We would like to use the score S uv , which is bounded in (∞, −∞), and derive from it a probability P uv .
to that end we project S uv onto (0, 1) using the sigmoid function, and define P uv in the following manner: Note that under this definition the log probability ratio is equal to the inverse of the sigmoid function: when we derive P uv from S uv with the sigmoid function, we can rewritê G prob as:Ĝ where we see that in this scenario the two objective functions are identical and the regularization term λ is related to the edge prior odds ratio by: λ = − log η.