Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [graphical-model]

Also called Probabilistic Graphical Model, used for statistical models expressed via graphs, causal or not. (Nb, "graph" as in graph theory, not as in figure or plot).

A graphical model is a probabilistic model which expresses the relationship among random variables using a graph (in the sense of graph theory). The nodes of the graph represent the random variables, while the edges of the graph encode the relationships between them.

Two broad categories of probabilistic graphical models are:

  1. Directed Acyclic Graphs (DAG) also known as Bayesian Networks.
    • DAGs are used to express the factorization of the joint probability distribution.
    • The direction of an edge indicates the conditional independence of random variables in a graph.
  2. Undirected Graphical Model (UGM) also known as Markov Random Fields.
    • UGMs, by definition, allow for cycles, therefore cannot express the induced dependence structure that a DAG can.
    • However, since the dependence structure of certain phenomena is difficult to establish, people use UGMs to express certain types of relationships that are more flexible. Notably, UGMs are used in spatial statistics and image analysis.
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When is Generalized Belief Propagation exact?

It is known that belief propagation gives exact result on trees, are there interesting examples when Generalized Belief Propagation is exact? (edit junction tree is not interesting because it is exactly solvable without GBP) On the surface, Belief…
Yaroslav Bulatov
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Log linear models advantages

What are the advantages of using a log linear representation rather than a table representation? Is it simply computational issue (avoid overflowing)? For example, in a markov network A-B we can represent the factor P(A,B) as a table: A B P(A,B) 0…
Dzung Nguyen
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Can graphical models represent independence besides conditional independence?

In a graphical model, two random variables are conditional independent given their common ancestors. Can graphical models represent independence besides conditional independence?
Tim
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Why can't Bayesian and Markov networks represent all conditional independencies in a joint distribution?

From here: An I-map is said to be perfect if $I(G)=I(p)$. Given a distribution $p$, it is not always possible to find a DAG $G$ such that $I(G)=I(p)$. Consider a joint distribution over four random variables such that $X_A \perp X_C|X_B,X_D$ and…
mhdadk
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Is factorization of Markov Random Field unique?

I have the following MRF graph and I need to find out about the clique factorization of the graph. I understand what it means for a graph to have a clique factorization. However it seems to be that it will not be unique. Is it true that that is the…
user10024395
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What exactly would be a perfect map in this situation? Is a perfect map a distribution which has the same independence assumptions?

I am currently studying Bayesian Reasoning and Machine Learning by David Barber, the 4th chapter exercise 4.7 (p 80). The exercise is the following: Consider the following belief network: Write down a Markov Network of $p(x_1,x_2,x_3)$ Is your…
user
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Can finding a graphical model be considered explatory data analysis?

I realize you infer the model structure and parameters from data. However, in some cases, you might want to find a GM for insight, just as you might want to calculate the mean or median for insight. And just as we can visualize the mean, we have…
yalis
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Graphical Model Equivalent of Matrix Pseudoinverse

The may sound like a strange question but I was wondering if a Pseudoinverse of a matrix could be found using SVD whether there was a graphical modelling equivalent that could be used to estimate the inverse of a matrix.
orbital
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Factorization for P(A, B, C, D) that includes P(A, B | C, D) and its visualization

I was revisiting some basic concepts on graphical models and factorization of distributions and noticed that all the examples I see only have factors that include, at most, one conditioned random variable (i.e. P(A | B, C, D)). Is there are reason…
echo66
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Tool to draw neural network directed graphs

I would like to reproduce the kind of graphs used in the book Deep learning. Do you know the tool which can do that kind of graphs? Ideally I would like the apparence to be exactly the same. Here is an example of Recurrent neural network graph:
mobupu
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Message passing (belief propagation) in practice - observed variables

In a graphical model with variables with continuous distriubtions, and some observed variables, how can I compute the messages to be passed? I know the messages but I don't know how to implement it? For continuous variables, and also for observed…
user3034939
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Explaining away

I am brushing up on graphical models, and doing the following problem 3.3 from the book PGM by Kophler. An alarm A can be set off by either Burglary B or earthquake E. Prove that if $P(a^1| b^1, e^1) = P(a^1 | b^0, e^1) = 1$ then $P(b^1| a^1, e^1) =…
Dzung Nguyen
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If the sample size is > 100, which graphical summarization is the best?

Box and whisker plot 3D doughnut plot Heatmap depicting expression levels Line plot Column scatterplot
user298057
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