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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Interpretation of “log-likelihood” in hidden Markov model, and requisite computations involved

I am currently debugging a hand-coded implementation of a hidden Markov model, and as part of this, am scrutinising whether I have appropriately specified the log-likelihood computation algebraically. ...
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Belief propagation on Polytree

I'm working through exercises on Belief Propagation and the Junction Tree Algorithm and I'm stuck with the following problem. Consider the distribution P(A,B,C,D,E,F,G,H)=P(A)P(B)P(C)P(F) P(D|A,B)P(E|...
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Bayesian belief updating on single values using the sum of log odds

Suppose I want to perform Bayesian belief updating using only two values (the value estimate for option 1 (x) and the value estimate for option 2 (y)). I don't have any knowledge about the underlying ...
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Making sense of the belief propagation on graphs

I sort of understand when do I use variational Bayesian and when do I use expectation maximization. But now I want to know when do I use belief propagation in graphs to solve an estimation problem. ...
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How to use belief propagation sum product algorithm in a factor graph to solve inference problem?

I've read about belief propagation and sum product algorithm but still don't know how to apply it. For simplicity, I want to apply it to estimate the variable $x$ from this equation, $y=x+n$, where $n$...
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Introduction to approximate message passing

I'm interested in learning approximate message passing from the paper "Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction". My background is in computer ...
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Do variational approximations capture the flow of influence or “conditional independence” relationships in graphical models?

Probabilistic Graphical Models (PGMs) are used to model all sorts of complex decision processes, such as medical diagnoses or robot positions, etc. In common machine learning textbooks, like ...
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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 do Graphical Models work in practice?

I know how graphical models work at a high level. I have knowledge about graphs in general, but the message passing is hard to understand and implement. I want to be able to understand what is going ...
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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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Drawing a bayesian network and then converting to a factor graph to implement max-product algorithm

I'm trying to understand the fully worked example 5.2 in "Bayesian Reasoning and Machine Learning" by David Barber. Frustratingly the explanations around the example are all about potentials and ...
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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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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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What is the difference between belief propagation and loopy belief propagation?

Belief propagation (BP) is an algorithm (or a family of algorithms) that can be used to perform inference on graphical models (e.g. a Bayesian network). BP can produce exact results on cycle-free ...
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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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How does Dempster-Shafer relate to Machine Learning?

I read Dempster-Schafer can be thought of as a generalization of Bayesian theory. Say I have data from disparate sources that indicate the class of some object. If I have some prior beliefs about the ...
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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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Graphical Model: MAP optimization vs belief propagation

Assume there are three types (sets) of variables $X$, $Y$ and $Z$ in a graphical model where $X = \{x_1,x_2,\dots,x_m\}$, $Y = \{y_1,y_2,\dots,y_n \}$ and $Z = \{z_1,z_2,\dots,z_k\}$. Further, $Z$ is ...
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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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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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Bethe approximation for factor graphs

I am confused at computing Bethe approximation for factor graphs in here. It generalizes Bethe approxmiation in a pairwise case. However, I am wondering why (75) goes to (78) with (76): We can verify ...
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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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How do you do belief propagation on nodes with conditional dependence?

Take this graph: $$ \overset{S}{\fbox{$+$}} \underset{\textstyle \nwarrow \!\underset{\overset{\scriptstyle X_2}{\textstyle\bigcirc}} {}} {\overset{\textstyle \swarrow \!\overset{\...
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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 ...
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Belief propagation using pgmpy lib - algorithm understanding

I am now starting to use pgmpy lib for probabailistic graphical model implementation. The probability that I get using this lib differs from the one I get manually (e.g. using SamIam). Here is a ...
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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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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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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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How do you find mathematical expressions for the posterior marginals i.e. $P(x_n|y_0, … , y_n)$ in an HMM?

My goal is to find closed form equations for posterior marginals $P(x_n|y_0, ... , y_n)$ in a general HMM. I was told that we can calculate it exactly via BP (belief propagation, thought not sure how ...