Cycle-Based Cluster Variational Method for Direct and Inverse Inference

Furtlehner, Cyril; Decelle, Aurélien

doi:10.1007/s10955-016-1566-0

Cited by 2 publications

(6 citation statements)

References 43 publications

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“…To do so we presented a new way of introducing the messages in the CVM that differs from standard parent-to-child messages in that messages are sent to a region from all its ancestors, and not only by its direct parents. While previous attempts to fix the guage invariance in GBP equations [18,19,21] relied on the idea of removing some selected messages from the equations, our approach increases the number of such messages, but with a restriction on their degrees of freedom.…”

Section: Discussionmentioning

confidence: 99%

“…At the end, it all amounts to discovering which are the redundant messages, and remove them from the representation, or set them to an arbitrary value, fixing the gauge [18,19,21]. In many case, although the final objective is clear (destroying the loops), there are many different ways to achieve it, and each one has selected his own way.…”

Section: A Moment Matching Is Gauge Freementioning

confidence: 99%

“…Previously [6,[18][19][20][21] the set of messages have been defined using the so called Parent-to-Child (P-t-C) approach. This means that messages m α→γ (x γ ) are indexed by two regions labels, the father one α and the child one γ.…”

Section: Gauge-free 4m-cvm: Maximal Messages and Moment Matchingmentioning

confidence: 99%

“…According to our experience, this invariance is not a big problem in the implementation of message passing algorithms on a given finite dimensional instance, but it certainly is a waist of computational resources, since more parameters need to be implemented. In [21], however, authors reports the gauge invariance as causing convergence problems. In any case this gauge invariance may obscure the connection between the average case prediction of the CVM equations derived for a disordered model and the solution of message passing equations in single instances of the model [8].…”

Section: Introductionmentioning

confidence: 99%

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Gauge-free cluster variational method by maximal messages and moment matching

et al. 2017

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We present a new implementation of the Cluster Variational Method (CVM) as a message passing algorithm. The kind of message passing algorithms used for CVM, usually named Generalized Belief Propagation, are a generalization of the Belief Propagation algorithm in the same way that CVM is a generalization of the Bethe approximation for estimating the partition function. However, the connection between fixed points of GBP and the extremal points of the CVM free-energy is usually not a one-to-one correspondence, because of the existence of a gauge transformation involving the GBP messages.Our contribution is twofold. Firstly we propose a new way of defining messages (fields) in a generic CVM approximation, such that messages arrive on a given region from all its ancestors, and not only from its direct parents, as in the standard Parent-to-Child GBP. We call this approach maximal messages. Secondly we focus on the case of binary variables, re-interpreting the messages as fields enforcing the consistency between the moments of the local (marginal) probability distributions. We provide a precise rule to enforce all consistencies, avoiding any redundancy, that would otherwise lead to a gauge transformation on the messages. This moment matching method is gauge free, i.e. it guarantees that the resulting GBP is not gauge invariant.We apply our maximal messages and moment matching GBP to obtain an analytical expression for the critical temperature of the Ising model in general dimensions at the level of plaquette-CVM. The values obtained outperform Bethe estimates, and are comparable with loop corrected Belief Propagation equations. The method allows for a straightforward generalization to disordered systems.

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Section: Discussionmentioning

confidence: 99%

Section: A Moment Matching Is Gauge Freementioning

confidence: 99%

Section: Gauge-free 4m-cvm: Maximal Messages and Moment Matchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gauge-free cluster variational method by maximal messages and moment matching

et al. 2017

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“…We considered two types of models involving either latent binary variables [21] or Gaussian copula models. Both come with an associated learning algorithm to generate models adapted respectively to Generalized Belief Propagation for binary variables [22] and Gaussian Belief Propagation for realvalued variables [23].…”

Section: Our Approachmentioning

confidence: 99%

Short-Term Forecasting of Urban Traffic Using Spatio-Temporal Markov Field

Furtlehner

Lasgouttes

Attanasi³

et al. 2022

IEEE Trans. Intell. Transport. Syst.

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The probabilistic forecasting method described in this study is devised to leverage spatial and temporal dependency of urban traffic networks, in order to provide predictions accurate at short term and meaningful for a horizon of up to several hours. By design, it can deal with missing data, both for training and running the model. It is able to forecast the state of the entire network in one pass, with an execution time that scales linearly with the size of the network. The method consists in learning a sparse Gaussian copula of traffic variables, compatible with the Gaussian belief propagation algorithm. The model is trained automatically from an historical dataset through an iterative proportional scaling procedure, that is well suited to compatibility constraints induced by Gaussian belief propagation. Results of tests performed on two urban datasets show a very good ability to predict flow variables and reasonably good performances on speed variables. Some understanding of the observed performances is given by a careful analysis of the model, making it to some degree possible to disentangle modeling bias from the intrinsic noise of the traffic phenomena and its measurement process.

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Cycle-Based Cluster Variational Method for Direct and Inverse Inference

Cited by 2 publications

References 43 publications

Gauge-free cluster variational method by maximal messages and moment matching

Gauge-free cluster variational method by maximal messages and moment matching

Short-Term Forecasting of Urban Traffic Using Spatio-Temporal Markov Field

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