Messagepassing algorithms for inferenceand optimization. By generalizing this technique, you can produce efficient algorithms for constraint satisfaction, optimization, and bayesian inference on models specified as programs. Factor a is a hard constraint, that either allows or disallows different local con. In this paper, we exploit this property along with appropriate graph partitioning. Inference by message passing on forneystyle factor graphs. A forneystyle factor graph ffg, also known as a normal factor graph, offers a graphical description of a factorized function forney, 2001. We then present our approach for training messagepassing inference procedures in sec. How to design message passing algorithms for compressed sensing. The book is a special issue that brings together the lectures given at the school statistical. A factor graph approach to automated design of bayesian. Thus, we split the graphbased optimization program.
A new message passing scheme for mrf optimization is proposed in this paper. We shall look at a short snippet of the clique tree message passing algorithm which is sometimes called the junction tree algorithm too. Feb, 20 we have outlined a particular framework for modelbased machine learning based on deterministic inference in probabilistic graphical models using local messagepassing algorithms. Hybrid inference optimization for robust pose graph estimation. Message passing algorithms for optimization the university of.
In an inference problem, one takes as input some noisy or ambiguous measurements, and tries to infer from those measurements the likely state. Both the methods and the considered models are implemented and stored within a single uniform multiplatform software framework, opengm 2 5. Most messagepassing algorithms approximate continuous. Message passing algorithms can solve a wide variety of optimization, inference, and constraint satisfaction problems. They are also a foundational tool in formulating many machine learning problems. The book is a special issue that brings together the lectures given at the school statistical physics, optimization, inference, and message passing algorithms held. How to design message passing algorithms for compressed. Continuouslyadaptive discretization for messagepassing. Graphical models and messagepassing algorithms for. Jun 25, 2014 message passing is a general mechanism, and there exist many variations of message passing algorithms. Continuouslyadaptive discretization for messagepassing cadmp is a new messagepassing algorithm for approximate inference. It outputs a set of data points that best represent the data.
Theoretical limits of streaming inference and minibatch. Messagepassing algorithms can solve a wide variety of optimization, inference, and constraint satisfaction problems. Using priors to avoid the curse of dimensionality arising in big data. This scheme inherits better theoretical properties than all other stateoftheart message passing methods and in practice performs equally welloutperforms them. Department of computer and software engineering, ecole. The algorithm was dubbed amp, for approximate message passing, and was inspired by the ideas from graphical models theory, message passing algorithms, and statistical physics. In an inference problem, one takes as input some noisy or ambiguous measurements, and tries to infer from those measurements the likely state of some hidden part of the world. A comparative study of modern inference techniques for.
This paper explores a specific probabilistic programming paradigm, namely message passing in forneystyle factor graphs ffgs, in the context of automated design of efficient bayesian signal processing. Simulating active inference processes by message passing. Oct 29, 2011 message passing algorithms can solve a wide variety of optimization, inference, and constraint satisfaction problems. He has an interest in the statistical physics of disordered systems, such as spin glasses, glasses, networks, optimization problems, inference and learning. A blog about compressive sensing, computational imaging, machine learning. Solving combinatorial optimization problems using relaxed. Jun 07, 2019 by generalizing this technique, you can produce efficient algorithms for constraint satisfaction, optimization, and bayesian inference on models specified as programs. We present messagepassing algorithms for quadratic programming qp formulations of map estimation for pairwise markov random. An important tool in the analysis of the minsum algorithm is the notion of a.
Nonnegative matrix factorization via archetypal analysis. Special issue, october 20 edited by florent krzakala, federico ricci. Implicitly, these messagepassing iterative algorithms are approximately solving certain optimization problems in an efficient way. The purpose of this meeting is to highlight various mathematical questions and issues. Messagepassing algorithms for inference and optimization 863 fig. Part i martin wainwright department of statistics, and department of electrical engineering and computer science, uc berkeley, berkeley, ca usa email. In this work, we provide a systematic study of message passing algorithms for the related. Statistical physics, optimization, inference, and message. Dec 23, 2014 message passing algorithms mpas have been traditionally used as an inference method in probabilistic graphical models.
We have also discussed a very general software development environment for modelbased machine learning called probabilistic programming, and described a specific. Graphical models, messagepassing algorithms, and convex optimization martin wainwright department of statistics, and department of electrical engineering and computer science, uc berkeley, berkeley, ca usa email. An instability in variational inference for topic models. In this paper, we exploit this property along with appropriate graph partitioning scheme to design approximate message passing algorithms for computing maxmarginal of nodes or maximum aposteriori assignment map in a binary mrf g. Florent krzakala, one of the organizers, mentioned earlier today that they had released the lecture notes of the talks. Convergent treereweighted message passing for energy. Fast iterative thresholding algorithms have been intensively studied as alternatives to convex optimization for largescale problems. We investigate the behavior of message passing algorithms mpas on approximate probabilistic graphical models pgms learned in the context of optimization.
The next section introduces forneystyle factor graphs as a graphical framework for automatic derivation of active inference algorithms. We adopt the recently proposed parallel map inference algorithm betheadmm and implement it using message passing interface mpi to fully utilize the computing power provided by the modern supercomputers with thousands of cores. Unfortunately known fast algorithms offer substantially worse sparsityundersampling tradeoffs than convex optimization. We adopt the recently proposed parallel map inference. Mathematical challenges in graphical models and message. The algorithm was dubbed amp, for approximate message passing, and was inspired by the ideas from graphical models. Graphical models, messagepassing algorithms, and variational methods. The algorithms operate on factor graphs that visually represent the problems. Analysis of messagepassing iterative algorithms via zeta. Statistical physics, optimization, inference and message. Other versions of the message passing algorithm are used in approximate inference as well.
Messagepassing algorithms for channel estimation and. Bp and dc messagepassing algorithms are used to solve inference problems, optimization problems, and constraint satisfaction problems. The algorithms operate on factor graphs that visually represent and specify. Use features like bookmarks, note taking and highlighting while reading statistical physics, optimization, inference, and message passing algorithms. Most messagepassing algorithms approximate continuous probability distributions using either.
Graphical models, messagepassing algorithms, and variational. Convergent messagepassing algorithms for inference over. Both the methods and the considered models are implemented and stored within. Continuouslyadaptive discretization for message passing cadmp is a new message passing algorithm for approximate inference. Note that for this factor graph the four variables are all discrete. To this end, we developed forneylab 2 as a julia toolbox for message passingbased inference in ffgs. This paper explores a specific probabilistic programming paradigm, namely message passing in forneystyle factor graphs ffgs, in the context of automated design of efficient bayesian signal processing algorithms. It includes stateoftheart optimization and inference algorithms beyond message passing. In particular, we use the concaveconvex procedure cccp to obtain a locally optimal algorithm for the nonconvex qp formulation. Message passing algorithms and junction tree algorithms. The algorithms operate on factor graphs that visually represent and specify the structure of the problems.
Lowcomplexity messagepassing algorithms for distributed. Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. We shall look at a short snippet of the clique treemessage passing algorithm. Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide. Some mpa variants have recently been introduced in the field of. Automated inference through message passing and a library. Zeta functions have been used to derive a variety of. Messagepassing algorithms for quadratic programming. From automatic differentiation to message passing microsoft. Theoretical limits of streaming inference and minibatch messagepassing algorithms andre manoel neurospin, cea universit. Markov chain monte carlo, belief propagation social networks e. Pdf messagepassing algorithms for inference and optimization. Bp and dc messagepassing algorithms are used to solve inference problems, optimizationproblems, and constraintsatisfactionproblems. The purpose of this meeting is to highlight various mathematical questions and issues associated with graphical models and message passing algorithms, and to bring together a group of researchers for discussion of the latest progress and challenges ahead.
Graphical models, messagepassing algorithms, and convex. Message passing algorithms in my research communication networks e. A constraint satisfaction problems such as satisfiability, coloring, packing, set cliquecover and dominating independent set and their optimization counterparts. Graphical models are used and studied within a variety of disciplines of computer science, mathematics and statistics. Learning messagepassing inference machines for structured. Extending the use of message passing algorithms to problems. Inference problems in graphical models can be represented as a constrained optimization of a free energy function. Special issue, october 20 edited by florent krzakala, federico riccitersenghi, lenka zdeborova, riccardo zecchina, eric w. Use features like bookmarks, note taking and highlighting while reading statistical physics, optimization, inference, and message. Florent krzakala, one of the organizers, mentioned earlier. Probabilistic graphical models provide a scalable framework for developing e. Starting from x0 0, the algorithm proceeds according to the following iteration. Graphical models, messagepassing algorithms, and convex optimization martin wainwright department of statistics, and department of electrical engineering and computer science, uc berkeley, berkeley. Statistical physics, optimization, inference, and messagepassing algorithms lecture notes of the les houches school of physics.
Internally, forneylab represents the model as a forneystyle factor graph 5, which is a conducive framework when work. We describe message passing algorithms, which are very similar to the. Message passing algorithms for optimization nicholas robert ruozzi 2011 the maxproduct algorithm, which attempts to compute the most probable assignment map of a given probability distribution via a distributed, local message passing scheme, has recently found applications in convex minimization and combinatorial optimization. Internally, forneylab represents the model as a forneystyle factor graph 5, which is a conducive framework when working with time series models such as dynamical statespace models. This scheme inherits better theoretical properties than all other stateoftheart message passing methods and in practice. The algorithms operate on factor graphs that visually represent and. Bilinear generalized approximate message passing bigamp for high dimensional inference phil schniter collaborators. Message passing for loopy graph local message passing for trees guarantees the consistency of local marginals computed is the correct one, computed is the correct on for loopy graphs, no consistency. Cugliandolo lecture notes of the les houches summer school. Several important combinatorial optimization problems can be formulated as maximum a posteriori map inference in discrete graphical models. Message passing algorithms mpas have been traditionally used as an inference method in probabilistic graphical models. A new messagepassing scheme for mrf optimization is proposed in this paper. In this context, variational bayesian inference in probabilistic models 3 have proven to be a very useful tool to design.
Inference problems, typically posed as the computation of summarizing statistics e. Graphical models and messagepassing algorithms for network. Belief propagation, also known as sumproduct message passing, is a messagepassing algorithm for performing inference on graphical models, such as bayesian networks and markov random fields. This approach can be broadly described as compiling into a message passing program. Affinity propagation is an exemplarbased clustering method that takes as input similarities between data points. Bilinear generalized approximate message passing bigamp. Distributed message passing for large scale graphical models ttic. Lecture notes of the les houches school of physics. Part i martin wainwright department of statistics, and department of electrical engineering and computer science, uc.
The key idea is a connection between the internals of sparse matrix factorization and. Most message passing algorithms approximate continuous probability distributions using either. Message passing is a general mechanism, and there exist many variations of message passing algorithms. Download it once and read it on your kindle device, pc, phones or tablets. Some mpa variants have recently been introduced in the field of estimation of distribution algorithms edas as a way to improve the efficiency of these algorithms. Journal of the american statistical association 2019, doi.
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