J. S. Yedidia, W. T. Freeman, Y. Weiss, "Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms", Merl Technical Report: TR2002-35, Oct. 2002, available online at http://www.merl.com/papers/TR2002-35/ Home/Search Document Details and Download
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....and for dual containing codes, the graph has an enormous number of cycles of length four. In the case of constructions B, N, and M, our decoder ignores these four cycles. It seems highly likely that a decoding algorithm that took these four cycles into account would perform significantly better [37, 38]. Our attempts to make such an improved algorithm have so far yielded only algorithms whose complexity scales as , where k is the row weight of the parity check matrix. Given that our preferred codes have k 20, these algorithms are regrettably not feasible. Construction U has an advantage ....
J. S. Yedidia, W. T. Freeman, and Y. Weiss. Constructing free energy approximations and generalized belief propagation algorithms. Technical report, Mitsubishi Electric Research Laboratories, 2002. TR-2002-35. 44
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....and for dual containing codes, the graph has an enormous number of cycles of length four. In the case of constructions B, N, and M, our decoder ignores these four cycles. It seems highly likely that a decoding algorithm that took these four cycles into account would perform significantly better [35, 36]. Our attempts to make such an improved algorithm have so far yielded only algorithms whose complexity scales as , where k is the row weight of the parity check matrix. Given that our preferred codes have k 20, these algorithms are regrettably not feasible. Construction U has an advantage ....
J. S. Yedidia, W. T. Freeman, and Y. Weiss. Constructing free energy approximations and generalized belief propagation algorithms. Technical report, Mitsubishi Electric Research Laboratories, 2002. TR-2002-35. 37
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....and handled identically to potentials arising from the prior. for the correlations induced by the graph s cycles. For more general graphical models, recently developed connections to the statistical physics literature have led to a deeper understanding of the approximations underlying loopy BP [15, 24, 25]. Recently, two independent extensions of the loopy BP algorithm have been proposed which allow exact computation of error variances, albeit with greater computational cost. Welling and Teh [26] have proposed propagation rules for computing linear response estimates of the joint probability of ....
J. S. Yedidia, W. T. Freeman, and Y. Weiss. Constructing free energy approximations and generalized belief propagation algorithms. Technical Report 2002-35, MERL, August 2002.
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.... free energy function, and by exploiting this interpretation, we will exhibit a one to one correspondence between the fixed points of PBP and the stationary points of the free energy. 1. Introduction. This paper, which is based largely on ideas first expounded by Yedidia, Freeman, and Weiss [12 14], introduces a class of iterative message passing algorithms called belief propagation on partially ordered sets, or PBP. PBP includes as special cases ordinary belief propaga tion [8] probability propagation [9] the generalized distributive law [1, 2] the sum product algorithm [6] ....
....L(v) In general, neither k connectivity nor k variable balance for k i hold. See Figure 4, which shows a junction graph and the corresponding junction poset. This junction poset is not 1,3 connected and does not satisfy 1, 3 variable balance. Construction 2. The cluster variation method [12 14]. Let = S, SK be a collection of subsets ( clusters ) of 1, n such that each Ri is a subset of at least one Sj. Now let P be the poset consisting of all intersections of elements of , ordered by inclusion. For each p P, we define L(p) p R(p) R : C p . Here ....
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J.S. YEDIDIA, W.T. FREEMAN, AND Y. WEISS, "Constructing free energy ap- proximations and generalized belief propagation algorithms," available at www.marl. com/papars/TI2002-35/
Mitsubishi Electric Research Laboratories - Http Www Merl (2003) Self-citation (Yedidia) (Correct)
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J.S. Yedidia, W.T. Freeman, and Y. Weiss, "Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms," MERL Technical Report TR2002-35, 2002, available online at http://www.merl.com/papers/TR2002-35/.
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J. S. Yedidia, W. T. Freeman, and Y. Weiss. Constructing free energy approximations and generalized belief propagation algorithms. MERL TR2002.
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J.S. Yedidia, W.T. Freeman, and Y. Weiss, "Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms," MERL Technical Report TR2002-35, 2002, available online at http://www.merl.com/papers/TR2002-35/.
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....methods for updating those approximations. The simplest method for approximating intractable continuous valued graphical models is discretization. Although exact inference in general discrete graphs is NP hard [2] approximate inference algorithms such as loopy belief propagation (BP) [17, 22, 24, 25] have been shown to produce excellent empirical results in many cases. Certain vision problems, including stereo vision [21] and phase unwrapping [8] are well suited to discrete formulations. For problems involving high dimensional variables, however, exhaustive discretization of the state space ....
....not only estimates of , but also corresponding measures of uncertainty. 2.1. Belief Propagation For graphs which are acyclic or tree structured, the desired conditional distributions p (x lY) can be directly calcu lated by a local message passing algorithm known as belief propagation (BP) [17, 25]. At iteration n of the BP algo rithm, each node t C V calculates a message m ( to be sent to each neighboring node s C F(t) 2) Here, c denotes an arbitrary proportionalfly constant. At any iteration, each node can produce an approximation b n (x I Y) to the marginal distributions p (x I Y) ....
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