# Questions tagged [markov-random-field]

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27 questions
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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'...
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### Is the Markov Network (Markov Random Field) property biconditional?

As far as I know, the property of a Markov Random Field is defined as follows: Let $G = (V, E)$ be a Markov Network. Let $X, Y, C \subseteq V$. If every path from a vertex in $X$ to a vertex in $Y$ ...
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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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### Conditional Random Field for Hyperspectral Image Classification

How can I separate training and test sets in a hyperspectral image and apply Conditional Random Field (CRF) for pixel classification? If I choose pixels randomly, some of the neighboring pixels of a ...
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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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### Simple way for calculating unary potential for an image pixel in segmentation problem?

In an image segmentation using a Markov network how do you calculate unary potential for each pixel? I have an original image(rgb) and a ground truth image and two classes(foreground|background). ...
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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 ...
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### What's the difference between a Markov Random Field and a Conditional Random Field?

If I fix the values of the observed nodes of an MRF, does it become a CRF?