Questions tagged [belief-propagation]

Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields.

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Model or State Uncertainty in Queueing Model due to uncertain arrival rate

$\textbf{Introduction}$ I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy ...
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613 views

Can (loopy) belief propagation be used to learn from a data set?

I'm trying to expand my experience with restricted Boltzmann machines to a more general class of graphical models and currently learning about belief propagation using message passing algorithms. One ...
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Is the posterior a sufficient statistic when observations are conditionally independent?

Suppose there are two random variables, $X_1$ and $X_2$, and we're trying to infer $\theta$. If $X_1$ and $X_2$ are conditionally independent, then is $f(\theta|X_1)$ a sufficient statistic for $X_1$?...
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What is the relation between message passing and probabilities in Bayesian inference?

The belief propagation algorithm is a message passing algorithm that can be used to estimate marginal probabilities on Bayesian networks. What is the definition of these messages? What is the ...
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Why do we fit Recurrent Neural Networks with backprop instead of message passing/expectation propagation?--as with hidden markov models

The form of a Recurrent Neural Network (RNN) seems to resemble that of a hidden markov model. With a hidden markov model we have transitions between discrete states, as well as an emission variable ...
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How to solve this belief propagation question?

I'm not sure how to solve this question. I understand that it involves belief propagation but beyond that I'm entirely lost. Generally speaking, we have G1, one machine that two others depending on; ...
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195 views

Bayesian Networks - Factor Graphs - Belief Propagation - Numerical stability

I am trying to do inference for a Bayesian Network with discrete probabilities. I converted the network to a factor graph and implemented the sum-product algorithm (belief propagation). My goal is ...
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27 views

Can belief propagation be used to infer latent variables?

Consider a simple Bayes net of linear Gaussian, $A\rightarrow B \leftarrow C$. If $B$ is observed, $A$ and $C$ are hidden (assume we have set priors for the hiddent variables), can we use belief ...
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166 views

Is this a really a belief propagation problem?

BACKGROUND This is basically a reputation problem that involves a set of interacting entities $e_i$. Each entity has, in principle, a reputation vector $\vec{b}_i$. That reputation depends on what ...
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35 views

Sum-product algorithm in polytrees

I want to do exact inference in a polytree structured DAG. I know that the Sum-product algorithm always converges for trees and I have also read that the algorithm can be extended for polytrees, but I ...
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151 views

How to compute the Gibbs free energy in Bethe approximation for MRF

Hi, I am learning loopy belief propagation for MRF. The general roadmap is to define a Bethe approximation, which is exact for a tree but wrong for general graphs. I'm currently stuck at the point to ...
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A question on notation in variational message passing

This paper introduces variational message passing. Formula (8) is based on Fig 1. Formula (a) is $\ln Q^*_j(H_j)=\langle\ln P(H_j\mid\vec{pa_j})\rangle_{\sim Q(H_j)}+\sum_{k\in ch_j}\langle\ln P(X_k\...
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Belief Propagation vs Gibbs Sampling

In general what are the cons and pros of using Gibbs sampling to estimate a complex posterior (assuming we can sample from the conditionals) over belief propagation (using a factor graph)?
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Updating a belief using a particle filter

I am using a particle filter to update a belief (the context is the POMCP algorithm found in Silver & Veness, "Monte-Carlo Planning in Large POMDPs"). A belief is represented as a probability mass ...