# Questions tagged [markov-random-field]

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### Approximate inference and the Hammersley-Clifford theorem

I recently submitted a manuscript to a journal in which we attempted to resolve the data association problem inherent in multi-object tracking by way of loopy belief propagation (LBP). We constructed ...
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### log trick on message passing in factor graphs

I'm reading Barbers book on Bayesian reasoning and Machine learning http://web4.cs.ucl.ac.uk/staff/D.Barber/textbook/200620.pdf page 90 To give context this is a proof of using the log trick for the ...
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### Local independence vs global independence in markov network

I am having a hard time understanding the basic differences between the local independence and global independence of a markov network. Please help me illustrate with a graph or any example
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### Most likely assignment in MRF with a global constraint

I have a MRF where all potentials are on pairs and all variables are binary. I want to find the most likely assignment of variables, under the constraint of at most $k$ variables being 1. Can this be ...
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### Are CRF/MRF/GRF still used widely in computer vision?

I've tried to find recent (the year 2020) popular works that use Markov/Gibbs/Conditional Random Fields. My approach was: go to Google Scholar and find the works, citing a few relevant works on this ...
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### Probability of at least one success in a long string of connected events

I have N events (i from 1 to N), each with an estimated probability of success, p(i). If all my events were independent I'd be able to calculate the probability of at least one success as (1 - product ...
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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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### Markov Random Field Implementation

Honestly, I'm having trouble understanding the general steps taken to actually use a Markov Random Field (MRF) in practice. Here's my current thinking on what I would have to do in practice. Specify ...
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### Replicating an experiment on GMRF (Gaussian Markov Random Field)

I am trying to understand an experiment from this paper, specifically Section 5.2. In the paper, they propose a new algorithm for computing the log-determinant of sparse matrices, and in section 5 ...
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### Equivalence between directed and undirected graph?

I am confused over something that may have an obvious explanation I am missing. In Koller's Probablistic Graphical models textbook, page 945, it is said that a Markov network $A-B-C$ is equivalent ...
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### Relation between Gaussian Processes and Gaussian Markov Random Fields

As a non expert in the field, I am relating Gaussian Processes (GP) and Gaussian Markov Random Fields (GMRF). I might just be confused by the fact that different resources use different formalism. ...
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### Edited --- Normalizing Constant Z in Markov Random Fields [closed]

I want to implement this paper in MATLAB. This is the formula: $$P(L)=\prod_{s \in S} \frac{1}{Z} exp(- \sum_{c \in N^w(s)}V_c(L_s))$$ However, I confused to compute $Z$ (normalizing constant) as ...
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### Why the nodes in a Boltzmann machine need to be sampled one at a time?

Typically, we use Gibbs sampling to update (or generate samples from) energy based models. This means we update each node while keeping its markov blanket constant. Why can't we update/sample all ...
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### Why is it difficult to sample from Energy Based Models?

I am trying to understand the following claim which is made in the Deep learning book by Goodfellow et. al about a toy energy-based model (with the apparent motivation of introducing Markov Chain ...
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### Graphical model of the Gaussian mixture: where is n?

TL;DR: Where are the occupation numbers in the Graphical model of the GMM? I am implementing a Finite (to be adapted to infinite later) Gaussian Mixture Model. I am using the Gibbs sampler-ready ...
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### Why do we have to convert Bayes' net to MRF before applying Belief propagation?

is that even correct in the first place? if yes, then why? I've seen articles talking about inference in Bayes' nets, and I've seen others talking about conversion. I don't have the full picture.
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### Extension of Potts model with non-constant interactions?

Is there any work that extends (allows) Potts model to have non-constant interactions between the lattice points? Specifically, the interaction matrix is a symmetric matrix that can have both positive ...
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### Discriminative Models with Class Priors

In discriminative models, we model $p(Y|X)$ directly while in generative models we model $p(X|Y)p(Y)$ where $X$ is the input and $Y$ is the output variable. I am confused when the parameters and ...
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### use MCMC posterior as prior for future inference

Would you kindly let me know how to use the estimated posterior distribution as the prior of another Bayesian update? Or even use that in an iterative manner, e.g. in my case the posterior is updated ...
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### Is every distribution factorizable by an MRF also factorizable via a Bayesian network? And vice versa?

This has probably been asked before, so if it has please provide a link to the original question and close this as a duplicate -- I was not able to find the original question myself. Question: Let's ...
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### Examples of applications of Markov random fields to data with a small number of variables

I am learning about some of the common applications of Markov random fields (a.k.a. undirected graphical models) to data science. A common feature of many applications I have read about is that the ...
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### How exactly does Gibbs sampling work in Markov Networks?

I was going through the Probabilistic Graphical Modelling course by Stanford and they used a network such as this one-https://imgur.com/gallery/k0C8FY2 Now if we want to sample P(A|B), how would we ...
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### Are self loops allowed in Markov networks?

I am studying about Markov networks from Probabilistic Graphical Models: Principles and Techniques Book by Daphne Koller and Nir Friedman. In Bayesian networks, it is clear that, it is a directed ...
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### How maximal clique parameterization obscures original structure

While reading the chapter on Markov networks, I came across the following statement: Although it can be used without loss of generality, the parameterization using maximal clique potentials ...
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### How does Markov random field (bs=mrf) in mgvc gam handle repeated measures on the spatial units?

I am attempting a spatio-temporal model in mgcv gam. I am using a factor smooth to define each of 27 areal units in a shapefile ("id") as subjects (essentially) which have undergone 23 repeated ...
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### Markov random field potentials

Consider a pairwise Markov random field, for any two neighbours $A$ and $B$, is it correct to use any function to describe the relationship between them? Is there any constraint or any condition that ...
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### References on simulating a raster with spatial dependence

I've simulated an N-by-N raster in the following way: define a set $S$ containing a finite number $|S| = K$ of possible raster values (in my simulation, $K=3$ and the elements of $S$ are land uses / ...
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### Mean field theory and neural networks

Mean field algorithm has been proposed to be used in combination with convolutional networks and recursive neural networks. What is the purpose of doing this? Is the goal to estimate a probability ...