The rule counts are then used to compute labeling probabilities P (s | t) and P (t | s) over left-handside usages of each source label s and each target label t. These are simple maximum-likelihood estimates: if #(s i , t j ) represents the combined frequency counts of all rules with s i ::t j on the left-hand side, the source-given-target labeling probability is: t∈T #(s i ::t) The computation for target given source is analogous.
we can thus write the extracted rule as: while the SAMT label formats can be trivially converted into joint labels X::t, X::t 1 +t 2 , X::t 1 /t 2 , X::t 1 \t 2 , and X::X, they cannot be usefully fed into the label collapsing algorithm because the necessary conditional label probabilities are meaningless.