatives C ij (x i , x j ) as approximations to the exact covariances (which are sec... |

14 | Semidefinite relaxations for approximate inference on graphs with cycles.
- Wainwright, Jordan
- 2004
(Show Context)
Citation Context ...t the covariance estimate is automatically positive semi-definite. Indeed the idea to include global constraints such as positive semi-definiteness in approximate inference algorithms was proposed in =-=[7]-=-. Other differences include automatic consistency between joint pairwise marginals from LR and node marginals from BP (not true for conditioning) and a convergence proof for the LR algorithm (absent f... |

10 |
Probabilistic inference by means of cluster variation method and linear response theory
- Tanaka
- 2003
(Show Context)
Citation Context ...ibutions of neighboring nodes. There are still a number of generalizations worth mentioning. Firstly, the same ideas can be applied to the MF approximation [9] and the Kikuchi approximation (see also =-=[5]-=-). Secondly, the presented method easily generalizes to the computation of higher order cumulants. Thirdly, when applying the same techniques to Gaussian random fields, a propagation algorithm results... |