singlenode_inference.md

single node inference

This example shows how to use the infer_MRF executable to do inference on pretty much the simplest possible graph: a single-node model.

   (x₀)

In this model, we have that

p(x₀=0) = exp(-1)/Z
p(x₀=1) = exp(+1)/Z

for some normalization factor Z. You can run this example by doing, from the command line

./infer_MRF -m examples/singlenode_inference/model.txt -f examples/singlenode_inference/theta.txt -mu marginals.txt -i 1 

This will read the graph specified in model.txt and the parameters specified in theta.txt, do inference, and produce marginals in the file marginals.txt’. -i 1` specifies that a single pass of updates over the variables is to be done.

model.txt has the following form:

1 2
1 1
1 0
1 0

These lines are explained as follows:

1. 1 2 specifies that there is 1 node, that can have 2 possible values.
2. 1 1 specifies that there is 1 factor, with an entropy countring number of 1
3. 1 0 specifies that there is 1 factor (must match above line) with a "type" of 0. (This is not used with MRF inference, but must be specified to be consistent with the model format used with CRFs)
4. 1 0 specifies that the first (and only) factor contains 1 node, namely node 0.

theta.txt has the following form:

2 -1 1

This line is explained as follows:

1. 2 -1 1 Specifies that the first (and only) factor has 2 possible configurations, and that these have parameter values -1 and +1.

After running the code, a file marginals.txt will be produced in the main directory:

2 0.119203 0.880797 

This is explained as follows:

1. The first (and only) factor has 2 possible configurations, and these have a marginal probability of 0.119203 and 0.880797

Note that this makes sense. If we look at the original specification of the model, we could have calculated the probabilities by hand:

p(x₀=0)=exp(-1)/(exp(-1)+exp(+1))=0.119203
p(x₀=1)=exp(+1)/(exp(-1)+exp(+1))=0.880797