Rapid Acquisition of Gold Codes and Related Sequences Using Iterative Message Passing on Redundant Graphical Models

MILCOM 2006 ◽  
2006 ◽  
Author(s):  
Fabio Principe ◽  
Keith Chugg ◽  
Marco Luise
Keyword(s):  
Graphical Models ◽  
Message Passing ◽  
Rapid Acquisition ◽  
Gold Codes

scholarly journals A Spectral Approach to Analysing Belief Propagation for 3-Colouring

2009 ◽  
Vol 18 (6) ◽  
pp. 881-912 ◽  
Author(s):  
AMIN COJA-OGHLAN ◽  
ELCHANAN MOSSEL ◽  
DAN VILENCHIK
Keyword(s):  
Graphical Models ◽  
Message Passing ◽  
Graphical Model ◽  
Belief Propagation ◽  
Graph Colouring ◽  
Rigorous Result ◽  
Theoretical Understanding ◽  
Message Passing Algorithm ◽  
Survey Propagation ◽  
Graphical Structure

Belief propagation (BP) is a message-passing algorithm that computes the exact marginal distributions at every vertex of a graphical model without cycles. While BP is designed to work correctly on trees, it is routinely applied to general graphical models that may contain cycles, in which case neither convergence, nor correctness in the case of convergence is guaranteed. Nonetheless, BP has gained popularity as it seems to remain effective in many cases of interest, even when the underlying graph is ‘far’ from being a tree. However, the theoretical understanding of BP (and its new relative survey propagation) when applied to CSPs is poor.Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a ‘planted’ solution; thus, we obtain the first rigorous result on BP for graph colouring in the case of a complex graphical structure (as opposed to trees). In particular, the analysis shows how belief propagation breaks the symmetry between the 3! possible permutations of the colour classes.

scholarly journals Chance-Constrained Active Inference

2021 ◽  
pp. 1-26
Author(s):  
Thijs van de Laar ◽  
Henk Wymeersch ◽  
İsmail Şenöz ◽  
Ayça Özçelikkale
Keyword(s):  
Graphical Models ◽  
Message Passing ◽  
Random Variable ◽  
Chance Constraints ◽  
Generative Model ◽  
Chance Constraint ◽  
Active Inference ◽  
Prior Beliefs ◽  
Constraint Violation ◽  
Goal Directed Behavior

Active inference (ActInf) is an emerging theory that explains perception and action in biological agents in terms of minimizing a free energy bound on Bayesian surprise. Goal-directed behavior is elicited by introducing prior beliefs on the underlying generative model. In contrast to prior beliefs, which constrain all realizations of a random variable, we propose an alternative approach through chance constraints, which allow for a (typically small) probability of constraint violation, and demonstrate how such constraints can be used as intrinsic drivers for goal-directed behavior in ActInf. We illustrate how chance-constrained ActInf weights all imposed (prior) constraints on the generative model, allowing, for example, for a trade-off between robust control and empirical chance constraint violation. Second, we interpret the proposed solution within a message passing framework. Interestingly, the message passing interpretation is not only relevant to the context of ActInf, but also provides a general-purpose approach that can account for chance constraints on graphical models. The chance constraint message updates can then be readily combined with other prederived message update rules without the need for custom derivations. The proposed chance-constrained message passing framework thus accelerates the search for workable models in general and can be used to complement message-passing formulations on generative neural models.

scholarly journals Learning General Latent-Variable Graphical Models with Predictive Belief Propagation

2020 ◽  
Vol 34 (04) ◽  
pp. 6118-6126
Author(s):  
Borui Wang ◽  
Geoffrey Gordon
Keyword(s):  
Em Algorithm ◽  
Graphical Models ◽  
Message Passing ◽  
Latent Variable ◽  
Belief Propagation ◽  
Learning Problems ◽  
Local Optima ◽  
Learning Framework ◽  
The Em Algorithm ◽  
Spectral Algorithm

Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe limitations that largely restrict their applicability and affect their performance. In order to overcome these limitations, in this paper we introduce a novel formulation of message-passing inference over junction trees named predictive belief propagation, and propose a new learning and inference algorithm for general latent-variable graphical models based on this formulation. Our proposed algorithm reduces the hard parameter learning problem into a sequence of supervised learning problems, and unifies the learning of different kinds of latent graphical models into a single learning framework, which is local-optima-free and statistically consistent. We then give a proof of the correctness of our algorithm and show in experiments on both synthetic and real datasets that our algorithm significantly outperforms both the EM algorithm and the spectral algorithm while also being orders of magnitude faster to compute.

Distributed message passing for large scale graphical models

CVPR 2011 ◽  
2011 ◽  
Author(s):  
Alexander Schwing ◽  
Tamir Hazan ◽  
Marc Pollefeys ◽  
Raquel Urtasun
Keyword(s):  
Graphical Models ◽  
Message Passing ◽  
Large Scale

scholarly journals Feedback Message Passing for Inference in Gaussian Graphical Models

2012 ◽  
Vol 60 (8) ◽  
pp. 4135-4150 ◽  
Author(s):  
Ying Liu ◽  
Venkat Chandrasekaran ◽  
Animashree Anandkumar ◽  
Alan S. Willsky
Keyword(s):  
Graphical Models ◽  
Message Passing ◽  
Gaussian Graphical Models ◽  
Feedback Message

scholarly journals Belief propagation for networks with loops

2021 ◽  
Vol 7 (17) ◽  
pp. eabf1211
Author(s):  
Alec Kirkley ◽  
George T. Cantwell ◽  
M. E. J. Newman
Keyword(s):  
Graphical Models ◽  
Message Passing ◽  
Probabilistic Models ◽  
Belief Propagation ◽  
Probability Distributions ◽  
Fast Calculation ◽  
Potential Applications ◽  
The Common ◽  
Bayesian Graphical Models ◽  
Standing Problem

Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works poorly in the common case of networks that contain short loops. Here, we provide a solution to this long-standing problem, deriving a belief propagation method that allows for fast calculation of probability distributions in systems with short loops, potentially with high density, as well as giving expressions for the entropy and partition function, which are notoriously difficult quantities to compute. Using the Ising model as an example, we show that our approach gives excellent results on both real and synthetic networks, improving substantially on standard message passing methods. We also discuss potential applications of our method to a variety of other problems.

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