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NormProduct Belief Propagation: PrimalDual MessagePassing for Approximate Inference
, 2008
"... Inference problems in graphical models can be represented as a constrained optimization of a free energy function. In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified me ..."
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Cited by 23 (7 self)
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Inference problems in graphical models can be represented as a constrained optimization of a free energy function. In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified messagepassing algorithm architecture. In particular we generalize the Belief Propagation (BP) algorithms of sumproduct and maxproduct and treerewaighted (TRW) sum and max product algorithms (TRBP) and introduce a new set of convergent algorithms based on ”convexfreeenergy” and LinearProgramming (LP) relaxation as a zerotemprature of a convexfreeenergy. The main idea of this work arises from taking a general perspective on the existing BP and TRBP algorithms while observing that they all are reductions from the basic optimization formula of f + ∑ i hi
FastInf: An efficient approximate inference library
 Journal of Machine Learning Research
"... The FastInf C++ library is designed to perform memory and time efficient approximate inference in largescale discrete undirected graphical models. The focus of the library is propagation based approximate inference methods, ranging from the basic loopy belief propagation algorithm to propagation ba ..."
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Cited by 5 (1 self)
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The FastInf C++ library is designed to perform memory and time efficient approximate inference in largescale discrete undirected graphical models. The focus of the library is propagation based approximate inference methods, ranging from the basic loopy belief propagation algorithm to propagation based on convex free energies. Various message scheduling schemes that improve on the standard synchronous or asynchronous approaches are included. Also implemented are a clique tree based exact inference, Gibbs sampling, and the mean field algorithm. In addition to inference, FastInf provides parameter estimation capabilities as well as representation and learning of shared parameters. It offers a rich interface that facilitates extension of the basic classes to other inference and learning methods.
What Cannot be Learned with Bethe Approximations
"... We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail. By fai ..."
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Cited by 3 (0 self)
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We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail. By failure we mean that the empirical marginals cannot be recovered from the approximated maximum likelihood parameters (i.e., moment matching is not achieved). We provide several conditions on empirical marginals that yield outer and inner bounds on the set of Bethe learnable marginals. An interesting implication of
Implicit Differentiation by Perturbation
"... This paper proposes a simple and efficient finite difference method for implicit differentiation of marginal inference results in discrete graphical models. Given an arbitrary loss function, defined on marginals, we show that the derivatives of this loss with respect to model parameters can be obtai ..."
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Cited by 3 (2 self)
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This paper proposes a simple and efficient finite difference method for implicit differentiation of marginal inference results in discrete graphical models. Given an arbitrary loss function, defined on marginals, we show that the derivatives of this loss with respect to model parameters can be obtained by running the inference procedure twice, on slightly perturbed model parameters. This method can be used with approximate inference, with a loss function over approximate marginals. Convenient choices of loss functions make it practical to fit graphical models with hidden variables, high treewidth and/or model misspecification. 1
Approximate Learning for Structured Prediction Problems
"... Prediction problems such as image segmentation, sentence parsing, and gene prediction involve complex output spaces for which multiple decisions must be coordinated to achieve optimal results. Unfortunately, this means that there are generally an exponential number of possible predictions for every ..."
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Cited by 1 (0 self)
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Prediction problems such as image segmentation, sentence parsing, and gene prediction involve complex output spaces for which multiple decisions must be coordinated to achieve optimal results. Unfortunately, this means that there are generally an exponential number of possible predictions for every input. Markov random fields can be used to express structure in these output spaces, reducing the number of model parameters to a manageable size; however, the problem of learning those parameters from a training sample remains NPhard in general. We review some recent results on approximate learning of structured prediction problems. There are two distinct approaches. In the first, results from the wellstudied field of approximate inference are adapted to the learning setting. In the second, learning performance is characterized directly, producing bounds even when the underlying inference method does not offer formal approximation guarantees. While the literature on this topic is still sparse, we review the strengths and weaknesses of current results, and discuss issues
Submitted to the Senate of the Hebrew University
"... ii ent approximate algorithms that are complementary to each other. These algorithms adopt insights from existing state of the art methods for inference in finite dimensional domains while exploiting the continuous time representation to obtain efficient and relatively simple computations that natur ..."
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ii ent approximate algorithms that are complementary to each other. These algorithms adopt insights from existing state of the art methods for inference in finite dimensional domains while exploiting the continuous time representation to obtain efficient and relatively simple computations that naturally adapt to the dynamics of the process. Our first inference algorithm is based on a Gibbs sampling strategy. This algorithm samples trajectories from the posterior distribution given the evidence and uses these samples to answer queries. We show how to perform this sampling step in an efficient manner with a complexity that naturally adapts to the rate of the posterior process. While it is hard to bound the required runtime in advance, tune the stopping criteria, or estimate the error of the approximation, this algorithm is the first to provide asymptotically unbiased samples for CTBNs. A modern approach for developing state of the art inference algorithms for complex finite dimensional models that are faster than sampling is to use variational principles, where the posterior is approximated by a simpler and easier to manipulate distribution. To adopt this approach we show that candidate distributions can be parameterized
Dual Decomposition for Marginal Inference
"... We present a dual decomposition approach to the treereweighted belief propagation objective. Each tree in the treereweighted bound yields one subproblem, which can be solved with the sumproduct algorithm. The master problem is a simple differentiable optimization, to which a standard optimization ..."
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We present a dual decomposition approach to the treereweighted belief propagation objective. Each tree in the treereweighted bound yields one subproblem, which can be solved with the sumproduct algorithm. The master problem is a simple differentiable optimization, to which a standard optimization method can be applied. Experimental results on 10x10 Ising models show the dual decomposition approach using LBFGS is similar in settings where messagepassing converges quickly, and one to two orders of magnitude faster in settings where messagepassing requires many iterations, specifically high accuracy convergence, and strong interactions.
Contents lists available at SciVerse ScienceDirect Information Processing Letters
"... www.elsevier.com/locate/ipl Recursive sum–product algorithm for generalized outerplanar graphs ..."
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www.elsevier.com/locate/ipl Recursive sum–product algorithm for generalized outerplanar graphs
Understanding the Bethe Approximation: When and How can it go Wrong?
"... Belief propagation is a remarkably effective tool for inference, even when applied to networks with cycles. It may be viewed as a way to seek the minimum of the Bethe free energy, though with no convergence guarantee in general. A variational perspective shows that, compared to exact inference, this ..."
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Belief propagation is a remarkably effective tool for inference, even when applied to networks with cycles. It may be viewed as a way to seek the minimum of the Bethe free energy, though with no convergence guarantee in general. A variational perspective shows that, compared to exact inference, this minimization employs two forms of approximation: (i) the true entropy is approximated by the Bethe entropy, and (ii) the minimization is performed over a relaxation of the marginal polytope termed the local polytope. Here we explore when and how the Bethe approximation can fail for binary pairwise models by examining each aspect of the approximation, deriving results both analytically and with new experimental methods. 1