As the name suggests, smoothed precisionq f (j) is a smoothed version of (raw) precision q f (j), which is the probability that rule f → j is correct given that it matches where Λ f is the set of labeled examples that possess feature f , and Λ fj is the set of labeled examples with feature f and label j. Smoothed precisionq(j|f ; ) is defined as follows: We also writeq f (j) when is clear from context.
recall that In the training step (2.1) of the algorithm, we hold φ fixed and change π, and in the labeling step (2.2), we hold π fixed and change φ.