Markov Networks Flashcards
What is the problem with directed models?
Directed models not optimal for mutual, symmetric dependencies
(see figure)
What are is a markov random field?
See figure
What are the use cases of mutual, symmetric dependencies?
social networks,
image processing
etc.
How are markov random field different than normal bayesian networks?
bayesian networks require a DAG (directed acyclic graph)
In markov random fields the graph is undirected, and we here deal with a set of clique potentials that determines how the connections can be established
How does conditional independence work in markov random fields / markov networks?
See figure - will explain it.
Can we sometimes loose information by converting a bayesian network to a MN?
Yes!
An example is in the figure where we see that we must create a connection between A and B for it to make sense. Thereby loosing information.
What is the partitioning function and why do we use it?
For each node we have some local amount of compatibility to each other node. We then use the function that adds up these compatibilities for each setting. These will give us some scores not going from 0 to 1. We use the partitioning function as a way of normalizing, these scores and thereby getting a value from 0 to 1 for each.
Please see figure.
So we have our probability distribution now, how can we say anything about the model?
As an example shown in the figure. We can say that even though A and B tend to agree, they are more likely to agree with D and C respectively. Therefore A and B will most likely disagree since they are more influenced by the other nodes.
see figure
Are bayesian networks and markov networks in the same space?
Not quite. They are overlapping, but since we lose information by going form BN to MN, we can conclude that they have shared space, but are not equivalent. (imagine two overlapping cirles - like in intersection).
What are gibbs samling?
Since it can be hard to estimate the network structure, we can use gibbs sampling to obtain a sequence of observations.
This sequence can be used to approximate the joint distribution
https://www.youtube.com/watch?v=QaojSzk7Hpw
A full and fun explanation is available at:
Briefly explain the iising model
Nodes in a grid network represent atoms that either spins in a positive or negative direction. All of these nodes has a clique potential, and an option is even to have a single nodes as a clique by involving external magnetic fields.
